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06 Feb 2012, 03:44
1
KUDOS
00:00

Difficulty:

5% (low)

Question Stats:

89% (02:27) correct 11% (02:21) wrong based on 72 sessions

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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 _________________ http://en.wikipedia.org/wiki/Kudos Last edited by fiendex on 06 Feb 2012, 04:04, edited 1 time in total. Math Expert Joined: 02 Sep 2009 Posts: 34029 Followers: 6081 Kudos [?]: 76338 [1] , given: 9973 Re: Elena purchased Brand X pens for$4.00 apiece and brand Y [#permalink]

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06 Feb 2012, 03:57
1
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). Answer: D. _________________ Manager Joined: 01 Dec 2011 Posts: 69 Followers: 1 Kudos [?]: 35 [0], given: 12 Re: Elena purchased Brand X pens for$4.00 apiece and brand Y [#permalink]

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06 Feb 2012, 04:08
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
_________________

http://en.wikipedia.org/wiki/Kudos

Math Expert
Joined: 02 Sep 2009
Posts: 34029
Followers: 6081

Kudos [?]: 76338 [0], given: 9973

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06 Feb 2012, 04:39
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 Moderator Joined: 01 Sep 2010 Posts: 2992 Followers: 691 Kudos [?]: 5551 [0], given: 968 Re: Elena purchased Brand X pens for$4.00 apiece and brand Y [#permalink]

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02 Jun 2012, 06:25
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
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