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

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

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New post Updated on: 06 Feb 2012, 04:04
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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

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Originally posted by fiendex on 06 Feb 2012, 03:44.
Last edited by fiendex on 06 Feb 2012, 04:04, edited 1 time in total.
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Re: Elena purchased Brand X pens for $4.00 apiece and brand Y  [#permalink]

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New post 06 Feb 2012, 03:57
1
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.
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Re: Elena purchased Brand X pens for $4.00 apiece and brand Y  [#permalink]

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New post 06 Feb 2012, 04:08
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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
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Re: Elena purchased Brand X pens for $4.00 apiece and brand Y  [#permalink]

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

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New post 06 Feb 2012, 04:39
2
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]

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

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New post 10 Mar 2017, 12:23
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...

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

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New post 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).

Answer: D.



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

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New post 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).

Answer: D.



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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Collection of Questions:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


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

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New post 21 Jun 2018, 19:58
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 purchase?

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


Answer required is number of brand X pens. - An integer

Brand X pen costs $ 4.00

So total cost of required brand X pens will be integer (No of brand X pens * $ 4)

$42 - integer = integer

Hence, we are looking for a number when multiplied with $ 2.8 will give integer.

A quick look at options tells - 5 (12 - 7). So required answer brand X pens = 7
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Re: Elena purchased Brand X pens for $4.00 apiece and brand Y  [#permalink]

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New post 21 Aug 2018, 08:30
Hello,

Notice that

4* some integer x+2.80 * some integer y = 42.00
Clearly 2.80 must be multiplied with a number that yields integer. So it can be 5,10,15,20 ... So on

Now If y=15 x=0,and y =5 x= 7 satisfies our conditions that 4x+2.8y=42

Hence Choice D
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Re: Elena purchased Brand X pens for $4.00 apiece and brand Y &nbs [#permalink] 21 Aug 2018, 08:30
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