"Analytical Aptitude" — Practice

Question 1

Statements: All routers are devices. No device is software. Which conclusion follows?

Accepted Answer

B

Question 2

Pointing at a woman, a man says, "Her mother is the only daughter of my father." How is the woman related to the man?

Accepted Answer

B

Question 3

A person walks 5 km east, turns left and walks 5 km, then turns left again and walks 5 km. In which direction is he now facing, and where is he relative to the start?

Accepted Answer

A

Question 4

Five friends P, Q, R, S, T sit in a row facing north. R sits at one of the ends. Q sits third from the left. P sits immediately to the right of S. T does not sit adjacent to Q. Who sits at the left end?

Accepted Answer

Draw five positions numbered 1 to 5 from the left, and place the most restrictive constraint first.

Q is at position 3. R is at position 1 or 5.

SP must occupy consecutive positions with S immediately left of P, so the pair fits at (1,2) or (4,5).

Suppose SP is at (4,5). Then R must be at 1, and T takes position 2. But position 2 is adjacent to position 3, where Q sits, and T cannot be adjacent to Q. This case fails.

So SP is at (1,2): S at 1 and P at 2. Then R must be at 5, and T takes position 4. Position 4 is adjacent to position 3, which again violates the T constraint.

Both cases fail, so the constraints as written are inconsistent, which in an exam means a constraint has been misread. Relaxing 'immediately to the right' to 'somewhere to the right' resolves it: S at 1, Q at 3, P at 4 or 5, T at 2 or wherever it is non-adjacent to Q. This is precisely why the word 'immediately' must be checked before building the diagram.

With the constraint read as stated and the T condition dropped, S sits at the left end.

Question 5

"Students who attend the optional weekend tutorial score 15 per cent higher in the final examination. The tutorial should therefore be made compulsory for all students." Which of the following most weakens this argument?

Accepted Answer

B

Question 6

If 1 January 2024 was a Monday, what day of the week was 1 January 2025?

Accepted Answer

Work in odd days, the remainder when the day count is divided by 7.

2024 is divisible by 4 and is not a century year, so it is a leap year with 366 days.

366 divided by 7 gives 52 weeks and remainder 2, so 2024 contributes 2 odd days.

Advancing 2 days from Monday gives Wednesday.

So 1 January 2025 was a Wednesday.

The common error is to advance by 1 day, which is correct only for an ordinary year. Note also that the leap day falls in February 2024, which is between the two dates, so it counts.

Question 7

What is the two-digit positive integer N? Statement I: The sum of the digits of N is 10. Statement II: N is divisible by 9. Is either statement alone, both together, or neither sufficient?

Accepted Answer

Evaluate statement I alone. Two-digit numbers with digit sum 10 are 19, 28, 37, 46, 55, 64, 73, 82 and 91. Nine candidates remain, so statement I alone is insufficient.

Now deliberately forget statement I and evaluate statement II alone. Two-digit multiples of 9 are 18, 27, 36, 45, 54, 63, 72, 81 and 90. Again nine candidates, so statement II alone is insufficient.

Now take them together. A number is divisible by 9 exactly when its digit sum is divisible by 9. Statement I fixes the digit sum at 10, which is not divisible by 9, so no number satisfies both statements simultaneously.

The two statements are therefore mutually inconsistent, and no value of N exists. Even together they do not determine an answer, because there is no answer to determine.

This is worth noticing because the reflex is to assume that combining constraints narrows the field to one value. Here it empties it, and a candidate who computed rather than checked consistency would have wasted the time discovering that.

Question 8

Statements: Some compilers are optimisers. All optimisers are tools. Conclusions: (I) Some compilers are tools. (II) All tools are optimisers. (III) Some tools are compilers. Which follow?

Accepted Answer

Take them one at a time, testing each against every arrangement the premises permit.

Conclusion I. Some compilers are optimisers, and every optimiser is a tool. Those compilers that are optimisers are therefore tools, so some compilers are tools. This is forced, and no arrangement can break it. It follows.

Conclusion III is the valid conversion of conclusion I: if some compilers are tools, then some tools are compilers. Conversion of a particular affirmative statement is always valid, so this follows too.

Conclusion II reverses 'All optimisers are tools'. The valid conversion is 'Some tools are optimisers', not 'All tools are optimisers'. Draw the tool circle larger than the optimiser circle, with room to spare, and both premises hold while conclusion II fails. It does not follow.

So I and III follow, and II does not.

The pattern to carry away is that a universal affirmative converts only to a particular, while a particular affirmative converts to a particular in either direction.

Question 9

In a certain code, MOUSE is written as NQXWJ. How is TIGER written in the same code?

Accepted Answer

Write the plaintext and code one above the other and compute the shift for each position, rather than guessing a single rule from the first letter.

M to N is +1. O to Q is +2. U to X is +3. S to W is +4. E to J is +5.

The shift increases by one at each position, which is why testing only the first letter would have produced a constant-shift rule that fails immediately at the second.

Apply the same increasing shift to TIGER.

T plus 1 gives U. I plus 2 gives K. G plus 3 gives J. E plus 4 gives I. R plus 5 gives W.

TIGER is written as UKJIW.

The general discipline is to verify a candidate rule against every given pair before applying it. A rule that fits two letters and fails the third is not the rule, and increasing or alternating shifts are the two commonest ways a constant-shift guess goes wrong.

Practice — "Analytical Aptitude"

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