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In a tin can, there is a certain number of pencils, 40

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In a tin can, there is a certain number of pencils, 40 [#permalink] New post 15 Nov 2012, 08:39
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In a tin can, there is a certain number of pencils, 40 percent without erasers, and 35 percent without points. If of the pencils 1/6 have no erasers and no points, what fractional part of the pencils have both points and erasers?

A) 11/12
B) 7/12
C) 5/12
D) 1/3
E) 1/4

There is a seemingly simple problem but I have got struck at a subtle point. Could someone post a solution so that I can compare it with the official explanation. Thanks
[Reveal] Spoiler: OA

Last edited by Bunuel on 15 Nov 2012, 09:43, edited 1 time in total.
Renamed the topic and edited the question.
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Re: Groups, Percents, Fractions [#permalink] New post 15 Nov 2012, 08:59
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mhadi wrote:
There is a seemingly simple problem but I have got struck at a subtle point. Could someone post a solution so that I can compare it with the official explanation. Thanks


In a tin can, there is a certain number of pencils, 40 percent without erasers, and 35 percent without points. If of the pencils 1/6 have no erasers and no points, what fractional part of the pencils have both points and erasers?

A) 11/12
B) 7/12
C) 5/12
D) 1/3
E) 1/4


Form a double matrix like shown, using some smart number (any multiple of 6 with enough 0s) eg 600.

from this, fraction that we want is = 250/600 = 5/12

Ans C it is.
Attachments

double_mat.jpg
double_mat.jpg [ 9.63 KiB | Viewed 1218 times ]


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Re: In a tin can, there is a certain number of pencils, 40 [#permalink] New post 15 Nov 2012, 13:17
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n(aUb)=n(a)+n(b)-n(anb)
so total without erasers and points will be 0.75-1/6 which will be 7/12.
So pencils with both erasers and points will be 1-7/12 which should be 5/12
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Re: In a tin can, there is a certain number of pencils, 40 [#permalink] New post 15 Nov 2012, 13:39
Amateur wrote:
n(aUb)=n(a)+n(b)-n(anb)
so total without erasers and points will be 0.75-1/6 which will be 7/12.
So pencils with both erasers and points will be 1-7/12 which should be 5/12
C


Can you explain more clearly
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Re: In a tin can, there is a certain number of pencils, 40 [#permalink] New post 15 Nov 2012, 14:57
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g3kr wrote:
Amateur wrote:
n(aUb)=n(a)+n(b)-n(anb)
so total without erasers and points will be 0.75-1/6 which will be 7/12.
So pencils with both erasers and points will be 1-7/12 which should be 5/12
C


Can you explain more clearly

Venn diagrams..... Consider two samples a, b which overlap..... we have the formula I wrote above....
so if you consider no erasers to be sample space a, and no points to be sample space b....
when they say 0.4 had no erasers, it means they also contain a few which donot have points too.... likewise when they say 0.35 had no points they contain pencils which didnot have erasers too.... so pencils without erasers and points are represented in both the cases above... so if you add no erasers and no points samples, think about it, you are adding pencils without erasers and points twice.... So subtract quantity (1/6) from what you got by adding 0.35+0.4=0.75. So on the whole pencils with no erasers only +pencils with no points only +pencils with no both erasers and points = 0.75-1/6=7/12....
so 7/12 are pencils which are defective on the whole.... but you want good pencils... anything apart from defective pencils are good right... Remember set theory, sum of all samples=1...
So good pencils will be 1-7/12 which is 5/12
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Re: In a tin can, there is a certain number of pencils, 40 [#permalink] New post 19 Jun 2014, 09:55
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Re: In a tin can, there is a certain number of pencils, 40 [#permalink] New post 19 Jun 2014, 22:52
Refer Venn Diagram (We require to find orange region)

Say total pencils = 100

Without erasers = 40

Without points = 35

So, without erasers & without points = \frac{100}{6} (Blue region)

Total pencils with defect

= 40 + 35 - \frac{100}{6}

= \frac{350}{6}

Total pencils without defect

= 100 - \frac{350}{6}

= \frac{250}{6}

Fraction = \frac{\frac{250}{6}}{100}

= \frac{5}{12}

Answer = C
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Re: In a tin can, there is a certain number of pencils, 40   [#permalink] 19 Jun 2014, 22:52
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