Logic Questions and Answers

Answer: B

Work out the marks of each person. Sunil got 500. Rumana got 50 less than Sunil, so 450. Seema got 20 more than Rumana, so 470. Pooja got 20 less than Seema, so 450.

\[ \text{Rumana} = 450,\quad \text{Pooja} = 450 \]

So Rumana and Pooja got exactly the same marks. Pooja and Seema differ by 20, Seema and Rumana differ by 20, and Rumana and Sunil differ by 50. The answer is Rumana and Pooja, option B.

Answer: C

Ram is 5 feet tall. Mohan is 2 feet taller than Ram, so Mohan is 7 feet. Sohan is 1 foot taller than Ram, which is the sentence the question repeats, so Sohan is 6 feet. Comparing the three heights, Mohan at 7 feet is taller than Sohan at 6 feet and Ram at 5 feet. So Mohan is the tallest. Sohan is only taller than Ram, and Ram is the shortest. The heights can be fixed from the data, so the option that says the tallest cannot be determined is wrong. The answer is Mohan, option C.

Answer: C

Neither reason explains the statement. Reason I says a fly-over was built in city X in the same year, which is a different city and gives no cause for the building in city A. Reason II concerns a promise in the 2019 election manifesto, which comes after the 2018 construction and so cannot have caused it.

Since neither is a possible cause, the answer is 'Neither I nor II is a possible reason'. Choosing only I, only II or both would accept a link that the facts do not support.

Answer: B

The valid inference is R2D2 is the only robot which can repair aeroplanes.

The statements say R2D2 is a robot, it can repair aeroplanes, and no other robot can. Put together, among robots R2D2 alone can repair aeroplanes.

The other options say things the statements never mention. 'Can only repair aeroplanes' and 'can repair only aeroplanes' both claim R2D2 has no other skills or repairs nothing else, but nothing limits what else it can do. 'Only R2D2 is a robot' denies that other robots exist, yet 'no other robot' implies that other robots may well exist.

Answer: C

The inference that follows is Mechanical engineering is a profession well suited for women with masters or higher degrees in mechanical engineering.

The research study found that 99% of women with masters or higher degrees in mechanical engineering were successful in their professions. That directly supports the claim that the profession suits such women, which also contradicts the belief held by 60% of the students polled.

The other options go beyond the paragraph. It shows a mistaken belief about one discipline, not misconceptions about 'various' disciplines. It says nothing about what men with advanced degrees believe, and nothing about how many women pursue such degrees.

Answer: C

The inferences that follow are (ii) and (iv) only.

The proposal says the SITs are to cater to the technological and industrial needs of a developing country. That is (iv) directly, and it is a national purpose of their own, which is (ii).

Statements (i) and (iii) are not supported. Being 'in line with' IITs means modelled on them, not that IIT awards SIT degrees or must be consulted before such institutions are set up. Any option including (i) or (iii) adds a claim the sentence does not make.

Answer: D

The only certain inference is Some Fields medalists have dropped out of college.

June Huh is a Fields medalist who dropped out of college, so at least one Fields medalist dropped out, which is all that “some” claims.

The other statements go beyond the one example. “Every Fields medalist has won an Olympiad medal” is contradicted by Huh himself, who won none. “Everyone who has dropped out of college has won the Fields medal” reverses the relationship and generalises from one person to all dropouts. “All Fields medalists are part-time poets” generalises from one medalist, who in any case was a poet when younger, not necessarily now.

Answer: B

The match is P - 3; Q - 4; R - 1; S - 2.

Each response uses a phrasal verb with 'up' that answers its statement:

• P, a messy house: 'let me clear it up' (tidy it), 3.
• Q, unhappy with marks: 'I will take it up with your teacher' (raise the matter), 4.
• R, avoiding politics: 'I won't bring it up' (mention it), 1.
• S, an unknown word: 'you can easily look it up' (in a dictionary), 2.

Option A pairs the mess with 'look it up' and the marks with 'clear it up', and the other two options likewise give replies that do not answer the statements.

Answer: B

The correct statement is \(a_{1} \lt 50 \lt a_{2}\).

The weight function rises strictly up to 50 years and falls strictly after it. On the rising part, different ages give different weights, and the same holds on the falling part. So two different ages can give the same weight only if one is on the rising side and the other on the falling side: the younger brother is under 50 and the elder over 50.

If both ages were below 50, or both above 50, strict monotonicity would make their weights different. Neither age can be exactly 50, since the weight at 50 is the maximum and is reached at no other age. That rules out the other three options.

Answer: A

The statement that is always true is There are at least 10 students who belong to the same standard.

This is the pigeonhole principle. If every one of the 10 standards had at most 9 students, the school could hold at most \(10 \times 9 = 90\) students. There are 100, so at least one standard must have 10 or more.

The other statements can fail. All 100 students could be in one standard, so a standard may be empty, and the 10th standard may hold more than 10. Equally, the 6th to 10th standards could hold all 100 students, leaving fewer than 50 in the 1st to 5th standards.