30 people in total attended an office party for a

Question

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.

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

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

Gnpth · Accepted Answer

(1)  One person ate exactly 2 slices of cake -- If one person ate 2 slices, then there are exactly 30 slices for 29 People. But we are not sure, whether all 29 people exactly had 1 slice.

(2)  One person ate exactly 3 slices of cake - Same as the above. If one person ate 3 slices, then there are exactly 29 slices for 29 People. But we are not sure, whether all 29 people exactly had 1 slice.

Combining (1) & (2)

Here, 2 persons had 5 slices of cake. It means there are only 27 slices for 28 People, which is not enough for everyone to have atleast one slice.

So Not everyone attended the party had atleast had a slice.

The answer is C.

MyRedemption · Answer

Both the statements combined would give the answer as NO. When one eats three slices as per statement 2, twenty-nine slices are left and there are 29 people. Now if one of the remaining guys eats two slices, then there for sure would be one person who didn't get any. Hence, both the statements together are sufficient to answer the question.

bankerboy30 · Answer

This is a horrible question... I choose D, by basically just assuming the statements were the only true statement. In this case I could always say well what if one of the remaining people ate 5 slices. What info provided would prevent me from thinking this way...

imsahlahno · Answer

Statement 1 says one person ate 2 slices of... how is this statement to be interpreted... does it mean that only one person ate 2 slices and no other person ate 2 slices or that we know one person ate slices and some other person(s) might also have eaten 2 slices.

vidurchanana · Answer

The latter one is correct. In addition, other person(s) might have eaten either two(or more) or none.

rajthakkar · Answer

Cannot this question be interpreted in more than one way??

Posted from my mobile device

Azizajones20 · Answer

Yes, this question can be interpreted into multiple ways, but it should not change the final answer: 
1) Lets assume they mean only one person ate 2 pieces of cake. In this case, if this is the only person that had more than one slice (which we do not know for sure), then every person had at least one slice. If someone had 3 pieces of cake or more, however, then everyone did not have a slice of cake. In this case we CANNOT conclusively say that everyone had a slice. 
1b) If we assume that one person ate 2 pieces of cake, but other people might have eaten 2 pieces of cake as well, then the answer depends on whether someone else had 2 pieces of cake as well. In this case we CANNOT conclusively say that everyone had a slice. 
2) Follow a similar line of reasoning for the second statement. No matter which way you assume the proctor meant the question to be understood, you should still arrive at C as the correct answer because: 
if we know that one person had 2 pieces of cake and another had 3 pieces of cake, no matter how many other people had 2 pieces of cake or 3 pieces of cake (or 4, or 5, or soforth) at the very least we do know that not everyone received a pieces of cake.

Hope this helps.

EMPOWERgmatRichC · Answer

Hi All,

In these types of questions, you have to pay careful attention to what you KNOW and what you DON'T KNOW. For example, in this prompt there are no restrictions on the number of pieces of cake that any one person could have eaten. 1 person could have potentially eaten ALL of the slices. THAT possibility impacts all of the steps that follow. It's also possible that 2 people ate 3 of the slices (1.5 slices for each).

We're told that there are 30 people and 32 slices of cake (and that all slices were eaten). The question asks if each person ate at least one slice of cake. This is a YES/NO question.

Fact 1: 1 person ate 2 slices.

That leaves 29 people and 30 slices of cake.
It IS possible that everyone ate a slice of cake (and the answer is YES)
It IS possible that 1 person ate the rest of the cake (and the answer is NO).
Fact 1 is INSUFFICIENT

Fact 2: 1 person ate 3 slices.

That leaves 29 people and 29 slices of cake.
It IS possible that everyone ate a slice of cake (and the answer is YES)
It IS possible that 1 person ate the rest of the cake (and the answer is NO)
Fact 2 is INSUFFICIENT

Combined, we know...
1 person ate 2 slices
1 person ate 3 slices

That leaves 28 people and 27 slices of cake.
It is NOT POSSIBLE that everyone ate a slice of cake (and the answer is ALWAYS NO).
Combined, SUFFICIENT

Final Answer:  C

GMAT assassins aren't born, they're made,
Rich

ananth95 · Answer

I interpreted the statement (1) as "Exactly one person ate 2 pieces of cake". This would mean that there are now 30 pieces and 29 people. If everyone else had one piece each, we'd be left with one piece of cake. However, the question says "all of which were eaten". This means that someone in the remaining 29 HAD to eat more than one piece, but not two pieces, since statement (1) says exactly one person ate 2 pieces of cake. So if that someone ate 3 pieces of cake, we'd be left with 28 people and 27 pieces, which means that it is not possible for everyone to have had a piece. Therefore, IMO, statement (1) is sufficient. Where am I going wrong?

EMPOWERgmatRichC · Answer

Hi ananth95,

You have not accounted for the possibility that someone could have eaten a FRACTION of a slice. Notice how the prompt asks if everyone at at least 1 (full) slice.... nothing in the prompt stated that the attendees could eat only full slices.

GMAT assassins aren't born, they're made,
Rich

ananth95 · Answer

Thanks, I'm clear now.

anupamadw · Answer

Sorry, but I am still not clear below step

That leaves 28 people and 27 slices of cake. It is NOT POSSIBLE that everyone ate a slice of cake (and the answer is ALWAYS NO). Combined, SUFFICIENT could you please explain, if possible?

anupamadw · Answer

sorry I got it now. there are 27 slices and 28 people. So even if we give each person one slice, there will be one person left without cake. This is most ideal situation. Otherwise, can unevenly distribute cake slices and still answer will be NO.

s1d1 · Answer

can we say there are 31 people. 30 guests and 1 whose birthday it is?

if we do that, then B is the answer

am i wrong somwehere?

JeffTargetTestPrep · Answer

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

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