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A stationery store sells pens and pencils. If the price of [#permalink]

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02 Aug 2010, 19:37

4

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Difficulty:

55% (hard)

Question Stats:

54% (02:08) correct
46% (00:55) wrong based on 109 sessions

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A stationery store sells pens and pencils. If the price of each item is expressed as a non-zero whole number of cents, how much do 5 pencils cost? 1. 5 pencils and 3 pens cost 30 cents. 2. 4 pencils and 4 pens cost 32 cents.

Let p be the price of pen and c price of pencils Statement 1 Consider the below scenarios: p=1, then c=(30-5)/3, which is not possible p=2, then c=(30-10)/3, which is not possible p=3, then c=(30-15)/3, which is possible p=4, then c=(30-20)/3, which is not possible p=5, then c=(30-25)/3, which is not possible

So the only solution is p=3 and c=5.

Statement 2 4p+4c=32, thus p+c=8 has several solutions. p=1, c=7 p=2, c=6.... etc

It's because of the fact that the number of pens and pencils must be integers. You can not have 0.2 or 1.5 or 2.5 pencils or pens.

Thus from statement 1, you get 5pencils+3pens = 30

Or 5*pencils = 30-3*pens ---> pencils = (30-3*pencils)/5

Now start by putting in pens = 1 such that you get an integer value of pencils and you can not have pencils = 0 or negative number. The only set of values that work is

Pens =5, pencils = 3 and this is the only unique set of values that you will get.

Thus this statement is sufficient.

Hope this helps.

The concept from this question can also be applied to questions asking number of oranges or bananas or students etc.

Re: A stationery store sells pens and pencils. If the price of [#permalink]

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26 Mar 2016, 20:26

Hi, in the question they are giving the number of pencils as 5 so theres no debate about pencils being 1.5 I think its A because the question stem mentions that the price has to be expressed in a non-zero whole number of cents therefore the price has to be a whole number and not a fraction (which is usually the case in prices). Usually a question which involves the reasoning that pencils cannot be fractions has prices given and not the number of pencils

gmatclubot

Re: A stationery store sells pens and pencils. If the price of
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26 Mar 2016, 20:26

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