IMAT 2011 Answers & Worked Solution

Full explanation

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.

Full explanation

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.

Full explanation

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.

Full explanation

- 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.

Full explanation

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.

Full explanation

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.

Full explanation

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.

Full explanation

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.

Full explanation

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.

Full explanation

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

Full explanation

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.

Full explanation

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.

Full explanation

The passage's real clue is tucked into one line: both crows and apes have brains far bigger than their body size alone would predict, and the same holds for humans, parrots and chimps — all animals already thought of as sharp. That's a pattern about brain-to-body proportion, not brain size in isolation, which is exactly what option D is pointing at.

Options A and B overreach: the passage never compares how similar apes are to humans, and it never claims crows outrank every other bird species — just that they show ape-like thinking. C mistakes one example (tool use) for the whole definition of intelligence, which the passage doesn't do. E sounds tempting but goes further than the evidence allows — showing crows can rival apes in this one respect isn't the same as declaring birds in general as intelligent as apes.

D is the only option that states the actual mechanism the passage is describing, so it's the soundest conclusion.

Full explanation

An argument that says 'ban young drivers and accidents will fall' only works if young drivers are the ones causing those accidents in the first place. That's the gap the argument quietly assumes it doesn't need to prove — and it's exactly what option B states outright.

Try denying it: if most of the accidents involving young people were actually someone else's fault, taking young drivers off the road wouldn't do much to reduce the toll — the argument would collapse. That's the hallmark of a necessary assumption.

The other options miss the point. A is about whether young people would accept the rule, not whether it would work. C questions driving tests, which the argument never relies on. D talks about dangerous driving in general, but you can drive dangerously without being at fault in a crash, so it doesn't quite nail the assumption. E compares the number of male and female drivers, which is beside the point about blame.

Full explanation

The argument moves in one leap: some buildings have steps, ramps usually fix that, so every public building needs a ramp. The leap it skips is whether a building without a ramp is necessarily inaccessible — plenty of older buildings could have a side entrance, a lift, or some other workaround that already solves the problem without a ramp in sight. That's precisely the gap option D names.

A shifts the goalposts to all buildings, not just public ones, which isn't the flaw here. B raises cost, a practical worry rather than a logical one. C simply disagrees with the goal of full accessibility rather than pointing out a hole in the reasoning. E proposes a different fix (replacing buildings) instead of diagnosing what's wrong with the argument as it stands.

Only D actually punctures the argument's hidden assumption, so it's correct.

Full explanation

Numbers run 1, 2, 3… up one side of the street, then continue back down the other side, so the highest number on the street ends up directly opposite house 1. That pairing rule holds all the way along: house 2 is opposite the second-highest number, house 3 the third-highest, and so on. So for a street of N houses, any two houses facing each other always have numbers that add up to the same total, N + 1.

Here, house 17 is opposite house 56, so N + 1 = 17 + 56 = 73, which gives N = 72 houses in the street altogether.

Full explanation

The courier keeps taking the next available flight back, so her day is fixed by working through the timetable one leg at a time rather than just picking the outer times.

Round trip 1: she leaves London on the first flight, 06:30, landing in Prague at 09:30. The next Prague→London departure after 09:30 is 10:10, landing back in London at 11:20.

Round trip 2: the next London→Prague departure after 11:20 is 12:30 (the 09:45 flight had already left before she landed), landing in Prague at 15:30. The next Prague→London departure after 15:30 is 16:40, landing back in London at 17:50 — completing her second round trip, as the question specifies.

Her day runs from the first take-off (06:30) to this last landing (17:50), a span of 11 hours 20 minutes.

Full explanation

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

Full explanation

Strip the passage down to its chain of cause and effect: skip the safety rules → can't guarantee safety → likely a heavy fine → carnival fund badly hurt → 'the future of the carnival may be under threat.' That last clause is where the argument is actually heading — everything before it is just the reasoning that gets you there. Option B restates that final destination in one sentence.

A overstates things — the passage warns safety might fail if the rules are ignored, not that it's already dangerously low. C and D each grab one link in the chain (the fine, the financial hit) and mistake it for the whole point, when really they're just steps on the way to the real worry. E flips the logic around, promising that following the rules guarantees a future the passage never actually promises.

B is the only option that captures the argument's actual endpoint.

Full explanation

The argument's whole case rests on treating 'left-handed and in the minority' as equivalent to 'disadvantaged.' The fastest way to break that is to show the minority isn't actually losing out — and that's what A does: if left-handed people show up disproportionately often among top scientists, athletes, artists and politicians, then being left-handed clearly hasn't held them back from success. That directly undercuts the claim that they need to be treated as disabled.

B and C actually pull the other way — genuine disadvantages would support labelling left-handedness a hardship, not weaken the argument. D just explains why tools favour right-handers, which reinforces the idea of a right-handed world rather than challenging it. E is a real historical detail about forced right-handed writing, but it doesn't touch the argument's central claim about ability or success.

A is the one fact that genuinely undermines the argument, making it the answer.

Full explanation

The key experimental finding is that reacting to someone else's move is faster than being the one who initiates it — different nerve pathways handle 'react' and 'decide to act first.' Applied to a gunfight, that means the person who waits and fires in response should, on average, draw and shoot quicker than the one who moves first. That's exactly what B says.

A only restates that the experiment was interesting, missing the actual finding. C overclaims — being quicker on the draw doesn't guarantee a win, since aim and nerve still matter. D gets the finding backwards: the passage says reactive movements use a different, faster pathway, not that the brain can't control them at all. E invents a claim about training that the passage never makes.

B is the only conclusion the evidence actually supports.

Full explanation

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.

Full explanation

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.

Full explanation

The five slices, by eye, split into two clearly bigger wedges (chocolate and strawberry, roughly equal in size and together well over a third of the circle), one mid-sized wedge (raspberry), and two small wedges (mint, then vanilla as the smallest of all — noticeably less than half of mint, and only around a third the size of strawberry).

Row A (vanilla 23, raspberry 41, strawberry 35, chocolate 35, mint 16) makes raspberry the biggest category of the five, ahead of chocolate and strawberry — that's backwards compared with the chart, so A is out straight away.

For the remaining rows, the vanilla-to-strawberry pair is the easiest ratio to check against the chart, since vanilla should come out at roughly a third of strawberry:

B: 5 to 36 — vanilla is under a sixth of strawberry, far too small.

C: 15 to 32 — vanilla is almost half of strawberry, too big.

D: 26 to 73 — that's just about 1 to 2.8, essentially a third. This fits.

E: 36 to 71 — vanilla is around half of strawberry again, too big.

Only row D keeps chocolate and strawberry as the two dominant, near-equal slices while also keeping vanilla at roughly a third of strawberry, matching the chart on both counts — so D is correct.

Full explanation

The passage stacks up several separate perks — less commuting and pollution, more jobs to go around, better productivity, lower stress — without settling on any single one of them as the headline reason for a four-day week. Because the case is a list of upsides rather than one specific consequence, the safest conclusion is the general one: there would be many benefits. That's E.

A invents a pay cut that's never mentioned. B and C each latch onto just one of the listed benefits (health services, economic competitiveness) and treat it as the takeaway, when the passage is really making a broader case. D pushes past what's argued — showing benefits is not the same as arguing government should force the policy on everyone.

E is the only option that matches the shape of the argument: several genuine advantages, no single overriding one.

Full explanation

The argument's plea — don't build the wind farms — only makes sense if those wind farms would actually put the migrating birds at risk. If they wouldn't, there'd be nothing left to object to. That unstated link is what option C spells out.

A pushes further than the passage does; it says some birds are rare, not that they're close to extinction. B assumes wind farms have to be sited on hills, which isn't part of the argument. D is true of some other species but says nothing about the birds actually at stake here. E is irrelevant to whether this particular route needs protecting.

C is the assumption the whole argument leans on, so it's correct.

Full explanation

The argument tries to dismiss brain-cancer worries by pointing out that texting has overtaken calling — but people still make plenty of calls, and a call is exactly the scenario (phone against the ear) the original worry was about. Brushing past that is the flaw, and it's what option E names directly.

A would matter if the argument denied microwaves reach the brain at all, but it doesn't make that claim. B's point about which age groups text more doesn't affect the underlying reasoning. C raises other uses of phones, which the argument was never trying to cover. D drags in an unrelated technology, wireless internet, that has nothing to do with this specific gap.

E is the only option that catches what the argument actually leaves unaddressed.

Full explanation

Working through the two overlaps in age one at a time:

- 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.

Full explanation

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.

Full explanation

Let a, b and o be the numbers of apples (30c), bananas (40c) and oranges (50c) bought, so 30a + 40b + 50o = 200, with a, b and o all non-negative whole numbers.

Statement 1 — he cannot have exactly 3 apples: with a = 3, the apples cost 90c, leaving 110c for 40b + 50o = 110. Testing whole values of b: b = 1 needs o = 70/50 = 1.4; b = 2 needs o = 10/50 = 0.2; b = 0 needs o = 110/50 = 2.2. None of these give a whole number of oranges, so 3 apples is impossible — statement 1 is correct.

Statement 2 — he must have at least one banana: try b = 0. Then 30a + 50o = 200, and a = 0, o = 4 is a whole-number solution (4 oranges, no apples or bananas, costing exactly 200c). Since a valid basket with zero bananas exists, statement 2 is false.

Statement 3 — he has 4, 5 or 6 fruits in total: checking every whole-number solution of 30a + 40b + 50o = 200 gives exactly six baskets: (a,b,o) = (4,0,0) and (5,0,1), each 6 fruit; (0,5,0), (1,3,1) and (2,1,2), each 5 fruit; and (0,0,4), 4 fruit. Every basket totals 4, 5 or 6 fruit, so statement 3 is correct.

Statement 4 — if he has all three types, apples are fewer than bananas plus oranges combined: only two of the baskets above use all three fruit types: (1,3,1) — 1 apple against 3 + 1 = 4 bananas and oranges — and (2,1,2) — 2 apples against 1 + 2 = 3. In both, apples are fewer than the other two combined, so statement 4 is correct.

Statements 1, 3 and 4 hold and statement 2 fails, so the answer is C.

Full explanation

The passage opens with its thesis — the fast food/factory comparison 'is not as unrealistic as it might first appear' — and everything that follows (mass production, routine jobs, low wages) is evidence stacked up in support of that opening claim. So the conclusion is the claim the passage set out to defend, which option C restates almost word for word.

A and D are individual pieces of supporting evidence, not the overall point. B talks about factories generally, which is really just the comparison's raw material rather than the argument's destination. E goes further than the passage does, claiming the two jobs are identical rather than simply comparable.

C is the thesis the whole passage is built to support, making it the answer.

Full explanation

The argument's logic is: people ignore doctors more than they used to, yet health outcomes have improved, so people must know better than doctors do. The cleanest way to undercut that is to show the improvement isn't coming from people's own judgement at all — and that's exactly what D offers: if the gains line up precisely with what doctors have been recommending, medical advice deserves the credit, not some new folk wisdom.

A explains why there's more advice floating around, but doesn't touch whether people are right to ignore it. B and C both describe why people might feel confident managing their own health, which if anything supports the original argument rather than weakening it. E is beside the point — how doctors prefer to communicate doesn't bear on whether people are ignoring good advice.

D is the only option that actually threatens the argument's conclusion.

Full explanation

The argument tries to pin rising obesity entirely on less exercise, using the fact that average calorie intake has fallen as proof that diet isn't the culprit. The trouble is 'average' can hide a lot: even if the population-wide average has dropped, the people actually becoming overweight could easily be the ones whose own intake went up. That's the hole option B points to.

A doesn't challenge the exercise-weight link at all. C brings up cost, a separate policy question rather than a flaw in this piece of reasoning. D talks about children specifically, which the argument never singles out. E raises individual medical causes, which doesn't address the general trend the argument is making.

B is the one option that actually exposes the gap between 'the average fell' and 'therefore nobody is eating more', so it's correct.

Full explanation

Let Quentin's age in 2005 be x, so Peter's age in 2005 was 4x (Peter was exactly four times Quentin's age that year).

By 2021 — 16 years later — Quentin is x + 16 and Peter is 4x + 16. The question says Peter is then exactly twice Quentin's age:

4x + 16 = 2(x + 16)

4x + 16 = 2x + 32 ⇒ 2x = 16 ⇒ x = 8

So in 2005, Quentin was 8 and Peter was 4 × 8 = 32. Their age difference is a constant every year: 32 − 8 = 24.

Full explanation

To use as many coins as possible, favour the smallest denominations and only bring in bigger coins when there's no other way to reach the exact total.

Every 1c and 2c coin fits comfortably inside 37c: 6 × 1c + 3 × 2c = 12c using 9 coins, leaving 37 − 12 = 25c still to find.

From here, using both 5c coins (10c) would leave 15c — and 15c can only be made from 10c coins at that point, but one 10c coin leaves 5c stranded with nothing small left to cover it, while two 10c coins overshoots to 20c. So one of the two 5c coins has to stay unused: take just one 5c coin (5c) plus two 10c coins (20c) to make up the remaining 25c exactly (5 + 20 = 25).

Total: 6 × 1c + 3 × 2c + 1 × 5c + 2 × 10c = 37c, using 6 + 3 + 1 + 2 = 12 coins — the one spare 5c coin and one spare 10c coin are the only two coins left unused. Any other exact combination for 37c needs even more of the larger coins, so 12 is the maximum. The answer is D.

Full explanation

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

Full explanation

Follow the passage's own logic: the public can't understand legal documents unless they're written simply, and citizens in a democracy need to understand their rights and duties — put those two together and the only thing left to conclude is that the traditional style of writing laws has to change. That's option A, and it's also the passage's literal final sentence.

B and D are the premises that get you to the conclusion, not the conclusion itself. C is a plausible real-world fact but the passage never actually states it. E sounds reasonable but introduces an idea (citizens playing their democratic role) that the passage doesn't raise.

A is the point everything else in the passage is building toward.

Full explanation

The passage's demand for an investigation only makes sense if there's actually something to investigate — meaning the original advice to buy the vaccines has to have been wrong in the first place. If the advice had genuinely been sound given what was known at the time, there'd be no misconduct to uncover and no one to hold accountable, no matter how much the drug companies stood to gain. That's the assumption option B supplies.

A explains a motive for wrongdoing but isn't required for the conclusion to follow — an investigation could still be warranted without proving influence occurred, as long as the advice was bad. C is irrelevant to whether an investigation is warranted. D would actually excuse the officials rather than justify investigating them. E is a sweeping generalisation the argument doesn't need.

B is the assumption the whole call for accountability depends on.

Full explanation

Each link is 8 units long end to end, with a 2-unit-thick rim at each tip — that's the solid part of the loop that a neighbouring link hooks through.

The very first link in the chain isn't hooked onto anything before it, so it counts for its full length: 8.

Every link after that is threaded through the rim of the one before it, and that overlap eats up 2 units from each of the two linked rims — 4 units of overlap in total. So each extra link only extends the chain by its length minus the overlap: 8 − 4 = 4, which is exactly what the diagram's repeated "4" arrows show.

With 6 links, that's the first link at 8, plus 5 more links adding 4 each:

Total length = 8 + (5 × 4) = 8 + 20 = 28.

Full explanation

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.

Full explanation

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%.

Full explanation

Sweat cools the body by evaporating, and evaporation is what draws heat out of the skin — a large amount of it, because water has an unusually high latent heat of vaporisation. Turning even a small amount of liquid sweat into vapour soaks up far more energy than simply warming that same water up would, which is exactly why evaporative cooling is so effective at shedding heat. That makes C the property doing the real work here.

High specific heat capacity (B) helps the body resist temperature swings in general, but it's the change of state — not the heat capacity — that actually removes the heat once you're sweating. The dipole nature of water (A) is why salts dissolve in sweat, useful for the sweat itself but unrelated to the cooling mechanism. Boiling point (D) never comes into play at body temperature, and water being densest at 4°C (E) matters for lakes and fish, not skin.

Full explanation

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.

Full explanation

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. Mitochondria do contain circular DNA, which might make choice 3 seem tempting, but no answer option pairs choice 3 with the other genuinely shared feature (choice 2) — so choice 3 can still be excluded.

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.

Full explanation

Mitochondria go where the energy demand is, since their job is churning out ATP. A heart never gets a break — it's contracting every second of every day — so cardiac muscle cells are packed with mitochondria to keep that supply constant. That single relentless demand is what sets option C apart from the rest.

Red blood cells (A) have no mitochondria at all; they lose them entirely and run on anaerobic respiration. Lymphocytes (B) do carry mitochondria but nowhere near the density muscle needs. Skin cells (D) and cheek cells (E) are metabolically fairly quiet, so neither needs much of an ATP factory.

Full explanation

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.

Full explanation

Burning the food released 830 kJ in total. Respiration only managed to capture part of that as usable energy, in the form of ATP.

Energy captured as ATP: 8 ATP × 31 kJ per ATP = 248 kJ.

Efficiency of respiration = (energy captured) / (total energy released) × 100% = 248/830 × 100% ≈ 30%.

Full explanation

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.

Full explanation

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. This 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.

Full explanation

Haemophilia is X-linked recessive: a male (XY) shows the condition as soon as he inherits one affected X, since he has no second X to cover for it, while a female (XX) only shows it if both her X chromosomes carry the recessive allele — one affected X just makes her a carrier.

Let X^H be the normal allele and X^h the haemophilia allele. The mother is a carrier, X^HX^h; the father is unaffected, X^HY. Crossing them gives four equally likely offspring:

X^H (from mum) + X^H (from dad) → X^HX^H, a healthy daughter.

X^H (from mum) + Y (from dad) → X^HY, a healthy son.

X^h (from mum) + X^H (from dad) → X^HX^h, a carrier daughter.

X^h (from mum) + Y (from dad) → X^hY, a haemophiliac son.

Each of those four outcomes has a 25% chance. Checking the statements against them:

1. 25% chance of a haemophiliac son — true, that's X^hY.

2. 25% chance of a haemophiliac daughter — false. A daughter always inherits the father's only X, which is X^H, so she can never end up X^hX^h; the worst she can be from this cross is a carrier.

3. 25% chance of a carrier son — false. A son only has one X chromosome, so he is either affected or unaffected; "carrier" describes a heterozygous female, not a male.

4. 25% chance of a carrier daughter — true, that's X^HX^h.

So statements 1 and 4 are the correct pair — option B.

Full explanation

A cross-over value works like a distance: the further apart two genes sit on the chromosome, the more often a crossover happens between them, so the single biggest COV in the list marks the two genes furthest apart — the two ends of the map. That's P to Q at 33, so P and Q anchor the two ends, 33 units apart, with S and R somewhere in between.

P to S is 10, so S sits 10 units in from P. Q to R is 8, so R sits 8 units in from Q — which is 33 − 8 = 25 units from P. That already matches the given P to R = 25, which is a good check that the placement is right.

Reading the positions from P outward: S at 10, R at 25, Q at 33. That order is P–S–R–Q, and the gap it predicts between S and R is 25 − 10 = 15, matching the given R to S = 15 as a second check.

So the correct sequence is P S R Q, option E.

Full explanation

In a dihybrid cross, each parent is heterozygous for both genes: AaBb × AaBb. Each parent can pass on four different gamete combinations — AB, Ab, aB, ab — each with equal (1 in 4) probability, so the cross is worked out with a 4×4 Punnett square, giving 16 equally likely boxes:

Counting the 16 boxes gives the classic 9:3:3:1 phenotype ratio, and by genotype the single most common box is AaBb (heterozygous at both genes), which turns up in 4 of the 16 boxes — a quarter (25%) of all offspring, more than any other individual genotype. That makes AaBb the most likely combination, option B.

Full explanation

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.

Full explanation

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.

Full explanation

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.

Full explanation

Everything else in this list is a genuine speed-up trick along the length of a neurone: a longer axon covers ground without extra relays, myelin insulates the membrane so current doesn't leak away, nodes of Ranvier let the impulse jump from node to node instead of crawling along every millimetre, and a fatter axon offers less internal resistance. A synapse does the opposite job — it's the junction between one neurone and the next, and crossing it means releasing neurotransmitter into a gap and waiting for it to bind on the other side, which takes measurably longer than the electrical signal itself. That built-in delay is why C is the one feature that slows things down rather than speeding them up.

Full explanation

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.

Full explanation

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.

Full explanation

Atomic radius shrinks as you move across a period, because each extra proton pulls the outer electrons in more tightly while they sit in roughly the same shell. That trend holds across all three stretches shown here.

K to Ca: still the main-group elements at the start of period 4, and radius drops as the extra proton in Ca pulls its electrons in tighter than K's.

Sc to Zn: the transition metals fill an inner 3d subshell here rather than the outer shell, so the radius doesn't fall as sharply as it does elsewhere — but successive atoms still get very slightly smaller across the series, since the modest shielding from d-electrons doesn't fully offset the growing nuclear charge.

Ga to Br: back among the main-group elements, radius resumes its steady period-wide decrease as electrons fill the outer shell and nuclear charge keeps climbing.

Put those three together and the pattern is decrease, decrease, decrease all the way across — option C.

Full explanation

Nitrogen has 5 valence electrons (Group 15), and in nitric acid, HONO₂, all 5 end up involved in bonding.

Nitrogen forms three bonds to oxygen: one single bond to the –OH oxygen (contributing 1 electron), one double bond to a second oxygen (contributing 2 electrons), and one dative (coordinate) bond to the third oxygen, where nitrogen supplies both electrons of the pair (contributing 2 electrons).

Adding those up: 1 + 2 + 2 = 5 electrons from nitrogen are involved in bond formation, so the correct answer is C.

Full explanation

Substitution swaps one group for another without touching the rest of the carbon skeleton, and that's exactly what happens when ethanol's –OH is replaced by bromine: C₂H₅OH + HBr → C₂H₅Br + H₂O, giving bromoethane.

None of the other routes are simple substitutions. Making ethene (A) means eliminating water, not swapping a group. Ethanal (B) and ethanoic acid (C) both come from oxidising ethanol, not substituting into it. Ethoxyethane (D) forms by condensing two ethanol molecules together, losing water in the process — a different kind of reaction again. Bromoethane is the only product on the list that comes from a genuine one-for-one substitution.

Full explanation

An aromatic compound with two benzene rings is typically a fused polycyclic aromatic hydrocarbon (PAH) or a biphenyl-type derivative, joined by a single bond. The molecular formula must correspond to one of these two ways of joining two benzene rings.

1. C₁₀H₈ (naphthalene) — two benzene rings fused together, sharing a pair of carbon atoms.

4. C₁₂H₁₀ (biphenyl) — two benzene rings linked by a single C–C bond.

Formulas 2, 3, and 5 (C₁₀H₁₀, C₁₀H₁₂, C₁₂H₁₂) don't correspond to either way of joining two intact benzene rings, so they can be ruled out.

Thus, the correct combination is 1 and 4, giving option A.

Full explanation

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%

Full explanation

The most violent reactions in this list come from pairing the most reactive metal with the most reactive non-metal, because that combination has the strongest pull to swap an electron. Sodium gives up its single outer electron easily, and chlorine grabs an extra electron just as eagerly, so Na → Na⁺ and Cl → Cl^– happens fast and releases a large burst of energy — enough to produce heat and light almost explosively.

Krypton (A, C) and neon (B) are noble gases that barely react with anything, so pairing them with a reactive metal doesn't lead anywhere energetic. Lithium and bromine (D) do react, just less violently — lithium doesn't lose its electron as readily as sodium does, and bromine isn't as hungry for one as chlorine is. Sodium and chlorine remain the most energetic pairing, so E is correct.

Full explanation

An acid-base reaction always comes down to one thing: does a proton (H⁺) move from one species to another? Checking each reaction against that test:

A: HNO₃ hands a proton to HClO₄, forming H₂NO₃⁺ and ClO^– — a clean proton transfer, so this is acid-base.

B: two ammonia molecules react together, one donating a proton to become NH₂^– and the other accepting it to become NH₄⁺ — ammonia acting as both acid and base at once, still a proton transfer.

C: the hydrated aluminium ion loses a proton to a water molecule, forming Al(H₂O)₅(OH)²⁺ and H₃O⁺ — again, a proton has moved.

D: the superacid H(SbF₆) protonates methane itself, forming CH₅⁺ — an unusual reaction, but still built on a proton handed from one molecule to another.

E: FeCl₃ dissolving in water to form the hydrated Fe³⁺ ion and free chloride ions is a hydration reaction — ionic bonds breaking apart as water molecules surround the ions — with no proton changing hands anywhere in the equation. That absence of proton transfer is what makes E the one reaction that isn't acid-base.

Full explanation

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

Full explanation

This is Group 13 (boron, aluminium, gallium, indium, thallium), and each statement needs checking against how these elements actually behave.

Statement 1 is right: indium's most stable oxidation state is +3, so its common oxide is In₂O₃ — the same pattern as Al₂O₃ and Ga₂O₃ further up the group.

Statement 2 is also right: boron sits at the top of the group and behaves quite differently from its heavier neighbours — its higher electronegativity and ionisation energy make it reluctant to lose electrons, so it's the least reactive element in Group 13.

Statement 3 doesn't hold up: gallium forms the +3 ion, so its sulfate needs three sulfate ions for every two gallium ions to balance the charge — Ga₂(SO₄)₃, not the simple GaSO₄ given here.

With 1 and 2 correct and 3 wrong, the answer is B.

Full explanation

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)

Full explanation

A redox reaction always involves a change in oxidation state somewhere — electrons genuinely moving from one atom to another. Checking each reaction for that:

A: iron goes from 0 to +3 while chlorine drops from 0 to –1 — clearly redox.

B: chlorine in Cl₂ (0) ends up as both –1 (in HCl) and +1 (in HClO) — the same element oxidised and reduced at once, still redox.

C: chlorine's oxidation state jumps from +7 in KClO₄ down to –1 in KCl, with oxygen going from –2 to 0 — redox again.

E: electrolysis reduces Na⁺ to metallic Na and oxidises Cl^– to Cl₂ — a textbook redox pair.

D stands apart: NaCl + H₂SO₄ → NaHSO₄ + HCl is just a proton moving from sulfuric acid onto the chloride ion — an acid-base swap, with sodium, sulfur, oxygen, hydrogen and chlorine all keeping the same oxidation states they started with. No electrons change hands, which is why D is the one reaction that isn't a redox process.

Full explanation

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.

Full explanation

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.

Full explanation

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.

Full explanation

We check the two extreme cases. The 5 Ω resistor and the variable resistor R are in series with each other, forming a branch that is in parallel with the fixed 10 Ω resistor.

When R = 0 Ω: the series branch is just the 5 Ω resistor (5 + 0 = 5 Ω), in parallel with the 10 Ω resistor:

R_eq = (5 × 10)/(5 + 10) = 50/15 = 3.33 Ω, so I = V/R_eq = 20/3.33 = 6 A. This rules out any option that doesn't start at 6 A (options B, C and D).

When R = 5 Ω: the series branch is now 5 + 5 = 10 Ω, in parallel with the fixed 10 Ω resistor:

R_eq = (10 × 10)/(10 + 10) = 100/20 = 5 Ω, so 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 (since increasing R increases the resistance of that branch, raising the overall equivalent resistance and reducing the total current drawn from the battery).

Therefore, the correct answer is E.

Full explanation

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.

Full explanation

Substituting directly into F = Gm₁m₂/r²:

F = (7×10⁻¹¹ × 6×10²⁴ × 7×10²²) / (4×10⁸)²

F = (7 × 6 × 7 × 10⁻¹¹⁺²⁴⁺²²) / (16 × 10¹⁶) = (294 × 10³⁵) / (16 × 10¹⁶)

F = 18.375 × 10¹⁹ ... normalising the mantissa: F = 1.8375 × 10²⁰ N

Therefore, the correct answer is B.

Note: the value of G used in this question, 7×10⁻¹¹ N·m²·kg⁻², is a rounded figure for the purposes of this problem — the standard measured value is 6.674×10⁻¹¹ N·m²·kg⁻². Solve using the numbers exactly as given in the question.

Full explanation

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.

Full explanation

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.

Full explanation

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.

Full explanation

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.

Full explanation

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.