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# At least one pencil is distributed to each of the 19 students. Did at

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Re: At least one pencil is distributed to each of the 19 students. Did at [#permalink]
We know that each student received at least 1 pencils and we know that there are 19 students in total.

let's say that if each student received a different number of pencils,then the total number of pencils distributed would've been 1+2+3...+19 = Sum of items * avg. = 190 total

1) We are told that the number of pencils distributed to each student is less than 19 => which means that at least two students received the same number of pencils. Sufficient
2) Sufficient. 187 is less than 190, which means that at least two students received the same number of pencils. Ans. D
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At least one pencil is distributed to each of the 19 students. Did at [#permalink]
ziyuen wrote:
At least one pencil is distributed to each of the 19 students. Did at least two students receive the same number of pencils?

1) The number of pencils distributed to each student is less than 19.

2) The total number of pencils distributed to students is 187.

It's testing something called the Pigeonhole Principle.

The GMAT has tested that before and the design is fine.

It's simple enough, if you have n boxes and (n+1) items that go in those boxes, at least one box has at least two items.

Suppose all the students got different numbers 1, 2, 3, ..., 18

There are only 18 different positive integers less than 19

So the 19th student must duplicate one of those numbers

You can't have 19 different positive integers that are all less than 19

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Re: At least one pencil is distributed to each of the 19 students. Did at [#permalink]
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Re: At least one pencil is distributed to each of the 19 students. Did at [#permalink]
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