Data Sufficiency Questions and Answers

Answer: D

The answer is Statement I alone is sufficient to answer the question while Statement II alone is not sufficient.

Statement I says Prabha is heavier than Meena and Kirti but lighter than Anita. So Anita is heavier than Prabha, who is heavier than the other two: Anita is the heaviest. Statement I alone answers the question.

Statement II says Meena is lighter than Prabha and Anita but heavier than Kirti. That leaves Prabha and Anita both above Meena, with no comparison between them, so the heaviest cannot be found from II alone.

Answer: D

The answer is Either statement I alone or statement II alone is sufficient to answer the question.

Rank from the last = total - rank from the top + 1, so we only need the class size.

Statement I: Reena is 10th from the top and 38th from the last, so the class has \(10 + 38 - 1 = 47\) students. Then Garima is \(47 - 18 + 1 = 30\)th from the last.

Statement II gives 47 students directly, and again Garima is 30th from the last.

Since each statement gives the total by itself, either alone is sufficient; neither is needed together with the other.

Answer: D

Both statements together are necessary. Statement I alone gives only that the second number is larger than the third and fifth, which leaves the first and fourth numbers unrelated to it, so it cannot name the greatest. Statement II alone says the first number is greater than the second and less than the fourth, which puts the fourth above the first and second but says nothing about the third and fifth. Taken together, the fourth number is greater than the first, the first is greater than the second, and the second is greater than the third and fifth, so the fourth number is the greatest. Neither statement alone is sufficient.

Answer: D

The data in both statements together are not sufficient. To say how Anurag is related to Arti, the two families have to be connected. Statement I says Anurag is the brother of Yeshica and that Arti is the daughter of Pooja's brother, but it does not say how Pooja is connected to Anurag's family. Statement II brings in Dheeraj, who is a brother of Yeshica's father and of Deepika, but Pooja and Arti do not appear in it. Pooja might be Deepika, or might not, and nothing in either statement settles it. So even together they cannot give the relationship, which is option D.

Answer: C

Both statements together are needed, so the answer is the third option. The building has six floors and parking is on the first, so the people live on floors 2 to 6. Statement I alone puts Ishan on the fourth floor with only Hitesh between him and Jagdish, which allows two cases: Jagdish on the second floor and Hitesh on the third, or Hitesh on the fifth and Jagdish on the sixth.

Statement II alone says only that Ishan lives immediately above Karan, which tells us nothing about Hitesh. Together, Karan is on the third floor, which rules out the first case, so Hitesh lives on the fifth floor. Neither statement alone is sufficient, and together they are.

Answer: D

The two statements together are not sufficient. Statement I places Amir 15th from the top. Statement II says there are 5 students between Amir and Salman, so Salman is 5 places beyond Amir on either side: 15 + 6 = 21st from the top, or 15 - 6 = 9th from the top.

Both are possible, because nothing says whether Salman is above or below Amir, so the rank cannot be fixed. Statement I alone gives nothing about Salman and Statement II alone gives no starting rank, so options A and B are wrong, and option C is wrong because even together they leave two answers.

Answer: D

Either statement alone is enough, and in both E is the tallest. Statement I: B is taller than only D, so exactly one person is shorter than B, and A, C and E are all taller than B. E is taller than A and C, so the order is E, then A and C, then B, then D, with E tallest. Statement II: A is shorter than only E, so only E is taller than A. D is shorter than B and A is above B, C and D, so E is again the tallest.

Options 1 and 2 each say that one statement is insufficient, which is false, and option 3 says both are needed, which is also false.

Answer: C

Both statements together are needed. Statement I alone gives the order L, J, M left to right but does not place K and N, so the middle person cannot be fixed. Statement II alone says only N is to the left of K, so N and K are the first two on the left, but the other three are unplaced. Together, N and K occupy the left end and the group L, J, M follows, giving N, K, L, J, M, so L is in the middle. Hence the data of both statements together are necessary. Each statement alone is not sufficient, and together they are sufficient, so the last option is wrong.

Answer: C

The data in both statements together are necessary and sufficient, so the answer is the third option.

From statement I, 'yu ui qw' means 'blood is red'. Statement II gives 'ls yu wd ui' for 'this is red flag'. The words yu and ui appear in both codes, and 'is' and 'red' appear in both meanings, so yu and ui stand for 'is' and 'red'. Then the remaining code qw in statement I must mean 'blood'.

Statement I alone cannot tell which of yu, ui and qw is 'blood', and statement II alone does not contain 'blood' at all. So both statements are needed together.

This kind of question is solved by looking for a common word in the codes. Only the words 'is' and 'red' appear in both sentences, and the codes yu and ui appear in both, so they must stand for those two words. Once they are known, the leftover word in the first sentence, 'blood', must be qw, and both statements are used.

Answer: D

Both statements together are needed, so statements I and II are both necessary. Statement I alone says Mahesh is the son of Devika, which does not connect him to Bipin. Statement II alone says Devika is the only daughter of Bipin's father, which makes Devika Bipin's sister but names nothing about Mahesh. Taken together, Mahesh is the son of Bipin's sister, so Mahesh is Bipin's nephew. Neither statement alone answers the question, so the options that call one statement sufficient, or either one sufficient, are wrong.