Joe bought only twenty cent stamps and thirty cent stamps.

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Joe bought only twenty cent stamps and thirty cent stamps. [#permalink]

13 Dec 2010, 06:53

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Joe bought only twenty cent stamps and thirty cent stamps. How many twenty cent stamps did he buy?

(1) Joe bought more than 8 twenty cent stamps.
(2) Joe bought a total of $2.50 worth of stamps.

The OA says C but I am getting B ..guys can you please explain

I applied my reasoning that .2x+.3y=2.50
so .2*5=1.0
.3*5=1.5
Hence we add and we can get 2.50 ..so B should be sufficient..I tried but there are no other integer choices for this combination.

Please help ....

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Re: Data Sufficiency-word problem [#permalink]

13 Dec 2010, 07:26

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rite2deepti wrote:

Actually there are more integer solutions possible to satisfy statement (2):

Joe bought only twenty cent stamps and thirty cent stamps. How many twenty cent stamps did he buy?

(1) Joe bought more than 8 twenty cent stamps --> clearly insufficient.
(2) Joe bought a total of $2.50 worth of stamps --> 2x+3y=25: as x and y must be an integers we must check whether this equation has unique solution (for more on this check below links) --> 2x=25-3y, so 25 minus multiple of 3 must be multiple of 2, following pairs of (x,y) are possible: (2, 7), (5, 5), (8, 3), (11, 1). Not sufficient.

(1)+(2) As from (1) x>8 then from (2) only one pair is left: x=11 and y=1. Sufficient.

Answer: C.

For more on this type of questions check:
eunice-sold-several-cakes-if-each-cake-sold-for-either-109602.html
martha-bought-several-pencils-if-each-pencil-was-either-a-100204.html
a-rental-car-agency-purchases-fleet-vehicles-in-two-sizes-a-105682.html
joe-bought-only-twenty-cent-stamps-and-thirty-cent-stamps-106212.html
a-certain-fruit-stand-sold-apples-for-0-70-each-and-bananas-101966.html
joanna-bought-only-0-15-stamps-and-0-29-stamps-how-many-101743.html
at-an-amusement-park-tom-bought-a-number-of-red-tokens-and-126814.html
collections-confused-need-a-help-81062.html

P.S. Also you should have spotted that x=5 and y=5 for (2) is not correct solution as (1) says that x>8. So if x=5 were correct solution then statements would clearly contradict each other, but on the GMAT, two data sufficiency statements always provide TRUE information and these statements never contradict each other.

Hope it's clear.
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Re: Data Sufficiency-word problem [#permalink]

13 Dec 2010, 08:20

Agreed--the x>8 is the key.

C for me.
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Re: Data Sufficiency-word problem [#permalink]

13 Dec 2010, 10:36

Let no.of 0. 20 cent stamps "x", and 0.30 cent stamps "y"
stmnt (1) is not sufficient because:
x(0.20)+(x+8)(0.30)=?. we do not know x and total amount. Eliminate it.

stmnt (2) is not sufficient because:
x(0.20) +y(0.30)= 2.50. two unknowns in one equation. eliminate it.

(1)+(2)
x(0.20)+(x+8)(0.30)= 2.50.
we can easily solve "x" and"y" values. so answer is C

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Re: Data Sufficiency-word problem [#permalink]

13 Dec 2010, 10:48

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TomB wrote:

About the red part: generally such kind of linear equations (ax+by=c) have infinitely many solutions for x and y, and we can not get single numerical values for the variables. But since x and y represent # of stamps then they must be non-negative integers and in this case 2x+3y=25 is no longer simple linear equation it's Diophantine equation (equations whose solutions must be integers only) and for such kind on equations there might be only one combination of x and y possible to satisfy it. When you encounter such kind of problems you must always check by trial and error whether it's the case.

So statement (2) is not sufficient not because there is one equation and two variables but because there exist more than one pair of integers x and y for which this equation holds true: (2, 7), (5, 5), (8, 3), (11, 1).

For more on such questions check:
equations-100204.html
gmat-prep2-92785.html
car-dealer-data-sufficiency-105682.html
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Re: Data Sufficiency-word problem [#permalink]

13 Dec 2010, 12:44

Bunnel, thanks for the explanation.

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Re: Data Sufficiency-word problem [#permalink]

13 Dec 2010, 22:23

For detailed explanation on how to solve for integral solutions, check out the following post:

http://gmatquant.blogspot.com/2010/11/integral-solutions-of-ax-by-c.html
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Re: Data Sufficiency-word problem [#permalink] 13 Dec 2010, 22:23

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Joe bought only twenty cent stamps and thirty cent stamps.

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