30 people in total attended an office party for a

[BTGmoderatorLU]

Source: Manhattan Prep

30 people in total attended an office party for a colleague's birthday. The birthday cake was sliced into exactly 32 pieces, all of which were eaten. Did everyone who attended eat at least one slice of cake?

1) One person ate exactly 2 slices of cake.
2) One person ate exactly 3 slices of cake.

The OA is C

[Jay@ManhattanReview]

Source: Manhattan Prep

30 people in total attended an office party for a colleague's birthday. The birthday cake was sliced into exactly 32 pieces, all of which were eaten. Did everyone who attended eat at least one slice of cake?

1) One person ate exactly 2 slices of cake.
2) One person ate exactly 3 slices of cake.

The OA is C

Let's take each statement one by one.

1) One person ate exactly 2 slices of cake.

This statement is open to a couple of interpretations. 1. EXACTLY one person ate exactly 2 slices of cake. 2. AT LEAST one person ate exactly 2 slices of cake.

If we take #1 as interpretation, we get that Statement 1 itself is sufficient. Let's discuss this.

EXACTLY one person ate exactly 2 slices of cake. So we have 30 slices for 29 persons. Considering that 29 ate one slice each; in that case, another person will have to eat 2 slices; however, it will contradict the statement.

Thus, one person ate 2 slices and another person ate 3 slices. Now, we have 27 slices for 28 persons. It is clear that one person did not eat a slice. The answer is No.

There is no need to consider the cases when two or more persons ate 3 or more slices as in those cases, we will get the answer as No. So Statement 1 itself is sufficient.

If we take #2 as interpretation, we get that Statement 1 itself is not sufficient. Let's discuss this.

Case 1: Each of the two persons ate exactly 2 slices each and none at more than 2 slices. Thus, we have 28 slices for 28 persons. Each ate one slice. The answer is Yes.

Case 2: We have already seen that if one person ate 3 or more slices, the answer is No.

No unique answer. Insufficient

2) One person ate exactly 3 slices of cake.

Case 1: Considering that EXACTLY one person ate exactly 3 slices of cake and EXACTLY one person ate 2 slices. Thus, there are 28 slices for 28 slices. Thus, each ate at least one slice.

Case 2: We have already seen that if one person ate 3 or more slices, the answer is No.

No unique answer. Insufficient

(1) and (2) together

Depending on the interpretation, the answer is either A or C.

-Jay
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