Items belonging to 2 overlapping sets can be in 4 distinct parts: the overlap between the sets, in only one set, in only the other set, or in neither set.
To calculate the part that is only nuts we need to know the other 3 (overlap, only chocolate, neither).
We'll look for a statement that gives us this information, a Logical approach.

Note that we're told the total amount of chocolate, that is the 'overlap' + 'only chocolate'. So all we need to know is the 'neither' part.

(1) this gives us the 'neither' part - enough!
Sufficient.

(2) this gives us the 'overlap' part - not enough.
Insufficient.

(A) is our answer.
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So basically there are four kinds of pastries: (1) having Only Chocolate, (2) having both Chocolate/Nuts, (3) having Only Nuts, (4) having Neither. We have to determine the number of type (3) pastries, i.e., having Only Nuts. And we know that (1) + (2) + (3) + (4) = 400

We are given that out of 400, 60% or 0.6*400 = 240 contain chocolates. So these 240 are sum of type (1) and (2). So we just need to know (4) to calculate the value of (3).

Statement 1 - gives us the number of type (4) pastries. these are 1/4 * 240 = 60. So we can find type (3). Sufficient.

Statement 2 - tells us that type (2) are 1/3 of type (1). But this is not sufficient to calculate type (3).

Hence A answer

Why the answer cannot be C?

Hello

If you check the above two solutions, first statement is sufficient to answer the question asked. Second statement is not sufficient on its own to answer.

when one or more of the statements is sufficient to answer the question, then we do NOT combine the statements. Statements have to be combined only when none of the statements is sufficient on its own to answer the question.

Thus the answer is A.

Answer: A.

Please see the attachment!

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This is Venn Diagram question.
Given, Universal set U = 400
Chocolate C = 0.6 * 400 = 240
N = nuts
To find : N-C

S1: not(C u N) = 0.25 * C = 60
now, C u N = 400-60 = 340
therefore, N-C = 340 - C = 100
Sufficient

S2: only information about the distribution in set C is given. i.e. C-N = 160, C intersection N = 80.
So, not sufficient.

Ans A

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