At a local coffee shop, pastries may have nuts, chocolate,

[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

Given:

1. Pastries may have nuts, chocolate, both, or neither.
2. 400 pastries were sold Friday, and if of those, 60% contained chocolate.

=> Number of pastries with chocolate = 60% of 400 = 240

Question: How many of those sold contained only nuts?

Say,

N = # of pastries with nuts;
C = # of pastries with chocolate = 240 (given);
B = # of pastries with nuts & chocolate;
X = # of pastries with neither nuts nor chocolate

Thus,

400 = N + C - B + X
400 = N + 240 - B + X

160 = N - B + X

We have to determine the value of the number of pastries contained only nuts, it means we have to get the value of (N - B).

If we get the value of X, we get the value of (N - B).

Question rephrased: How many pastries have neither nuts nor chocolate or what is the value of X?

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/4 = 240/4 = 60. Sufficient.

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

=> B = C/3 = 240/3 = 80.

We can't get the value of X. Insufficient.

The correct answer: A

Hope this helps!

-Jay
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[swerve]

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 the correct answer.