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 fixes the mother’s birth year: the brother was born in 1964 and is 35 years younger, so she was born in 1929. Statement 1 then places Rahul 25 years after her, in 1954. Neither works alone - the first gives only a gap with no anchor, and the second says nothing about Rahul - so both are needed.

Answer: C

From 1, we conclude that weight of each pole = (4x5) kg = 20 kg.

So, total weight of 10 poles = (20 x 10) kg = 200 kg.

From 2, we conclude that:

Weight of each pole = (weight of 3 poles) - (weight of 2 poles) = 20 kg.

So, total weight of 10 pojes = (20 x 10) kg = 200 kg.

Answer: D

Correct answer: Neither 1 nor 2 is sufficient

Statement 1 establishes that H is M’s only daughter, which leaves the number of sons entirely open. Statement 2 concerns M’s own brothers and says nothing about M’s children at all. Together they still give no count of the sons, so the question cannot be answered from either statement or from both.

Answer: D

From 1, total sale of product A = Rs. (8000 x 25) = Rs. 200000.

From 2, we know that the company deals only in product A.

This implies that sale of product A is the total sale of the company, which is Rs. 200000.

Answer: C

From 1, we conclude that 5th, 12th, 19th and 26th of March, 2006 were Sundays.

So, the last Sunday fell on 26th.

From 2, we conclude that 31st March, 2006 was Friday. Thus, 26th March, 2006 was the last Sunday of the month.

Answer: D

Correct answer: Neither 1 nor 2 is sufficient

The two statements share only the word ‘clear’, and comparing them shows ‘de’ must be its code. That leaves ‘ra’ and ‘fa’ standing for ‘sky’ and ‘is’ in some order, with nothing to distinguish them. A third statement containing one of those two words but not the other would be needed.

Answer: D

From 2, Q being in the middle, there are 10 children to his right as well as to his left. So, Q is 11th from the left. From 1, P is 15th from the left.

Thus, from both 1 and 2, we conclude that there are 3 children between P and Q.

Answer: D

From 1, we know that L is T's brother and J's husband. Since L is the only son of his parents, T is L's sister.

From 2, we know that K is L's daughter.

Thus, from 1 and 2, we conclude that T is the sister of K's father i.e. T is K's aunt.

Answer: B

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

Statement 2 says P’s mother is married to J’s husband, so P’s mother and J are the same person - J is P’s mother. Statement 1 gives only P’s siblings and never mentions J, so it contributes nothing to the relationship asked about.