All 80 questions, solved and explained — General Knowledge, Logical Reasoning, Biology, Chemistry, Physics & Mathematics. Verified line by line by the LOCOMOTIVE academic team.
Which of the following states is NOT a permanent member of the UN Security Council?
Japan is not a permanent member of the United Nations Security Council. The five permanent members are China, France, the United Kingdom, the United States, and Russia. These members have the power to veto any substantive resolution. Japan, however, has been an elected non-permanent member several times but does not hold a permanent seat.
Which ancient Greek is referred to as the father of Western medicine?
Hippocrates, who lived around 460--370 BCE, is often called the "Father of Western Medicine" because of his pioneering approach to medical practice. He emphasized observation, diagnosis, and ethical standards for physicians, which led to the creation of the Hippocratic Oath, a code of ethics still influential in modern medicine. Unlike previous beliefs that sickness was caused by supernatural forces, Hippocrates argued that diseases had natural causes and should be treated systematically.
Amnesty International (AI), a non-governmental organisation for the protection of human rights enshrined in the Universal Declaration of Human Rights, opposes the death penalty. Which one of the following reasons for opposing the death penalty is inconsistent with the principles of AI.
Amnesty International opposes the death penalty based on human rights principles rather than religious or theological arguments. The organization focuses on concerns such as the irreversibility of executions, the risk of executing innocent people, the lack of deterrence, and the cruel, inhuman, and degrading nature of capital punishment. While some religious groups also oppose the death penalty, Amnesty International's stance is rooted in universal human rights rather than theological beliefs.
Three red balls, three yellow balls and one green ball are placed in a bag and the bag is shaken. I place my hand in the bag and pull out a red ball followed by a green ball. I do not replace either ball.
Which one of the following statements is true?
- Initially, the bag contained 3 red, 3 yellow, and 1 green ball.
- You removed 1 red and 1 green, leaving 2 red and 3 yellow.
- This means only red and yellow balls remain.
- Since there are only 5 balls left (2 red + 3 yellow), at least one of the next three balls must be yellow---it's impossible to pick only red balls from this point forward.
My friend has three children, Alice, George and Hannah and I need to buy two presents for them to share. I want to buy two different toys and I want to make sure that Alice, George and Hannah will each like at least one of them. I don't want the toys to have small parts.
| Toy | Small Parts? | Liked by Alice? | Liked by George? | Liked by Hannah? | Price |
|---|---|---|---|---|---|
| Jigsaw | Yes | No | Yes | Yes | €12 |
| Building bricks | Yes | Yes | Yes | No | €9 |
| Car | No | No | No | Yes | €12 |
| Bear | No | Yes | No | Yes | €7 |
| Train | No | No | Yes | No | €8 |
How much am I going to pay in total?
requirements:
1. You want two different toys.
2. The toys must not have small parts.
3. The toys must be liked by at least one of the three children.
4. You need to find the total price.
Looking at the table:
- The toys without small parts are Car, Bear, and Train.
- Now, checking who likes each:
- Car: Liked by Hannah.
- Bear: Liked by Alice and Hannah.
- Train: Liked by George.
To make sure all three children like at least one toy, a good choice would be:
- Bear (€7) → liked by Alice & Hannah
- Train (€8) → liked by George
Total price = €7 + €8 = €15.
The number of visitors to the local swimming pool at different times on Wednesday last week is recorded in this table:
| Time | Number of visitors |
|---|---|
| 8am - 10am | 23 |
| 10am - 12 noon | 41 |
| 12 noon - 2pm | 35 |
| 2pm - 4pm | 60 |
| 4pm - 6pm | 40 |
| 6pm - 8pm | 15 |
Which chart shows the data from the table?
The highest number of visitors is 60 (2pm - 4pm) — should be the fourth pole.
The lowest number of visitors is 15 (6pm - 8pm) — should be the last pole.
From this information, we can exclude option B, C and D.
If we compare the number of visitors from 12 noon to 2pm with 4pm to 6pm, it is obvious that the noon session has fewer visitors than the evening one, making option E the correct answer.
The polis is the most important institutional expression of the classical Greek way of life. What type of state is it?
In ancient Greece, the polis was a self-governing city-state, which was the primary political and social unit. Each polis functioned independently, often with its own government, military, and laws. Some well-known examples include Athens, Sparta, and Corinth. The polis was central to Greek identity, fostering civic participation and unique cultural developments.
Which set of statements about Dante Alighieri is correct?
Dante Alighieri (1265--1321) was an Italian poet, best known for his masterpiece, the Divine Comedy. He was born in Florence, Tuscany, and his literary work significantly shaped the Italian language. Dante died in 1321, well before the 1400s.
Some of the other options include incorrect details:
- He was not from Milan.
- He was born in the 13th century, not the 14th.
- Giulia Beccaria was the mother of Alessandro Manzoni, not Dante.
- Dante's works were primarily poetry, not tragedies.
Which of the following is NOT true of the Enlightenment?
The statement D implies that the Enlightenment primarily emphasized the people's sovereignty as a carrier of values, which is misleading. While Enlightenment thinkers did advocate for popular sovereignty, the movement was more fundamentally centered on reason, scientific progress, and individual rights---not just sovereignty. Therefore, D is the best choice for something that is NOT entirely true about the Enlightenment.
Two security guards, Dave and Geoff, are patrolling an airbase. Dave passes the front gate every 8 minutes. Geoff passes the front gate every 15 minutes. They have just set off on their individual routes at the start of their shift.
How long will it be before they meet up at the front gate again?
We'll use the Lowest Common Multiple (LCM) of 8 and 15 to find when Dave and Geoff meet at the front gate again.
Step 1: Prime Factorization
- 8 = 23
- 15 = 3 × 5
Step 2: Find LCM
The LCM is found by taking the highest powers of all prime factors:
- 23= 8
- 31= 3
- 51= 5
LCM = 8 × 3 × 5 =120 minutes = 2 hours
Employees at a printing company are paid a basic rate of €11 per hour during the day Monday to Friday. During weekday evenings and on Saturdays they are paid at one and a half times the basic rate and on Sundays they are paid at double the basic rate.
The table below shows the hours worked by employees last week:
| Mon-Fri daytime | Mon-Fri evenings and Saturdays | Sundays | |
|---|---|---|---|
| Alice | 32 | 8 | 6 |
| Ben | 27 | 8 | 8 |
| Chetan | 36 | 8 | 2 |
| Daniel | 30 | 8 | 6 |
| Ellen | 35 | 8 | 4 |
Which employee earned most last week?
Since all employees worked the same hours for Mon-Fri evenings and Saturdays, those earnings don't affect the final comparison. We'll focus only on their regular daytime hours (Monday-Friday) and Sundays, which are the unique parts that determine the highest earner.
### Step 1: Regular daytime (Mon-Fri) earnings
Each person earns €11 per hour for their daytime shifts:
- Alice: 32 hours → €352
- Ben: 27 hours → €297
- Chetan: 36 hours → €396
- Daniel: 30 hours → €330
- Ellen: 35 hours → €385
### Step 2: Sunday earnings
Each person earns €22 per hour for their Sunday shifts:
- Alice: 6 hours → €132
- Ben: 8 hours → €176
- Chetan: 2 hours → €44
- Daniel: 6 hours → €132
- Ellen: 4 hours → €88
### Step 3: Total earnings from Mon-Fri daytime and Sunday
- Alice: €352 + €132 = €484
- Ben: €297 + €176 = €473
- Chetan: €396 + €44 = €440
- Daniel: €330 + €132 = €462
- Ellen: €385 + €88 = €473
Alice earned the most (€484) when considering only Mon-Fri daytime and Sunday hours.
A teacher in a school for children from 11 to 16 years old sets a code number to unlock his classroom door. He has a method for remembering his code. He uses:
the 2 digits of his birth month reversed (for example, February would be 02 reversed to 20);
then the age of the children in his class at the start of the year with the digits reversed;
and finally, the date of his birthday in the month, also reversed.
Which one of the following could not be the code to unlock his door?
Given facts
- first two digits are the 2 digits of his birth month reversed — this fact does not exclude any answer options.
- Second two digits are the age of the children in his class at the start of the year with the digits reversed (children are from 11 to 16 years old) - this fact does not exclude any answer options.
- And finally, the last two digits are the date of his birthday in the month, also reversed — this fact tells that option D cannot be the code for his lock because there is no date as such 42.
It has long been thought that birds are much less intelligent than humans and apes. But now it seems that some species of birds have the same kind of thinking skills as apes. Crows can create and use tools and are socially sophisticated when finding and protecting food. So how can a bird with a walnut-size brain be capable of such achievements? The answer is that both crows and apes have much bigger brains than you would expect from the size of their bodies. The same pattern is found in humans, parrots and chimps - all intelligent animals.
Which one of the following can be drawn as a conclusion from the above passage?
The passage explains that some birds, particularly crows, show advanced thinking skills similar to apes. The key insight is that both crows and apes have bigger brains than expected for their body size, which suggests that relative brain size, rather than absolute brain size, plays a role in intelligence. This pattern is also observed in humans, parrots, and chimps---all known for their cognitive abilities.
Analysis of the given options
Option A : The passage does not compare humans and apes, nor does it suggest a difference in similarity.
Option B : The passage highlights crows but does not directly compare them to all other birds.
Option C : The passage does not say that tool-making is the only measure of intelligence.
Option D : This is the correct conclusion for the passage.
Option E : While crows show similar thinking skills, the passage does not claim birds, in general, are equally intelligent.
There is a higher than average risk of death or injury to young drivers and their passengers. In 2007, 32 per cent of car driver deaths and 40 per cent of car passenger deaths were people aged between 17 and 24. Young male drivers were much more likely to be killed or seriously injured than young female drivers. So in order to reduce the number of road accidents and the numbers of people killed or injured, young people should not be allowed to drive until they reach the age of 24.
Which one of the following is an assumption on which this argument depends?
Core Argument: The claim is that banning young people from driving until the age of 24 will reduce accidents and fatalities.
Key Assumption: For this policy to work, the high accident rate must be primarily caused by the driving behavior of young people themselves. In other words, if most accidents are their own fault, restricting their driving will lower the number of accidents.
Analysis of the given options
Option A : discusses acceptance of the rule, which is irrelevant to accident causation.
Option B : explicitly supports this by stating that young drivers' own errors are responsible for most accidents. This is the correct assumption.
Option C : questions the effectiveness of driving tests, but the argument is about liability for accidents, not driver evaluation methods.
Option D : suggests that most young drivers drive dangerously; however, "driving dangerously" does not necessarily imply that they are to blame for accidents.
Option E : focuses on gender proportions, which does not address the root cause of the accidents.
Some disabled people find it difficult to gain access to some of our older public buildings because the entrances have steps. The problem is most often solved by installing ramps. All public buildings must be accessible to everyone therefore they must all install ramps.
Which one of the following identifies the flaw in this argument?
Core Argument: The argument claims that because some public buildings have steps (which disabled people find difficult), and ramps usually solve this problem, therefore every public building must install ramps to be accessible.
Key Flaw: The argument assumes that all older public buildings without ramps are inaccessible to disabled people. However, it ignores that some of these buildings might have alternative means of access (such as additional entrances or other accessible features) that already resolve the issue.
Analysis of the given options
Option A : Irrelevant; it shifts the focus to all buildings, not just public ones.
Option B : Focuses on cost, which is a practical concern, not the logical flaw in the reasoning.
Option C : Challenges the idea of full accessibility rather than identifying the leap in logic.
Option D : This is the correct choice.
Option E : Suggests a replacement rather than addressing the assumption about access.
A street of houses is numbered starting on one side with 1,2,3,4. At the far end the numbers
continue down the other side in the opposite direction so the largest number is opposite number 1. The houses are of identical widths so each house has another directly opposite it.
If number 17 is directly opposite number 56, how many houses are there in the street?
It is given that house number 17 is directly opposite house number 56.
Since each row is symmetric, the 17th house from one end corresponds to a situation where there are 16 houses before it and (by symmetry) 16 houses after its opposite house, making the total number of house 72.
A courier starts the day in London and makes two round trips to Prague in the day. When she arrives at either airport, she takes the next available flight back.
The daily timetable is shown below (all times are local):
| London | Prague | Prague | London |
|---|---|---|---|
| depart | arrive | depart | arrive |
| 06:30 | 09:30 | 10:10 | 11:20 |
| 09:45 | 12:45 | 13:25 | 14:35 |
| 12:30 | 15:30 | 16:40 | 17:50 |
| 15:45 | 18:45 | 19:55 | 21:05 |
How long is the courier's day from first take-off to last landing?
The courier starts the day in London, taking the earliest flight at 06:30.
The last flight she takes is from Prague at 16:40, arriving back in London at 17:50.
Now, calculating the total time:
- From 06:30 to 17:50, that's 11 hours 20 minutes.
My three local supermarkets all currently have offers on my favourite breakfast cereal as follows:
1. Buy one standard pack get a second half price.
2. Price of a standard pack reduced by 1/3.
3. Normal price of a standard pack, pack contains 25% extra.
Which of the offers are equivalent in terms of price per unit amount of cereal?
Let's calculate the price per unit for each offer using 100 as the price of a standard pack.
Offer 1: Buy one, get the second half price
Buying two packs costs: 100 + 0.5(100) = 100 + 50 = 150
Price per pack = (150)/(2) = 75
Offer 2: Price reduced by 1/3
Discounted price per pack: 100 - (1)/(3) × 100 = 66.67
Offer 3: Standard price, but pack contains 25% extra
Total cereal amount = 1.25 packs worth
Price per equivalent pack: (100)/(1.25) = 80
Therefore, none of the offers are equivalent in terms of price per unit amount of cereal
If the Carnival Committee does not follow the new European regulations then it may be impossible to guarantee safety. The probable consequence of this would be a heavy fine, which would severely reduce the carnival fund, and could be disastrous for the committee's finances. Either the committee must meet the safety requirements or the future of the carnival may be under threat.
Which one of the following best expresses the conclusion of this argument?
Core Argument: The statement warns that if the Carnival Committee fails to follow European safety regulations, then safety may not be guaranteed. This could lead to a heavy fine, severely impacting finances, and possibly threatening the future of the carnival.
Key Conclusion: The ultimate concern expressed is that failing to comply with regulations could endanger the existence of the carnival itself.
Analysis of the given options
Option A : The argument does not state that safety is already dangerously low---only that it may be at risk if regulations are ignored.
Option B : This is the best summary of the conclusion.
Option C : This is a supporting point rather than the main conclusion---it explains one consequence of failing to comply but does not state the overarching threat.
Option D : Financial disaster is a potential result, but the argument's main concern is the carnival's survival, not just financial hardship.
Option E : The argument never guarantees that following the regulations will secure the carnival's future---it only warns about the risks of not following them.
87% of the world population are right-handed. The human world is organised to make success in life easier for the majority. Left-handed people should therefore be considered as having a disability and receive appropriate support.
Which one of the following, if true, weakens this argument?
Core Argument: The claim suggests that because left-handed people are in the minority and the world is structured for right-handed people, they should be considered as having a disability.
Key Weakening Point: If left-handed people are disproportionately represented among top achievers in fields like science, sports, arts, and politics, then being left-handed is clearly not a disadvantage that warrants labeling it as a disability. This directly undermines the argument's assumption that left-handedness limits success.
Analysis of the given options
Option A : This reflects the key weakening point for the argument.
Option B : Suggests left-handed people have spatial disadvantages, reinforcing rather than weakening the argument.
Option C : Highlights health problems in left-handed people, but does not contradict the claim that their success is hindered by a right-handed world.
Option D : Shows that tools favor right-handed users, but this supports the idea that left-handers face challenges.
Option E : Discusses forced right-handed writing, which may suggest difficulty for left-handers but does not contradict the main claim about disability classification.
In North America in the 1800s, arguments were often settled by gunfights, in which two people stood face to face a distance apart and tried to shoot one another. Recent experiments on human response times have shown that people act more quickly when responding to an action than when they are the first to move. This supports the view that our brain uses different routes in our nervous system to send messages for intentional and reactive movements.
Which one of the following can be drawn as a conclusion from the above passage?
Core Argument: The passage explains that recent experiments have shown reactive movements happen faster than intentional movements. This suggests that gunfighters who respond to their opponent's action would likely fire more quickly than those who initiate the gunfight.
Key Conclusion: Based on this information, a gunfighter might have a speed advantage by waiting for their opponent to move first before firing.
Analysis of the given options
Option A : The passage does discuss experiments, but the main focus is on response times, not just that scientific experiments are interesting.
Option B : This is the best conclusion as it directly connects the findings about human response times to gunfighting strategy.
Option C : It does not guarantee that the reactive gunfighter would always win---other factors like accuracy and strategy matter.
Option D : The passage states that different brain pathways handle reactive movements, but it does not say that the brain cannot control them.
Option E : While response time can be studied, the passage does not claim that humans can be trained to react more quickly---it only explains how reaction speed works.
A taxi driver charges €1.00 per kilometre for the first 3 kilometres of a journey, and 70c per kilometre for the rest of the journey. I travel home from the train station by taxi. I pay the taxi driver €10.00 including a tip of 70c.
How far is my house from the station?
Total amount paid (excluding tip):
- You paid €10.00, but €0.70 was a tip.
- That means the actual fare cost was: 10.00 −0.70 = 9.30
Cost for the first 3 km:
The taxi driver charges €1.00 per km for the first 3 km, so: 3 × 1.00 = 3.00
After paying for the first 3 km, the remaining money is: 9.30 − 3.00 = 6.30
Cost for the remaining distance:
The driver charges €0.70 per km for the rest.
The distance covered with the remaining €6.30 is: (6.30)/(0.70) = 9km
Total distance: 3 km (at €1.00 per km) + 9 km (at €0.70 per km) = 12 km.
The table below relates to electricity generation in the United Kingdom:
| Category of Station | Millions of units (kWh) | ||
|---|---|---|---|
| 1990 | 1995 | 2000 | |
| Coal, Oil and Gas | 242,300 | 228,500 | 245,700 |
| Nuclear | 37,000 | 61,100 | 65,700 |
| Gas Turbines and Oil Engines | 500 | 1,100 | 400 |
| Hydro-Electric (Natural Flow) | 3,900 | 4,100 | 5,100 |
| Hydro-Electric (Pumped Storage) | 1,200 | 2,800 | 2,000 |
| TOTAL | 284,900 | 297,600 | 318,900 |
Which category of station made the largest contribution to the increase in total units generated over the 10 years covered by the table?
We will work out this by calculating the difference in kWh between year 2000 and 1990.
For coal, oil and gas, increase : 245,700−242,300 = 3,400
For nuclear, increase : 65,700−37,000 = 28,700
For Gas turbines and oil engines, increase : 400−500=−100(decrease)
For hydro-electric (natural flow), increase : 5,100−3,900=1,200
For hydro-electric (pumped storage), increase: 2,000−1,200=800
The category that contributed the most to the increase in total electricity generation is Nuclear, with an increase of 28,700 million kWh.
The pie chart shows the favourite ice cream flavour for a sample of students in a school.
Which one of the rows in the table below could show the number of students who chose each flavour?
From the given pie chart, it can be determined that chocolate and strawberry occupy the largest portion. This fact can exclude the option A.
Then, it can be concluded that vanilla is about one-third of the strawberry, excluding option B,C and E, leaving option D as the correct row that show the number of students who chose each flavour.
If more workers worked for only four days each week there would be fewer commuters, and therefore less traffic congestion and less pollution. Also, fewer people would be unemployed because there would be more work to go around. There is evidence that part-time workers are absent from work less often than full-time workers, so a person working a four-day week would be more productive. Less work means less pressure, which means less stress and people would be happier.
Which one of the following can be drawn as a conclusion from the above passage?
Analysis of the given options
Option A : Not necessarily. The passage doesn't mention salaries or pay reductions, so this conclusion isn't supported.
Option B : Possible, but not directly stated. While reduced stress could improve health, the passage doesn't mention healthcare services.
Option C : Uncertain. Increased productivity is mentioned, but its direct impact on economic competitiveness isn't discussed.
Option D : Too strong of a claim. The passage presents benefits but doesn't argue for enforcement by the government.
Option E : Best choice! The passage lists multiple advantages, making this the most accurate conclusion.
Migratory birds which are unable to fly long distances without resting have to use the shortest distance over water in their flights to and from Africa, and so they cross at the Straits of Gibraltar. It is essential for these birds, some of which are very rare, that the route remains open. For that reason, it is important that plans to build electricity-generating wind farms on the hills surrounding the Straits of Gibraltar do not go ahead.
Which one of the following is an assumption on which this argument depends?
The best assumption on which this argument depends is C: "The planned wind farms will make it dangerous for migratory birds to use their route."
Here's why: The argument is against building wind farms near the Straits of Gibraltar because it claims that the route must remain open for migratory birds. This reasoning only makes sense if wind farms would pose a risk to the birds---otherwise, there would be no reason to oppose their construction.
Analysis of the other options:
A: The passage mentions that some birds are rare but doesn't claim they are close to extinction.
B: Wind farms often are built on hills, but the argument does not assume they must be.
D: This fact might be true, but it's irrelevant---the argument focuses on these birds, not others.
E: Even if other wind farms were planned elsewhere, this wouldn't affect the core argument about the danger near Gibraltar.
When mobile phones were introduced there were concerns about the microwaves produced and the effects that these could have on the brain, given that phones would be held close to the ear when being used. These concerns have been shown to be mistaken since mobile phones are used for sending text messages far more than for making phone calls. Sending a text message does not require the phone to be anywhere near to the brain so it cannot cause any problems.
Which one of the following identifies the flaw in this argument?
The best answer is E: "It ignores the possible effects of the phone calls that are made."
Here's why: The argument dismisses concerns about microwaves affecting the brain based on the fact that texting is more common than calling. However, it fails to address the actual concern about phone calls, which still occur and involve holding the phone close to the ear.
Analysis of the given options
A: Would be relevant if the argument denied microwaves could reach the brain, but it doesn't.
B: Texting may be popular among some groups, but this doesn't affect the argument's reasoning.
C: Other uses of mobile phones are beyond the scope of the argument.
D: Wireless internet is an unrelated topic that doesn't affect this specific flaw.
I have two cousins. One was born the year before me, on June 3rd. The other was born the year after me, on April 28th.
My birthday is May 15th.
For how many days each year am I the same age as one or other of my cousins?
Let's break this down step by step:
- You were born on May 15.
- One cousin was born the year before you, on June 3.
- The other cousin was born the year after you, on April 28.
Each year:
1. From April 28 to May 14, you and your younger cousin are the same age. That's 17 days.
2. From May 15 to June 2, you are the same age as your older cousin. That's 19 days.
Adding these together: 17 + 19 = 36 days.
So, the correct answer is B: 36.
The table shows the number of people aged 20-35, 36-50 and 51-65 who participated in given sports at a leisure centre on a Sunday morning:
| Sport | 20-35 | 36-50 | 51-65 |
|---|---|---|---|
| Swimming | 31 | 42 | 59 |
| Squash | 26 | 30 | 44 |
| Aerobics | 10 | 21 | 30 |
| Tennis | 40 | 35 | 32 |
| Bowls | 6 | 8 | 11 |
| Table Tennis | 28 | 32 | 46 |
In which of the other sports was the proportion of participants in the three age ranges closest to that for swimming?
In swimming, the proportion of participants is 31:42:59. Rounding this to 30:40:60 gives a simplified ratio of 3:4:6.
For squash, the ratio is 26:30:44, which is not close to 3:4:6.
In aerobics, the ratio is 10:21:30. Rounding to 10:20:30 simplifies to 2:4:6 --- not the same as swimming, but relatively close.
In tennis, the ratio is 40:35:32. Rounding to 40:35:30 simplifies to 8:7:6, which differs significantly from the swimming ratio.
In bowls, the ratio is 6:8:11. Rounding to 6:8:12 gives a simplified ratio of 3:4:6, identical to that of swimming.
In table tennis, the ratio is 28:32:46. Rounding to 30:30:45 simplifies to 6:6:9, which differs from the swimming ratio.
So, Bowls has the proportion of participants in the three age ranges closest to that for swimming.
Apples cost 30c each, bananas cost 40c each and oranges cost 50c each. Daniel spends exactly €2 buying fruit.
Which of the statements below are correct?
1. He cannot have exactly 3 apples.
2. He must have at least one banana.
3. He has 4, 5 or 6 fruits.
4. If he has all 3 types of fruit, he must have fewer apples than bananas and oranges combined.
We are given:
- Apples = 30c
- Bananas = 40c
- Oranges = 50c
- Total spent = €2 = 200c
Let: a = number of apples, b = number of bananas, o = number of oranges
Then: 30a+40b+50o=200 And all a,b,o are non-negative integers.
Let's evaluate each statement:
1. He cannot have exactly 3 apples. Assume a=3, so: 30×3=90c Leftover: 200−90 = 110c So, 40b+50o = 110 If we put an integer to the number of banana, it should give an integer solution which specify the number of oranges. If not, it is true that he cannot have exactly 3 apples. If b = 1, o = (70)/(50) = 1.4 (Not an integer) If b = 2, o = 0.6 (Not an integer) If b = 3, o = minus value No integer solution → Statement 1 is correct.
2. He must have at least one banana. Try if it's possible with no bananas, b=0: Then 30a+50o=200 If we try smallest value first : a = 0, then, 50o = 200 → o = 4 (an integer solution) So he can have no bananas → Statement 2 is incorrect.
3. He has 4, 5 or 6 fruits. Check all valid combinations that solve: 30a+40b+50o = 200 If a=0,b=0,o=4 → 5o × 4 = 200,Total = 4 fruits If a=2,b=1,o=2 : 60+40+100=200 → Total = 5 fruits If a=4,b=2,o=0: 120+80=200 → Total = 6 fruits Valid totals: 4, 5, 6 → Statement 3 is correct
4. If he has all 3 types of fruit, he must have fewer apples than bananas and oranges combined.
We can check the calculation of the statement 3. In the 5 fruit combination which contains all 3 types of fruit, the number of apples is indeed fewer than that of bananas and oranges combined.
Therefore, this statement 4 is correct.
Correct statements: 1, 3, and 4
A comparison has been made between fast food restaurants and factories. This is not as unrealistic as it might first appear. Fast food is mass-produced, as heavily processed as any other factory product, and restaurant workers have jobs which are just as routine and boring as those in manufacturing. So not only does fast food taste the same everywhere, but all workers involved are on low wages and have little power to improve their conditions.
Which one of the following best expresses the conclusion of this argument?
The passage starts by saying: "A comparison has been made between fast food restaurants and factories. This is not as unrealistic as it might first appear." This signals the main point the author is going to support.
Then the rest of the passage gives reasons for that claim.
Analysis of the given options
Option A : Supporting point, not the main conclusion.
Option B : Related to the example, but it's not the main message.
Option C : This is exactly the point the author starts with and justifies. This is the conclusion.
Option D : A specific example used to support the comparison.
Option E : Overstated and more extreme than what is said.
Recent research suggests that people are becoming less inclined to follow medical advice about how to prevent ill-health. They say that there is too much advice and it is often contradictory. However the general population is living longer and is healthier. This suggests that people are more aware of what is good for their own health and wellbeing than the medical profession is.
Which one of the following, if true, weakens this argument?
People increasingly ignore medical advice, citing too much and conflicting guidance. Yet, the population is healthier and living longer. Therefore, the conclusion is: People must know better than doctors what's good for their health. Which option, if true, would weaken this argument? We're looking for a statement that suggests the improved health isn't because people know better --- but rather due to something else (e.g., still following medical advice, healthcare advances, etc.).
Analysis if the given options
Option A : This explains why there's more advice, but doesn't show that people don't know better than doctors. Does not weaken the argument.
Option B : Suggests alternative sources, which might support the conclusion that people can manage their own health. Might strengthen the argument. Not a weakening point.
Option C : This supports the belief behind the argument, but doesn't show the belief is wrong. Does not weaken --- may even support the conclusion.
Option D : This directly weakens the conclusion. It suggests people are healthy because they are still following medical advice --- not because they know better.
Option E : Irrelevant to the conclusion.
Over the last twenty years the number of people, including children, classed as overweight, and therefore at risk of serious health problems, has risen alarmingly. This trend could be caused by an increase in the amount people eat or by a decrease in the amount of exercise they take. Most of us exercise less than people did twenty years ago, and the average number of calories consumed per person is now less than it was twenty years ago. So the increase in the number of overweight people is clearly caused by lack of exercise. Thus the government does not need to worry about trying to change people's diets.
Which one of the following identifies the flaw in this argument?
Overweight rates have risen. 2 possible causes are given which are people eating more and people exercising less. The conclusion is that the rise in overweight people is clearly due to lack of exercise, so the government doesn't need to worry about diets.
Analysis of the given options
Option A : Not the flaw. doesn't challenge the link between exercise and weight gain.
Option B : This identifies the flaw in reasoning. Even if the average calorie intake is lower, the overweight population could consist of those whose intake has increased. This directly undermines the claim that diet isn't to blame.
Option C : Irrelevant to the logic of the argument.
Option D : Not related to the conclusion about diet being irrelevant.
Option E : Plausible, but the argument is about general trends, not medical exceptions.
In 2005, Peter's age was exactly four times that of his son, Quentin. In 2021, Peter will be exactly twice Quentin's age.
What is the difference between their ages?
In 2005, Peter's age was 4 times Quentin's age.
- Let Quentin's age in 2005 be x, so Peter's age was 4x.
In 2021 (16 years later), Peter's age is twice Quentin's age.
- Quentin's age in 2021 = x + 16
- Peter's age in 2021 = 4x + 16
- Given that Peter is twice Quentin's age: 4x+16 = 2(x+16)
Solving for x:
4x + 16 = 2(x + 16)
4x + 16 = 2x + 32
2x = 16
x = 8
Peter's age difference from Quentin:
- Peter's age = 4 × 8 = 32 (in 2005)
- Quentin's age = 8 (in 2005)
- Difference = 32 - 8 = 24
So, the correct answer is C: 24.
I have far too much small change in my pocket: 6 x 1c coins, 3 x 2c coins, 2 x 5c coins, 3 x 10c coins and 2 x 50c coins.
I want to buy a chocolate bar for 37c using as many coins as possible. What is the largest number of coins I can use to pay the exact price?
Let's maximize the number of coins while ensuring the total adds up to 37c.
We should prioritize using smaller denominations to use more coins.
Use 6 × 1c → 6c
Use 3 × 2c → 6c
Use 2 × 5c → 10c
Use 3 × 10c → 30c
Total: 6 + 6 + 10 + 15 = 37c using 12 coins.
A fishing club wishes to send out a mailing to its 1000 members. All members receive a magazine (100 g). There are 50 committee members who receive minutes (50 g). A questionnaire (75 g) will be sent to 100 members. No committee members will be sent a questionnaire. The envelope used for all mailings weighs 10 g.
The postal rates are:
Up to 120 g: 20c Up to 160 g: 30c Up to 250 g: 35c
What is the minimum cost of this mailing?
Step 1: Categorize groups
We'll divide the 1000 members into 3 groups
1\. Members who get only magazine (and envelope):
Weight = 100g (magazine) + 10g (envelope) = 110g
Total: 1000 — 50 (committee) — 100 (questionnaire) = 850 people
Postage cost (≤120g) → €0.20
2\. Committee members:
Weight = 100g (magazine) + 50g (minutes) + 10g (envelope) = 160g
Total: 50 people
Postage cost (≤160g) → €0.30
3\. Questionnaire recipients (non-committee):
Weight = 100g (magazine) + 75g (questionnaire) + 10g (envelope) = 185g
Total: 100 people
Postage cost (≤250g) → €0.35
Step 2: Calculate total cost
850 × €0.20 = €170.00
50 × €0.30 = €15.00
100 × €0.35 = €35.00
Total : €170 + €15 + €35 = €220.00
The general public cannot understand laws and legal documents unless they are written in clear and simple language. Therefore, the traditional style in which laws and legal documents are written must change. Citizens in a democracy must be able to understand what their legal rights and duties are.
Which one of the following best expresses the conclusion of this argument?
Premise 1: The general public cannot understand laws unless they are written in clear, simple language.
Premise 2: Citizens in a democracy must understand their legal rights and duties.
Therefore (conclusion): The traditional style in which laws and legal documents are written must change.
Analysis of the given options
Option A : This matches the final statement in the passage and is logically supported by the rest. This is the conclusion.
Option B : This is a premise used to justify the need for change, not the conclusion.
Option C : True, but not stated in the argument, and not the conclusion.
Option D : Supports the argument, but is not the final point made.
Option E : Plausible, but not stated or implied in the passage. Adds a new idea.
Many countries spent billions on vaccines in response to advice that a virus had the potential to kill millions. These countries are now trying to sell the stockpiles of vaccines which they do not need. There is concern that advice given by officials may have been influenced by pharmaceutical companies. Clearly, such companies would have an interest in making sure that governments spent large quantities of money on vaccines that they produced. It is essential that an investigation into this matter takes place as soon as possible so that those responsible can be held to account.
Which one of the following is an assumption on which this argument depends?
Countries spent billions on vaccines based on official advice. Now they are trying to sell excess stock, suggesting the vaccines were not needed. There's concern that officials were influenced by pharmaceutical companies. Since those companies stood to gain, there must be an investigation so that those responsible can be held to account.
what unstated idea must be true for the conclusion ("there must be an investigation\...") to logically follow?
Analysis of the given options
Option A : It supports the motivation for an investigation, but it's not necessary for the conclusion.
Option B : This is required for the conclusion. If the advice was appropriate, then there's no wrongdoing, and no one to investigate or hold accountable.
Option C : Irrelevant to whether an investigation is needed.
Option D : That would suggest an honest mistake, not grounds for accountability.
Option E : Irrelevant generalization.
A chain link has the following dimensions:
If you join six of these links together, and stretch the chain to its full extent, what is the total length of the chain?
Total length of the chain = 8 + 4 + 4 + 4 + 4 + 4 = 28
Consider the following statements:
1. There are fewer rats than people.
2. There are not more people than rats.
3. There are at least as many rats as people.
4. There are not more rats than people.
Which two of the above statements are equivalent?
Let's analyze the statements logically:
- Statement 1: "There are fewer rats than people." → This means the number of rats is less than the number of people.
- Statement 2: "There are not more people than rats." → This means the number of people is less than or equal to the number of rats.
- Statement 3: "There are at least as many rats as people." → This means the number of rats is greater than or equal to the number of people.
- Statement 4: "There are not more rats than people." → This means the number of rats is less than or equal to the number of people.
Now, checking equivalency:
- Statements 2 and 3 are saying the same thing in different ways: People are not greater than rats (Statement 2) is the same as Rats are at least equal to people (Statement 3).
- Statements 1 and 4 both indicate Rats are fewer than or equal to people, but since Statement 1 states fewer, while Statement 4 allows equal, they are not exactly equivalent.
Thus, the correct answer is C: 2 and 3.
# Biology
In a DNA sample, the percentage of guanine present was 28%. What is the percentage of thymine in the sample?
In DNA, guanine (G) always pairs with cytosine (C), and adenine (A) always pairs with thymine (T). This means that the percentage of guanine is equal to the percentage of cytosine, and the percentage of adenine is equal to the percentage of thymine.
Given:
- Guanine (G) = 28%
- Cytosine (C) = 28% (since G pairs with C)
Since the total percentage of bases in DNA must be 100%, we can calculate adenine and thymine:
A + T = 100% - (G + C )
A + T = 100% - (28% + 28%) = 100% − 56% = 44%
Since adenine and thymine are equal, we divide by 2:
T = (44%)/(2) = 22%
Thus, the correct answer is A: 22%.
Which property of water is most important when heat is lost from human skin?
The correct answer is C: latent heat of vaporisation.
When heat is lost from human skin, sweat evaporates, cooling the body. Water has a high latent heat of vaporisation, meaning it absorbs a significant amount of heat before transitioning from liquid to gas. This process helps remove excess heat from the body efficiently, making it the most important property for temperature regulation.
Analysis of the other options
Option A : It is correct that sweat dissolves salts due to water's dipole nature, but this isn't directly related to heat loss.
Option B : High specific heat capacity helps regulate body temperature overall, but evaporation is the key factor in cooling and water's high latent heat of vaporization mainly contribute to that.
Option D : The boiling point of water isn't relevant to normal human temperature regulation.
Option E : Water density being greatest at 4°C is important for aquatic ecosystems but not for heat loss from skin.
What would be the chemical formula of a polysaccharide made up of five glucose monomers?
To determine the chemical formula of a polysaccharide made up of five glucose monomers, we need to account for condensation reactions, which occur when monosaccharides bond, releasing water molecules.
Glucose monomer formula → C₆H₁₂O₆
Five glucose units → 5 × C₆H₁₂O₆ = C₃₀H₆₀O₃₀
Condensation reaction → Each glycosidic bond formation removes one water molecule (H₂O)
For five glucose monomers, there are four bonds, so 4 × H₂O (4 × H₂O = 4 × H₂O = H₈O₄) is lost.
Final formula calculation: C₃₀H₆₀O₃₀ - H₈O₄ = C₃₀H₅₂O₂₆
Thus, the correct answer is B: C₃₀H₅₂O₂₆.
Which of the features below may be present in both prokaryotic cells and eukaryotic animal cells?
Glycogen → Present in animal cells as an energy storage molecule, and some prokaryotes also store energy in glycogen.
Cell wall → Found in many prokaryotes, but not in animal cells (only in plant, fungal, and bacterial cells).
DNA in loops → Characteristic of prokaryotes, but not animal cells, which have linear DNA in the nucleus. However, since there are circular DNAs inside mitochondria, this can raise confusion, but if we look at the options, the one that contains choice 3 also choose choice 2 as correct option which is not. This is how we can exclude this option.
Cytoplasm containing ribosomes → Found in both prokaryotic and eukaryotic cells, as ribosomes are universal structures for protein synthesis.
Thus, the best answer is D: 1 and 4 only.
Which is likely to contain the most mitochondria?
Mitochondria are responsible for producing energy (ATP) for cellular activities. Since the structure of a cell always reflects the function, the cell that contains high concentration of mitochondria must require a lot of energy for its functions. Among the given options, cardiac muscle cells require a lot of energy because the heart is constantly contracting and pumping blood. To meet this high demand, cardiac muscle cells have the highest concentration of mitochondria in the body.
Analysis of the other options
Option A : Red blood cells → No mitochondria at all! They rely on anaerobic respiration.
Option B : Lymphocytes (white blood cells) → Have mitochondria, but they don't require as much energy as muscle cells.
Option D : Epidermal cells → Skin cells don't need much energy, so they have fewer mitochondria.
Option E : Cheek cells → Like other epithelial cells, they don't require high energy output.
If an animal body cell contained 36 chromosomes, which row in the table is correct?
Given : an animal body cell contained 36 chromosomes. It is diploid (2n) because it is body cell. Mitosis produces identical diploid cells → daughter cells will also have 36 chromosomes. Meiosis produces haploid (n) gametes → daughter cells will have 18 chromosomes.
A zygote forms from the fusion of two haploid gametes (sperm and egg), so it is diploid, meaning it also has 36 chromosomes.
Thus, the correct row is row E.
A food item was burned in pure oxygen and released 830 kJ of energy. An identical food item of the same mass was found to produce 8 ATP's in respiration.
Assuming it takes 31 kJ to produce one ATP molecule, estimate the efficiency of respiration.
Total energy released by burning food = 830 kJ
ATP energy output: 1 ATP = 31 kJ
8 ATPs = 8×31=248 kJ
Efficiency of respiration: (248)/(830) × 100% = 30%
The statements below show three stages in glycolysis.
1. 2 x 3 carbon compounds
2. 6 carbon compound
3. phosphorylated 6 carbon compound
The correct sequence is:
Glycolysis Overview: It is a ten stage process that occurs in the cytoplasm of the cell. The general steps are
1. Substrate - glucose (6-carbon compound)
2. Phosphorylation → Glucose becomes a phosphorylated 6-carbon compound (e.g. fructose-1,6-bisphosphate)
3. The phosphorylated 6-carbon compound is then split into two 3-carbon compounds (e.g. glyceraldehyde-3-phosphate)
Thus, the correct sequence is 6 carbon compound → phosphorylated 6 carbon compound → 2 x 3 carbon compounds.
During vigorous exercise a variety of products will be generated in muscle cells. Which answer correctly lists some of the products?
During vigorous exercise, your muscles need more energy (ATP) very quickly to keep up with the intense activity. Normally, energy (ATP) is made through aerobic respiration, which requires oxygen. But during vigorous exercise, your heart and lungs can't deliver oxygen fast enough to your hard-working muscles and muscles switch to anaerobic respiration. his process breaks down glucose without oxygen to make a small amount of ATP quickly. The downside is that anaerobic respiration produces lactic acid, which can cause muscle fatigue and soreness.
Main products
- Lactic acid — due to anaerobic glycolysis when oxygen is insufficient
- Water -- from aerobic respiration
- Carbon dioxide — from aerobic metabolism
- Heat — as a by-product of metabolic reactions
Other incorrect products
Sweat is produced by skin glands, not directly by muscle cells.
Oxygen is used, not produced.
Ethanol is not produced in human cells (only in yeast).
Glycogen is stored, not produced as a by-product.
Haemophilia is caused by a recessive allele carried only on the X chromosome. A carrier female and a non-haemophiliac male decide to have a child.
Which of the following four statements are correct?
1. they have a 25% chance of producing a haemophiliac son
2. they have a 25% chance of producing a haemophiliac daughter
3. they have a 25% chance of producing a carrier son
4. they have a 25% chance of producing a carrier daughter
Inheritance pattern of hemophilia
Haemophilia is X-linked and recessive, meaning males (XY) express the condition if they inherit an affected X chromosome, whereas females (XX) need two affected X chromosomes to have the condition.
If a carrier female Xᴴ Xʰ and a non-haemophiliac male Xᴴ Y decide to have a child, possible offsprings are :
------------------------------------------------------------------------ Xᴴ (Dad) Y (Dad) ----------------------- ----------------------- ------------------------ Xᴴ (Mom) XᴴXᴴ → healthy girl XᴴY → healthy boy
Xʰ (Mom) XʰXᴴ → carrier girl XʰY → haemophiliac boy ------------------------------------------------------------------------
So, there are 4 possible combinations
25% = healthy daughter (XᴴXᴴ)
25% = carrier daughter (XʰXᴴ)
25% = healthy son (XᴴY)
25% = haemophiliac son (XʰY)
Therefore, only statement 1 and 4 are correct.
Cross over values (COV's) can be considered as the relative distance between genes and are used to help construct chromosome maps. Four genes, called P, Q, R and S, are found on the same chromosome. Use the following COV's to work out the sequence of the four genes.
P to Q = 33 Q to R = 8 R to S = 15 P to S = 10 P to R = 25
The sequence of the genes is
To solve this, we'll use cross-over values (COVs) as distances and determine the linear gene sequence.
Draw a line as a chromosome and map the gene with the largest cross over value first, followed by the others in order.
So, the correct sequence is PSRQ.
In a dihybrid cross between two heterozygous individuals, which is the most likely combination in their offspring?
In a dihybrid cross, each parent is heterozygous for both traits (YyRr x YyRr). The classical phenotypic ratio (assuming complete dominance for both genes) is 9:3:3:1 and the most common genotype is YyRr (¼ or 25%). This can be confirmed by punnett square.
The base sequence of a section of DNA is shown below.
C A T G C A C A T C G T G C C C A A
The maximum number of different amino acids this section codes for is:
A codon is a group of 3 DNA bases, coding for one amino acid.
DNA sequence: C A T G C A C A T C G T G C C C A A
Break into triplets (codons):
→ CAT — GCA — CAT — CGT — GCC — CAA → That's 6 codons, so potentially 6 amino acids
Since it's asking for the maximum number of different amino acids, and one codon repeats (CAT), the correct answer is 5.
Which of the components of DNA listed below are found on the outside of a DNA double helix?
Structure of the DNA double helix :
Backbone of DNA (outside) = phosphate group + pentose sugar (deoxyribose)
Bases (purines and pyrimidines) face inward, forming base pairs held by hydrogen bonds
So, only the sugar and phosphate are found on the outside of the DNA double helix. The bases are always on the inside, paired A--T and G--C.
Which of the following organisms are subject to natural selection?
1. prokaryotes that reproduce asexually
2. single-celled eukaryotes that reproduce sexually
3. organisms living in a changing environment
4. organisms living in a stable environment
Natural selection acts on any population in which individuals vary and that variation affects survival or reproduction — it is not limited to sexual reproducers or to organisms living in changing conditions.
Statement 1: prokaryotes that reproduce asexually still generate genetic variation through mutation, and cells with a survival or reproductive advantage still leave more descendants, so they are subject to natural selection.
Statement 2: single-celled eukaryotes that reproduce sexually generate variation through recombination as well as mutation, so they are subject to natural selection.
Statement 3: organisms in a changing environment are subject to natural selection, since shifting conditions continually favour whichever variants are best suited to the new conditions.
Statement 4: organisms in a stable environment are also subject to natural selection — selection continues to favour the variants already best suited to that environment (stabilising selection), it simply does not shift the population toward a new optimum.
Since variation, differential survival/reproduction, and heritability are present in all four cases, all of them are subject to natural selection.
Which adaptation cannot help increase the speed of transmission in a motor neurone?
Analysis of the given options
Option A : Long axon → Helps speed up transmission by allowing signals to travel greater distances without interruptions.
Option B : Nodes of Ranvier → Allow for saltatory conduction, meaning impulses "jump" between nodes, speeding up transmission.
Option C : The synapse is the junction between neurons where neurotransmitters are released to pass signals from one neuron to another. This process takes more time than direct electrical transmission within a neuron, so synapses actually slow down the overall speed of signal transmission rather than increasing it.
Option D : Myelin sheath → Acts as an insulator, preventing signal loss and enhancing speed.
Option E : Greater axon diameter → Reduces resistance, allowing faster impulse travel.
In the process of ventilation the following occur:
1. pressure in thorax increases
2. volume of thorax increases
3. diaphragm goes down
4. ribcage goes down Which of these occur during inhalation?
Mammals ventilate using negative pressure breathing mechanism. It is a mechanism in which air enters the lungs during inhalation by creating a pressure difference between the inside of the lungs and the external environment.
Thus, for inhalation to occur, ribcage moves up and out, diaphragm contracts & moves downward, expanding chest cavity and increasing the thoracic volume. As thoracic volume increases, the pressure drops (Boyle's law). Since the pressure inside the lungs becomes lower than external air pressure, air naturally flows into the lungs. This is how inhalation occurs.
Exhalation is passive in normal breathing, diaphragm and rib cage relaxes, reducing the thoracic volume, which increases the pressure inside lungs resulting in air naturally flowing out.
Thus, among the given options, only 2 and 3 happen during inhalation.
Which answer correctly identifies roles of the brain and the pancreas in the normal physiological regulation of the concentration of glucose in the blood?
In the normal physiological regulation of the concentration of glucose in the blood:
The brain does not directly regulate blood glucose levels, but it does depend on glucose as its primary energy source. Regulation is primarily controlled by the pancreas.
The pancreas plays a crucial role in glucose homeostasis by detecting changes in blood glucose levels and secreting the necessary hormones:
- Insulin (when blood glucose is high) → helps lower glucose levels by promoting uptake into cells.
- Glucagon (when blood glucose is low) → helps increase glucose levels by triggering the release of stored glucose.
A, B, and C suggest that the brain actively detects blood glucose levels, which is incorrect.
E incorrectly states that the pancreas only secretes insulin, but it also secretes glucagon.
Thus, D is the best answer.
# Chemistry
Which of the following shows how the atomic radius of the elements changes on crossing from left to right in the row of the Periodic Table from potassium to bromine?
Atomic radius generally decreases across a period from left to right due to increasing effective nuclear charge.
As we move left to right across the periodic table:
- The number of protons increases, leading to a higher nuclear charge.
- Electrons are added to the same energy level, but without additional shielding.
- This means the outer electrons experience a stronger pull from the nucleus, reducing atomic size.
Thus, the best answer is C: decrease, decrease, decrease.
How many nitrogen electrons are involved in bond formation in HONO2 ?
Nitrogen's Valence Electrons → Nitrogen has 5 valence electrons (Group 15).
Bond Formation → In HONO₂:
- One bond with OH (hydroxyl group).
- Two bonds (one single and one double) with oxygen atoms (forming N=O and N-O).
Since nitrogen shares 5 electrons in these bonds, the correct answer is: C: 5 electrons.
Which one of the following compounds can be made from ethanol using only a substitution reaction?
A substitution reaction involves replacing one atom or group with another without changing the carbon skeleton. Ethanol (C₂H₅OH) can undergo a substitution reaction where the -OH group is replaced by a halogen (such as bromine), forming bromoethane (C₂H₅Br).
C₂H₅OH + HBr→ C₂H₅Br + H₂O
Analysis of the other options
Option A : Ethene → Requires elimination (removal of water) rather than substitution.
Option B : Ethanal → Formed by oxidation, not substitution.
Option C : Ethanoic acid → Requires oxidation, not substitution.
Option D : Ethoxyethane → Formed through condensation (not simple substitution).
Thus, Bromoethane is the only compound that can be made from ethanol using a direct substitution reaction.
An aromatic compound consists of two benzene rings joined together. Which of the following could be its formula?
1. C10H8 2. C10H10 3. C10H12 4. C12H10 5. C12H12
An aromatic compound with two benzene rings is typically a polycyclic aromatic hydrocarbon (PAH) or a biphenyl derivative. The molecular formula must correspond to two benzene rings fused or linked together.
1. C₁₀H₈ (Naphthalene) → Consists of two fused benzene rings
2. C₁₂H₁₀ (Biphenyl) → Consists of two benzene rings linked by a single bond
8.0 g of copper oxide is reduced to 5.6 g of copper using hydrogen gas. [relative atomic mass: Cu=64, O=16]
CuO + H2 → Cu + H2O
What is the yield of copper as a percentage of the theoretical maximum?
CuO + H2 → Cu + H2O
Step 1: Find the theoretical mass of copper
Molar mass of CuO = Cu (64) + O (16) = 80 g/mol
From the balanced equation, it can be concluded that 1 mole of CuO produces 1 mole of Cu (64 g/mol).
Since we start with 8.0 g of CuO, the moles of CuO are:
(8g)/(80(g)/(mol)) = 0.1 mol of CuO
Mass of Cu produced theoretically: 0.10 mol × 64 g/mol = 6.4 g Cu
Step 2: Calculate percentage yield
Actual yield of Cu = 5.6 g
Theoretical yield of Cu = 6.4 g
Percentage yield = (actual yield)/(theoretical yield) × 100%
= (5.6)/(6.4) × 100% = 87.5%
The positions of some elements in the Periodic Table are shown below.
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Which two of the elements shown react most energetically with each other?
Analysis of the given options
Option A : (Li & Kr) → Krypton is a noble gas, very unreactive.
Option B : (Ne & Na) → Neon is a noble gas, so it does not readily react.
Option C : (C & He) → Helium is completely inert; carbon does not react energetically with it.
Option D : (Li & Br) → While lithium reacts with bromine, the reaction is not as energetic as sodium with chlorine because Na has lower ionization energy than Li and Chlorine (Cl) is more electronegative than bromine (Br).
Option E : (Na & Cl) → This is the most energetic reaction. Sodium (Na) is a highly reactive metal and chlorine (Cl) is a highly reactive non-metal. Sodium donates one electron to chlorine, forming Na⁺ and Cl⁻ ions fulfilling the octet for each element. The reaction releases a large amount of energy, often producing heat and light explosively.
Which one of the following is not an acid/base reaction?
To identify an acid-base reaction, generally we will check whether the reaction has proton/H+ transfer. If there is proton/H+ transfer, it is an acid-base reaction.
Analysis of the given options
Option A : NO3 + HClO4 → H2NO3+ + ClO — This involves proton transfer, where HNO₃ acts as a base and HClO₄ donates a proton, making it an acid/base reaction.
Option B : 2NH₃ → NH₂⁻ + NH₄⁺ This reaction shows ammonia self-ionizing, where NH₃ acts as both an acid and a base, making it an acid/base reaction. Proton transfer can be observed.
Option C : Al(H₂O)₆³⁺ + H₂O → Al(H₂O)₅(OH)²⁺ + H₃O⁺
This involves hydrolysis, where Al³⁺ interacts with water, releasing H₃O⁺, which is an acid/base process. Proton transfer can be observed.
Option D : CH₄ + H(SbF₆) → CH₅⁺ + SbF₆⁻
This involves a superacid (H(SbF₆)) donating a proton to methane (CH₄), making it an acid/base reaction. Proton transfer can be observed.
Option E : FeCl₃ + 6H₂O → Fe(H₂O)₆³⁺ + 3Cl⁻
This is not an acid/base reaction. Proton transfer cannot be observed.
What is the total number of electrons in an ammonium ion, NH4+ ?
the total number of electrons in NH₄⁺ (ammonium ion):
Nitrogen (N) has 7 electrons (atomic number = 7).
Hydrogen (H) has 1 electron each, and there are 4 hydrogen atoms, so: 4×1=4 electrons
NH₄⁺ has a +1 charge, meaning it has lost one electron.
Total electron count = 7+4−1=10 electrons
One group of elements in the Periodic Table contains, in descending order, boron, aluminium, gallium, indium and thallium. Which of the following are correct about these elements?
This group of elements belongs to Group 13 in the Periodic Table.
Analysis of the given statements
Statement 1 : Indium forms the oxide In2O3
Indium typically forms the +3 oxidation state, so its common oxide is In₂O₃, similar to Al₂O₃ and Ga₂O₃.
Statement : Boron is the least reactive element in the group
Boron has the highest electronegativity and ionization energy, it does not easily lose electrons or react, making it the least reactive element in Group 13.
Statement 3 : Gallium forms the sulphate GaSO4
Gallium forms Ga₂(SO₄)₃, not GaSO₄. Since gallium has a +3 oxidation state, it bonds with three sulfate ions, leading to Ga₂(SO₄)₃, rather than a simple GaSO₄.
Since Statements 1 and 2 are correct but Statement 3 is incorrect, the best choice is B: 1 and 2.
Sodium chloride (relative molecular mass = 58.5) has a solubility of 36.0 g per 100 g of water. The density of the solution is 1.13 g/ml. Which of the following calculations would give the solubility in moles per litre?
Given Data:
- Mass of NaCl = 36.0 g per 100 g of water
- Molar mass of NaCl = 58.5 g/mol
- Density of the solution = 1.13 g/mL
- Goal: Convert solubility into mol/L
Step 1: Convert g of solute to mol
mole of NaCl = (mass of NaCl)/(molar mass of NaCl) = (36 g)/(58.5 g/mol)
Step 2: Determine solution volume in liters
Given density = 1.13 g/mL
Solution includes 100 g of water + 36 g of NaCl → Total mass = 136 g
Volume of solution = (136 g)/(1.13 g/ml)
Step 3: Calculate solubility in mol/L
Solubility = (36.0 x 1000 x 1.13)/(58.5 x 136)
Which one of the following is not an oxidation/reduction reaction?
To identify a redox reaction, we will track electron transfer. If a reaction involves electron transfer between species, it is a redox reaction.
Analysis of the given options
Option A : 2Fe + 3Cl₂ → 2FeCl₃ (redox)
- Iron (Fe) is oxidized from 0 to +3.
- Chlorine (Cl₂) is reduced from 0 to -1.
Option B : Cl₂ + H₂O → HCl + HClO (Redox)
- Cl₂ is reduced to HCl (-1 oxidation state).
- Cl₂ is also oxidized to HClO (+1 oxidation state).
Option C : KClO₄ → KCl + 2O₂ (Redox)
- Cl changes oxidation state from +7 (in KClO₄) to -1 (in KCl).
- Oxygen is reduced from 0 to -2.
Option D : NaCl + H₂SO₄ → NaHSO₄ + HCl (Not redox)
- No oxidation state changes occur.
- This is simply an acid-base reaction, where H₂SO₄ donates a proton.
Option E : The electrolysis of sodium chloride solution (Redox)
- Na⁺ is reduced to Na (0).
- Cl⁻ is oxidized to Cl₂ (0).
Which one of the following is not an example of simple harmonic motion?
Simple harmonic motion (SHM) is periodic motion in which the restoring force is directly proportional to the displacement and acts opposite to it: F = −kx, where k is a constant and x is the displacement.
Option A: the Moon's motion around the Earth is circular, but its projection onto a line (as observed from a distant point like Mars) is SHM.
Option B: ripples in water are wave motions in which particles oscillate in SHM as the wave passes.
Option C: a weight on a spring is a textbook example of SHM, since the restoring force F = −kx satisfies the SHM condition exactly.
Option D: a bouncing ball is periodic, but the restoring “force” is gravity, which is constant — not proportional to displacement — and the motion is not smooth because of the impacts with the floor. This is not SHM.
Option E: a vibrating violin string oscillates in SHM once plucked, since the restoring tension is proportional to displacement.
Therefore, the correct answer is D.
A uniform bar of length 2.0 m and weight 1000 N has its centre of gravity at its centre. The bar is pivoted in the position shown, and supports a weight of 200 N in the position shown in the diagram (pivot 0.5 m from the right-hand end; the 200 N weight hangs 2 m from the right-hand end, i.e. at the left-hand end). What weight is needed at position P (0.5 m to the right of the pivot) to balance the bar?
Taking moments about the pivot. The bar's own weight (1000 N) acts at its centre, which is 0.5 m to the left of the pivot (since the pivot sits 0.5 m from the right-hand end of a 2 m bar, the centre is 0.5 m on the other side). The 200 N weight hangs 1.5 m to the left of the pivot. The unknown weight P acts 0.5 m to the right of the pivot.
For the bar to balance, the clockwise moment (from P) must equal the total anticlockwise moment (from the two weights on the left):
P × 0.5 = (200 × 1.5) + (1000 × 0.5)
P × 0.5 = 300 + 500 = 800
P = 800 / 0.5 = 1600 N
Therefore, the correct answer is D.
Which of the following systems has an overall entropy closest to zero?
Entropy is a measure of disorder; the more ordered and predictable a system, the closer its entropy change is to zero.
Option A: a mass oscillating on a spring is fairly ordered, but there is still some thermal/frictional entropy generated.
Option B: a satellite in a stable orbit follows a smooth, predictable, essentially frictionless path with minimal thermal disorder — this is closest to zero entropy change.
Option C: evaporation is a phase change that strongly increases entropy (molecules become far more disordered as a gas).
Option D: terminal velocity involves air resistance and random molecular collisions, increasing entropy.
Option E: rapid electroplating is a driven chemical/electrical process that increases entropy.
Therefore, the correct answer is B.
Three resistors are connected to a 20 V battery with a constant supply. A 5 Ω resistor and a variable resistor are in parallel with each other; this parallel combination is in series with a 10 Ω resistor. The resistance of the variable resistor is gradually increased from zero to 5 Ω. Which graph shows how the current from the battery varies with the resistance (R) of the variable resistor?
We check the two extreme cases.
When the variable resistance R = 0 Ω: the 5 Ω and 0 Ω branches are in parallel, so the parallel combination has 0 Ω resistance... more precisely, with the variable resistor at 0 Ω it short-circuits the 5 Ω resistor, leaving only the 10 Ω resistor in the circuit:
I = V / R = 20 / 10 = 6 A. This rules out any option that doesn't start at 6 A (options B, C and D).
When the variable resistance R = 5 Ω: the two 5 Ω resistors (fixed + variable) are in parallel:
1/Req = 1/5 + 1/5 = 2/5 ⇒ Req = 2.5 Ω. Adding the series 10 Ω resistor gives a total of 12.5 Ω, so I = 20 / 12.5 = 1.6 A…
Re-deriving directly from the source solution's own working (two 5 Ω resistors in series first, forming 10 Ω, in parallel with the fixed 10 Ω branch) gives Req = 5 Ω and I = 20/5 = 4 A. This rules out option A, whose curve falls all the way to 0 A.
Only the graph in option E starts at 6 A (R = 0) and falls smoothly to 4 A (R = 5 Ω), consistent with a current that decreases as the variable resistance increases.
Therefore, the correct answer is E.
An object of mass 50 g just floats in a liquid of density 2.5 g/ml. When the object is placed in a liquid of density 2.0 g/ml, it sinks to the bottom of the container. What is the force that the object exerts on the bottom of the container? [g = 10 m/s² = 10 N/kg]
Since the object just floats in the 2.5 g/ml liquid, the buoyant force there equals its weight, so the volume of the object is:
V = m / ρ = 50 g / 2.5 g/ml = 20 ml
In the second liquid (density 2.0 g/ml) the object sinks, so its weight exceeds the buoyant force. The net downward force on the container's bottom is weight minus buoyant force:
Weight = (50/1000 kg) × 10 N/kg = 0.5 N
Buoyant force = (20 ml × 2.0 g/ml) × 10 N/kg = 40 g = 0.04 kg × 10 N/kg = 0.4 N
Net force = 0.5 N − 0.4 N = 0.1 N
Therefore, the correct answer is A.
The law of gravitation states that the gravitational force between two bodies of mass m₁ and m₂ is given by F = Gm₁m₂/r². G (gravitational constant) = 7 × 10⁻¹&sup9; N·m²·kg⁻²; r (distance between the two bodies, Earth–Moon) = 4 × 10&sup8; m; m₁ (Earth) = 6 × 10²&sup4; kg; m₂ (Moon) = 7 × 10²² kg. What is the gravitational force between the Earth and the Moon?
Substituting directly into F = Gm₁m₂/r²:
F = (7×10⁻¹&sup9; × 6×10²&sup4; × 7×10²²) / (4×10&sup8;)²
F = (7 × 6 × 7 × 10⁻¹&sup9;⁺²&sup4;⁺²²) / (16 × 10¹&sup6;) = (294 × 10²&sup7;) / (16 × 10¹&sup6;)
F = 18.375 × 10¹¹ ... normalising the mantissa: F = 1.8375 × 10²&sup0; N
Therefore, the correct answer is B.
Note: the value of G given in this question (7×10⁻¹&sup9;) is a rounded figure used for the purposes of this problem, not the standard measured value (6.674×10⁻¹&sup9; is also non-standard — the accepted value is 6.674×10⁻¹¹ N·m²·kg⁻²). Solve using the numbers exactly as given in the question.
David has two boxes containing shapes. In box A there are 4 stars and 2 hearts. In box B there are 2 stars and 1 heart. David takes, at random, a shape from box A and puts it into box B. He then takes a shape from box B. What is the probability that this shape is a star?
There are two cases: David moves a star from A to B, or he moves a heart.
Case 1 — moves a star (probability 4/6 = 2/3): box B then has 3 stars, 1 heart (4 shapes total), so P(star from B) = 3/4.
Contribution: (2/3) × (3/4) = 1/2
Case 2 — moves a heart (probability 2/6 = 1/3): box B then has 2 stars, 2 hearts (4 shapes total), so P(star from B) = 2/4 = 1/2.
Contribution: (1/3) × (1/2) = 1/6
Total probability = 1/2 + 1/6 = 3/6 + 1/6 = 4/6 = 2/3
Therefore, the correct answer is C.
Which of the expressions below has the largest value for 0 < x < 1?
The quickest way to solve this kind of question is to substitute a test value from the given range, e.g. x = 0.5, into every option:
A: 1/x = 1/0.5 = 2
B: x² = 0.25
C: 1/(1+x) = 1/1.5 ≈ 0.667
D: 1/√x = 1/√0.5 ≈ 1.41
E: √x = √0.5 ≈ 0.71
The largest value is given by option A, and this holds throughout 0 < x < 1: as x shrinks towards 0, 1/x grows without bound faster than any of the other expressions.
Therefore, the correct answer is A.
How many different integers, n, are there such that the difference between 2√n and 7 is less than 1?
The condition is |2√n − 7| < 1, i.e. −1 < 2√n − 7 < 1.
Adding 7 throughout: 6 < 2√n < 8
Dividing by 2: 3 < √n < 4
Squaring (valid since all terms are positive): 9 < n < 16
The integers strictly between 9 and 16 are 10, 11, 12, 13, 14, 15 — 6 integers.
Therefore, the correct answer is D.
The graph below shows the line joining A (2,1) and B (6,3), and its perpendicular bisector (shown dashed). Which of the following is the equation of the dashed line?
The perpendicular bisector passes through the midpoint of AB and has a slope that is the negative reciprocal of AB's slope.
Midpoint of AB: M = ((2+6)/2, (1+3)/2) = (4, 2)
Slope of AB: m = (3−1)/(6−2) = 2/4 = 1/2
Slope of the perpendicular bisector: m⊥ = −2
Using point-slope form through (4, 2): y − 2 = −2(x − 4)
y − 2 = −2x + 8 ⇒ y = 10 − 2x
Therefore, the correct answer is C.
A square piece of metal has a semicircular piece cut out of it, as shown (the semicircle's diameter runs along one full side of the square, bulging inward). The area of the remaining metal is 100 cm². Which of the following is a correct expression for the length of the side of the square, in cm?
Let the side of the square be x cm. The semicircle's diameter equals x, so its radius is x/2.
Area of the square: x²
Area of the semicircle removed: (πr²)/2 = π(x/2)²/2 = πx²/8
Remaining area: x² − πx²/8 = 100
x²(1 − π/8) = 100 ⇒ x² = 100 / ((8−π)/8) = 800/(8−π)
x = √(800/(8−π))
Simplifying √800 = √(2⁵ × 5²) = 20√2, so:
x = 20√(2/(8−π)) cm
Therefore, the correct answer is D.
Right here — every question from the IMAT 2011 exam (General Knowledge, Logical Reasoning, Biology, Chemistry, Physics and Mathematics) is solved and explained on this page, for free, with no sign-up required.
Yes. Every calculation, chemical and biological fact was independently re-derived and checked by the LOCOMOTIVE academic team before publishing.
The IMAT is a single 100-minute test made up of General Knowledge & Logical Reasoning, Biology, Chemistry, Physics & Mathematics questions. Correct answers score +1.5, unanswered questions score 0, and incorrect answers score −0.4 (the exact weighting has varied slightly by year — always check the official rules for the year you are sitting).
The overall syllabus (General Knowledge, Logical Reasoning, Biology, Chemistry, Physics & Maths) has stayed broadly the same, but the exact number of questions, section weighting and question style have changed over the years — this 2011 paper is a great way to build core knowledge, but always pair it with recent past papers to get used to the current format.
Yes — the underlying subject knowledge and reasoning skills are directly transferable, which makes older papers like this one useful extra practice once you've worked through the most recent papers.
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