At a local coffee shop, pastries may have nuts, chocolate, both, or neither. If 400 pastries were sold Friday, and if of

[BTGmoderatorDC]

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

[Jay@ManhattanReview]

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

Say the # of pastries having only nuts = n; the # of pastries having only chocolate = c; the # of pastries having both nuts and chocolate = b; and the # of pastries having none = x

So, we have n + c + b + x = 400;

c + b = 60% pf 400
c + b = 240

Thus, from n + c + b + x = 400 and c + b = 240, we have n + x = 160.

We have to get the value of n.

Let's take each statement one by one.

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

x = (c + b)/4 = 240/4 = 60

Thus, from n + x = 160, we have n = 100. Sufficient.

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

=> b = (c + b)/3 = 240/3 = 80

However, with this information, we cannot get the value of n. Insufficient.

The correct answer: A

Hope this helps!

-Jay
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