BTGmoderatorDC wrote:At a local coffee shop, pastries may have nuts, chocolate, both, or neither. If 400 pastries were sold Friday, and if of those, 60% contained chocolate how many of those sold contained only nuts?

(1) The number of pastries containing neither is one-fourth of the number containing chocolate.

(2) One third of pastries sold containing chocolate also contained nuts.

OA A

Source: Veritas Prep

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

Statement 1: not\((C u N) = 0.25 \cdot C = 60\)
now, \(C\) u \(N = 400-60 = 340\)
therefore, \(N-C = 340 - C = 100\)
Sufficient. \(\color{green}\checkmark\)

Statement 2: only information about the distribution in set \(C\) is given. i.e. \(C-N = 160\), \(C\) intersection \(N = 80\).
So, not sufficient. \(\color{red}{\Large{\times}}\)

Hence, the correct answer is __A__