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# Elena purchased Brand X pens for \$4.00 apiece and brand Y

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Manager
Joined: 01 Dec 2011
Posts: 67

Kudos [?]: 52 [1], given: 12

Elena purchased Brand X pens for \$4.00 apiece and brand Y [#permalink]

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06 Feb 2012, 03:44
1
KUDOS
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5% (low)

Question Stats:

90% (01:26) correct 10% (02:13) wrong based on 124 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

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Last edited by fiendex on 06 Feb 2012, 04:04, edited 1 time in total.

Kudos [?]: 52 [1], given: 12

Math Expert
Joined: 02 Sep 2009
Posts: 42249

Kudos [?]: 132567 [1], given: 12326

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).

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Kudos [?]: 132567 [1], given: 12326

Manager
Joined: 01 Dec 2011
Posts: 67

Kudos [?]: 52 [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

Kudos [?]: 52 [0], given: 12

Math Expert
Joined: 02 Sep 2009
Posts: 42249

Kudos [?]: 132567 [0], given: 12326

Re: Elena purchased Brand X pens for \$4.00 apiece and brand Y [#permalink]

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06 Feb 2012, 04:16
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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Kudos [?]: 132567 [0], given: 12326

Manager
Joined: 31 Jan 2012
Posts: 74

Kudos [?]: 26 [1], given: 2

Re: Elena purchased Brand X pens for \$4.00 apiece and brand Y [#permalink]

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06 Feb 2012, 04:39
1
KUDOS
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

Kudos [?]: 26 [1], given: 2

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Joined: 01 Sep 2010
Posts: 3372

Kudos [?]: 9278 [0], given: 1168

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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Kudos [?]: 9278 [0], given: 1168

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Kudos [?]: 281 [0], given: 0

Re: Elena purchased Brand X pens for \$4.00 apiece and brand Y [#permalink]

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08 Mar 2017, 11:33
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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).

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Kudos [?]: 281 [0], given: 0

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Kudos [?]: 3505 [0], given: 173

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Re: Elena purchased Brand X pens for \$4.00 apiece and brand Y [#permalink]

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10 Mar 2017, 12:23
Expert's post
1
This post was
BOOKMARKED
Hi All,

This question has a great Number Property 'shortcut' built into it than can help you avoid having to do too much math.

Since the total spent is exact \$42 and Brand Y pens cost \$2.80 each, we have to 'multiply away' all of those \$0.80 increments and end up with a round number. The smallest positive integer that will do that is 5... 5(\$2.80) = \$14.

Considering that there are only 12 total pens and the answers choices are 4-8 inclusive, there's only one possible number of Brand X pens that makes sense...

[Reveal] Spoiler:
D

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Kudos [?]: 3505 [0], given: 173

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Kudos [?]: 43 [0], given: 274

Re: Elena purchased Brand X pens for \$4.00 apiece and brand Y [#permalink]

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15 Nov 2017, 11:45
Bunuel wrote:
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).

Bunuel
I need a little help with this question.

x+y= 12...................1
4x+2.80y=42.............2

From 1, y= 12-x

Substitute in eq. 2

I approximated 2.80 to 3 as the multiplication would be a little long and I thought that as I am taking a higher value, the answer will be less than the approximated answer.

4x+36-3x= 42

x= 6

But the answer is more than 6. Where did I really make the mistake?

Kudos [?]: 43 [0], given: 274

Math Expert
Joined: 02 Sep 2009
Posts: 42249

Kudos [?]: 132567 [0], given: 12326

Re: Elena purchased Brand X pens for \$4.00 apiece and brand Y [#permalink]

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15 Nov 2017, 21:01
Shiv2016 wrote:
Bunuel wrote:
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).

Bunuel
I need a little help with this question.

x+y= 12...................1
4x+2.80y=42.............2

From 1, y= 12-x

Substitute in eq. 2

I approximated 2.80 to 3 as the multiplication would be a little long and I thought that as I am taking a higher value, the answer will be less than the approximated answer.

4x+36-3x= 42

x= 6

But the answer is more than 6. Where did I really make the mistake?

4x + 2.80y = 42

When you change 2.8 with 3, you increase the value of the red summand. So, the value of 4x, and therefore of x itself, will be lower than they actually are.
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Kudos [?]: 132567 [0], given: 12326

Re: Elena purchased Brand X pens for \$4.00 apiece and brand Y   [#permalink] 15 Nov 2017, 21:01
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