prachi18oct wrote: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.

We are given that a total of 30 people attended a party and ate a total of 32 slices of cake. We need to determine whether everyone ate at least one slice.

Statement One Alone:

One person ate exactly 2 slices of cake.

Since one person ate exactly 2 slices of cake, the remaining 29 people ate a total of 30 slices of cake. However, we cannot determine whether everyone ate at least one slice of cake.

It's possible that 28 of the remaining 29 people each ate exactly 1 slice of cake and the 29th person ate 2 slices of cake. However, it's also possible that 27 of the remaining 29 people each ate exactly 1 slice of cake, the 28th person ate 3 slices of cake, and the 29th person did not eat a slice of cake.

Statement one alone is not sufficient to answer the question. We can eliminate answer choices A and D.

Statement Two Alone:

One person ate exactly 3 slices of cake.

Since 1 person ate exactly 3 slices of cake, the remaining 29 people ate a total of 29 slices of cake. However, we cannot determine whether everyone ate at least one slice of cake.

It's possible that the remaining 29 people each ate exactly 1 slice of cake. However, it's also possible that 27 of the remaining 29 people each ate exactly 1 slice of cake, the 28th person ate 2 slices of cake, and the 29th person did not eat a slice of cake.

Statement two alone is not sufficient to answer the question. We can eliminate answer choice B.

Statements One and Two Together:

With the information given in the two statements, we know that the remaining 28 (30 - 1 - 1 = 28) people ate a total of 27 (32 - 2 - 3 = 27) slices of cake. Since there are more people than slices of cake, we can determine that not every person ate a slice of cake. The two statements together are sufficient to answer the question.

Answer: C