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

Author Message
Manager
Joined: 04 Apr 2010
Posts: 88

Kudos [?]: 67 [1], given: 17

Schools: UCLA Anderson
Joe bought only twenty cent stamps and thirty cent stamps. [#permalink]

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16 Jun 2010, 13:01
1
KUDOS
00:00

Difficulty:

55% (hard)

Question Stats:

50% (01:07) correct 50% (02:08) wrong based on 6 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. Just want to make sure my reasoning is correct on this one - we can only use integers values for the numbers stamps, correct? OPEN DISCUSSION OF THIS QUESTION IS HERE: https://gmatclub.com/forum/joe-bought-o ... 06212.html [Reveal] Spoiler: OA _________________ If this post was helpful, please give Kudos. Kudos [?]: 67 [1], given: 17 Current Student Status: Three Down. Joined: 09 Jun 2010 Posts: 1914 Kudos [?]: 2230 [2], given: 210 Concentration: General Management, Nonprofit Re: Joe bought only twenty cent stamps and thirty cent stamps. [#permalink] ### Show Tags 16 Jun 2010, 13:50 2 This post received KUDOS I am not sure if this is the most accurate solution, but here's my explanation as to why the answer is C. Looking at the first statement: 20 cent stamps: > 8 This is insufficient, so we can eliminate answer choices A and D Now looking at second statement, we see that $$0.20a + 0.30 b = 2.5$$ But there are many possible values that will satisfy this condition, and hence this statement is insufficient by itself. So we can eliminate B. Combining the two statements, we know that $$a > 8$$, so let us assume $$a = x + 8$$ where x can take the values of 1, 2, 3 and so on (Number of stamps can only be integers; you can't buy half a stamp :D) Substituting $$a = x+8$$ into the equation we had from statement 2 we get 0.20a + 0.30b = 2.5 0.20(x+8) + 0.30b = 2.5 0.20x + 1.60 + 0.30b = 2.5 0.20x + 0.30b = 2.5 - 1.6 = 0.9 Now, we know that x can take the values of 1, 2 and 3 and so on For x = 1 b = $$\frac {0.7}{0.3}$$ - Eliminate (Not an integer) For x = 2 b = $$\frac {0.5}{0.3}$$ - Eliminate (Not an integer) For x = 3 b = 1 - This is an integer, that would give rise to the answer being a = 11 and b = 1. But to be sure, we can check one or two more values. For x = 4, b = $$\frac{0.1}{0.3}$$ For x = 5, b becomes negative. So we can stop here. Hence, on combining the statements we see it's sufficient to answer the question. Hope this helps. I wonder if there are other shorter methods to figure this out? Kudos [?]: 2230 [2], given: 210 Manager Joined: 15 Apr 2010 Posts: 189 Kudos [?]: 18 [0], given: 29 Re: Joe bought only twenty cent stamps and thirty cent stamps. [#permalink] ### Show Tags 16 Jun 2010, 14:05 thanks for the answer above.... my solution is similar but doesnt use equations.... I assumed 9 *20cents stamps => 1.80 => 70 cents leftover (but this is not a integer value for the # of 30 cent stamps!) so i moved to 10*20 cent stamps => 2.00 with 50 cents leftover for calculating # of 30 cent stamps used and yet again, we see that we dont get integer value for the # of 30 cent stamps....ie: 50/30=> 1.67 30c stamps.... hence the answer is 11 20cent stamps yielding 1 30cent stamp ...11,1 is the pair and good answer hence C. Kudos [?]: 18 [0], given: 29 Manager Joined: 04 Apr 2010 Posts: 88 Kudos [?]: 67 [0], given: 17 Schools: UCLA Anderson Re: Joe bought only twenty cent stamps and thirty cent stamps. [#permalink] ### Show Tags 16 Jun 2010, 15:27 Thanks guys! Good reasoning for both responses. Pran's solution is a little faster but both work. _________________ If this post was helpful, please give Kudos. Kudos [?]: 67 [0], given: 17 Math Expert Joined: 02 Sep 2009 Posts: 42305 Kudos [?]: 133079 [0], given: 12403 Re: Joe bought only twenty cent stamps and thirty cent stamps. [#permalink] ### Show Tags 11 Aug 2017, 03:14 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.

OPEN DISCUSSION OF THIS QUESTION IS HERE: https://gmatclub.com/forum/joe-bought-o ... 06212.html
_________________

Kudos [?]: 133079 [0], given: 12403

Re: Joe bought only twenty cent stamps and thirty cent stamps.   [#permalink] 11 Aug 2017, 03:14
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