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# Joe bought only twenty cent stamps and thirty cent stamps.

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Joined: 02 Sep 2010
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Joe bought only twenty cent stamps and thirty cent stamps. [#permalink]  13 Dec 2010, 05:53
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66% (02:19) correct 34% (00:45) wrong based on 262 sessions
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 .... [Reveal] Spoiler: OA Math Expert Joined: 02 Sep 2009 Posts: 27123 Followers: 4196 Kudos [?]: 40528 [1] , given: 5540 Joe bought only twenty cent stamps and thirty cent stamps. [#permalink] 13 Dec 2010, 06:26 1 This post received KUDOS Expert's post 3 This post was BOOKMARKED 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.

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. _________________ Senior Manager Status: Bring the Rain Joined: 17 Aug 2010 Posts: 407 Location: United States (MD) Concentration: Strategy, Marketing Schools: Michigan (Ross) - Class of 2014 GMAT 1: 730 Q49 V39 GPA: 3.13 WE: Corporate Finance (Aerospace and Defense) Followers: 7 Kudos [?]: 43 [0], given: 46 Re: Data Sufficiency-word problem [#permalink] 13 Dec 2010, 07:20 Agreed--the x>8 is the key. C for me. _________________ Senior Manager Joined: 18 Sep 2009 Posts: 373 Followers: 3 Kudos [?]: 144 [0], given: 2 Re: Data Sufficiency-word problem [#permalink] 13 Dec 2010, 09:36 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 Math Expert Joined: 02 Sep 2009 Posts: 27123 Followers: 4196 Kudos [?]: 40528 [2] , given: 5540 Joe bought only twenty cent stamps and thirty cent stamps. [#permalink] 13 Dec 2010, 09:48 2 This post received KUDOS Expert's post TomB wrote: 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). For more on such questions check: equations-100204.html gmat-prep2-92785.html car-dealer-data-sufficiency-105682.html _________________ Senior Manager Joined: 18 Sep 2009 Posts: 373 Followers: 3 Kudos [?]: 144 [0], given: 2 Re: Data Sufficiency-word problem [#permalink] 13 Dec 2010, 11:44 Bunnel, thanks for the explanation. Veritas Prep GMAT Instructor Joined: 16 Oct 2010 Posts: 5436 Location: Pune, India Followers: 1325 Kudos [?]: 6721 [0], given: 176 Re: Data Sufficiency-word problem [#permalink] 13 Dec 2010, 21:23 Expert's post 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 _________________ Karishma Veritas Prep | GMAT Instructor My Blog Veritas Prep GMAT course is coming to India. Enroll in our weeklong Immersion Course that starts March 29! Veritas Prep Reviews GMAT Club Legend Joined: 09 Sep 2013 Posts: 4695 Followers: 291 Kudos [?]: 52 [0], given: 0 Re: Joe bought only twenty cent stamps and thirty cent stamps. [#permalink] 27 Jun 2014, 02:00 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. _________________ Manager Joined: 07 Apr 2014 Posts: 148 Followers: 1 Kudos [?]: 10 [0], given: 81 Re: Joe bought only twenty cent stamps and thirty cent stamps. [#permalink] 05 Sep 2014, 22:59 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.

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.

Hence 11 - 20 cents stamps
Re: Joe bought only twenty cent stamps and thirty cent stamps.   [#permalink] 05 Sep 2014, 22:59
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