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

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13 Dec 2010, 06:53

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A

B

C

D

E

Difficulty:

35% (medium)

Question Stats:

63% (02:21) correct
37% (00:50) wrong based on 454 sessions

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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.

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

About the red part: generally such kind of linear equations (ax+by=c) have infinitely many solutions for x and y, and we cannot 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 a 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).

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 ....

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.

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.

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

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

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27 Jun 2014, 03:00

Hello from the GMAT Club BumpBot!

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

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05 Sep 2014, 23:59

rite2deepti wrote:

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 ....

1--> no suff. 2--> .20x+ .30y= 2.5 muliple by 5 to remove clumsy.

1x +1.5y= 12.5 ---> now if x= 11 then y=1 or if x= 6 then y= 5 and similar way you could get different count for 20 cent stamps.

now 1+2 --> from one we got more than 8 hence it must be suff cuz, if x= 9 or 10 , you wont get proper value for y as y should be an integer.

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

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23 Oct 2015, 06:16

Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
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