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Kudos [?]: 40 [1] , given: 12

Elena purchased Brand X pens for $4.00 apiece and brand Y [#permalink] ### Show Tags 06 Feb 2012, 02:44 1 This post received KUDOS 00:00 Difficulty: 5% (low) Question Stats: 89% (02:29) correct 11% (02:22) wrong based on 81 sessions ### HideShow timer Statistics Elena purchased Brand X pens for$4.00 apiece and brand Y for $2.80 apiece. If Elena purchased a total of 12 of these pens for$42.00, how many brand X pens did she purchase?

A) 4
B) 5
C) 6
D) 7
E) 8
[Reveal] Spoiler: OA

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Last edited by fiendex on 06 Feb 2012, 03:04, edited 1 time in total.
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Re: Elena purchased Brand X pens for $4.00 apiece and brand Y [#permalink] ### Show Tags 06 Feb 2012, 02:57 1 This post received KUDOS Expert's post fiendex wrote: Elena purchased Brand X pens for$4.00 apiece and brand Y for $2.80 apiece. If Elena purchased a total of 12 of these pens for$42.00, how many brand X pens did she pruchase?

A) 4
B) 5
C) 6
D) 7
E) 8

4x+2.8y=42 --> multiply by 2.5 (to get the integers) --> 10x+7y=105 --> only one positive integers solutions x=7 and y=5 (how to solve: 7y must have the last digit of 5 in order the last digit of the sum to be 5).

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Kudos [?]: 40 [0], given: 12

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06 Feb 2012, 03:16
fiendex wrote:
I took a different approach that is more intuitive to me:

4x + 2.80 (12 - x) = 42.00
4x + 33.60 - 2.80x = 42.00
1.20x = 8.40
x = 7

Interestingly enough even if we were not told that Elena purchased a total of 12 items we could still solve the problem. Another non-negative solution of 10x+7y=105 is x=0 and y=15, but since x=0 is not listed then x=7 is correct answer anyway.
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Re: Elena purchased Brand X pens for $4.00 apiece and brand Y [#permalink] ### Show Tags 06 Feb 2012, 03:39 I have been using this one which I feel is pretty simple as well. Maximum cost of 12 units ($4 *12 pens)= 48
Difference in price between pen and pencil = 4 -2.8 = 1.2.
48 - 42 = $6$6/1.2 = 5
You need to make 5 pen into pencil for the sum to be 42.

12 - 5 = 7 pens
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Re: Elena purchased Brand X pens for $4.00 apiece and brand Y [#permalink] ### Show Tags 02 Jun 2012, 05:25 Bunuel wrote: fiendex wrote: I took a different approach that is more intuitive to me: 4x + 2.80 (12 - x) = 42.00 4x + 33.60 - 2.80x = 42.00 1.20x = 8.40 x = 7 Interestingly enough even if we were not told that Elena purchased a total of 12 items we could still solve the problem. Another non-negative solution of 10x+7y=105 is x=0 and y=15, but since x=0 is not listed then x=7 is correct answer anyway. I agree with Bunuel.........even though a similar problem on MGMAT guide is not sub 600 but 650 up........ 40x + 28y = 420 We have 12 pens looking at the answer choices pick D : 7*40 + 28*5 = 420.......> 420 = 420. D _________________ Re: Elena purchased Brand X pens for$4.00 apiece and brand Y   [#permalink] 02 Jun 2012, 05:25
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