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A pencil costs $3 and a pen costs $7. If pens and pencils

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A pencil costs $3 and a pen costs $7. If pens and pencils [#permalink] New post 16 Aug 2013, 07:36
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A pencil costs $3 and a pen costs $7. If pens and pencils have to be bought independently and in lots
which are multiples of 5. Are the number of pens bought equal to the number of pencils bought.

1)Total money spend was $100.

2)Total money spend was $ 200.
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Re: A pencil costs $3 and a pen costs $7. If pens and pencils [#permalink] New post 16 Aug 2013, 07:47
Expert's post
innocous wrote:
A pencil costs $3 and a pen costs $7. If pens and pencils have to be bought independently and in lots
which are multiples of 5. Are the number of pens bought equal to the number of pencils bought.

1)Total money spend was $100.

2)Total money spend was $ 200.


Let the no of pencils bought = 5x and no of pens = 5y

The question asks is x=y?

From F.S 1, we know that \(3*5x+7*5y = 100\)

or 3x+7y = 20. The only solution for this equation with positive integrals values for (x,y) is \(x=y=2\). Sufficient.

From F.S. 2, we know that\(3x+7y = 40\). Now, \(y=1,x=11\) satisfies this equation. Also, \(y=4,x=4\) satisfies the equations. Insufficient.

A.

Though not a good question for GMAT.
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Re: A pencil costs $3 and a pen costs $7. If pens and pencils [#permalink] New post 19 Aug 2013, 06:21
innocous wrote:
A pencil costs $3 and a pen costs $7. If pens and pencils have to be bought independently and in lots
which are multiples of 5. Are the number of pens bought equal to the number of pencils bought.

1)Total money spend was $100.

2)Total money spend was $ 200.



No of pencils = x, no of pens = y. SInce they have to bought in lots which are multiples of 5, we may assume -
5*3x + 5*7y = total cose = 15x + 35y

Cond1: 15x + 35y = 100 => 3x + 7y = 20. Clearly this gives us x =y = 2 as only solution. SO sufficicent
Cond2: 15x + 35y = 200 => 3x + 7y = 40. This gives us x = y= 4 and x = y = 5. Two criterias satisy the equation and hence insufficient.
Hence ans should be 'A'.
Re: A pencil costs $3 and a pen costs $7. If pens and pencils   [#permalink] 19 Aug 2013, 06:21
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