Data Sufficiency Questions and Answers

Answer: C

The question can be answered using statements A and B together but not by either statement alone.

Statement A ties x to z, \(x = 2(z + 10)\); statement B ties y to z, \(y = 2(z - 10)\). Alone, each says nothing about the other variable, so neither is sufficient.

Together:

\[ \begin{aligned} x - y &= 2(z + 10) - 2(z - 10) \\ &= 40 \gt 0 \end{aligned} \]

so x is greater than y whatever z is. The same holds if the statements are read as \(x = 2z + 10\) and \(y = 2z - 10\), where the difference is 20.

The 'A alone' and 'B alone' options fail because each statement mentions only one of x and y. The last option fails because the two together do settle the question.

Answer: D

Correct answer: Both 1 and 2 are sufficient

Statement 2 makes P the mother of R’s sister and therefore of R. Statement 1 makes P the wife of M’s brother, so that brother is R’s father and M is R’s uncle or aunt - R is M’s nephew or niece. Neither statement alone connects R to M, so both are required.

Answer: D

Correct answer: Neither 1 or 2 is sufficient

Statement 1 is self-contradictory in a row of five: C cannot be both third to the left of D and second to the left of E while also immediately right of A. Statement 2 is similarly inconsistent with D at an end. Neither yields a workable arrangement, so neither determines who stands in the middle.

Answer: A

Correct answer: 1 alone is sufficient while 2 alone is not sufficient

Statement 1 puts A and D above B, E and F, and adds that neither A nor D is the heaviest - which leaves only C, so C is the heaviest. Statement 2 orders C above A above D but says nothing about B, E and F, so it cannot rule out one of them being heavier still.

Answer: A

From 1, we conclude that P is the mother of M and N, while Q is the daughter-in-law of P and sister-in-law of N. Thus, Q is M's wife and hence, M is N's brother.

From 2, we conclude that M and N are the children of S. Also, R is the daughter-in-law of S and sister-in-law of M. So, R is N's wife and thus, N is M's brother. Hence, M is either brother or sister of N.

Answer: D

From 1 and 2, we conclude that Mathematics period began at 9.00 a.m., Biology period began at 8.00 a.m. and Physics period began at 11 a.m. So, the Chemistry period began at 10.00 a.m.

From 1 and 3, we conclude that Mathematics period ended and Chemistry period began at 10.00 a.m.

Answer: A

From 1, we have: P > D, P > N, T > P i.e. T > P > D > N or T > P > N > D ...(i)

From 2, we have: R > Q, T > R i.e. T > R > Q ...(ii)

From 3, we have: T > Q, R > Q ...(iii)

Clearly, from (i) and (ii), we conclude that T is taller than each one of P, N, D, R and Q. So, T is the tallest.

Answer: B

From 1, we conclude that the man is the only son of Tanya's grandfather i.e. he is Tanya's father or Tanya is the man's daughter.

From 2, we conclude that the man's father is Tanya's grandfather. Since the man has no brothers or sisters, so he is Tanya's father or Tanya is the man's daughter.

Answer: D

From 1, we find that number of speakers who attended programme =18-(1/6) of 18 = 15.

From 2, we find that one-third of 15 i.e. 5 speakers gave 2 speeches each, while each of the remaining 10 speakers delivered only one speech.

So, total number of speeches delivered = (5 x 2 + 10 x 1) = 20.

Answer: D

Correct answer: Both 1 and 2 are sufficient

Statement 2 says Anil equals Vimal and Kunal together and the three total 32, so Anil is 16 and Vimal and Kunal share 16. Statement 1 makes Vimal and Kunal equal to each other and to Gagan, so each is 8 and Gagan is 8. Neither reaches the answer alone: the first gives no numbers and the second cannot split the 16 without the equality.