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GMAT Focus Question -- Any Simpler Methods?

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by bryan22583 » Sat Apr 13, 2013 10:35 am
If x + y = 24 and 2x-7y=15, which of the following is equal to 13?

A. x-y
B. x+y
C. x-2y
D. 2x + y
E. 2x-y



[spoiler][C][/spoiler][/spoiler]


Through either substitution or combination I can get to the right answer, but it involves several sort of messy fractions and was thus somewhat time consuming...any experts have a faster method?
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by rintoo22 » Sat Apr 13, 2013 10:49 am
If x + y = 24 and 2x-7y=15, which of the following is equal to 13?
Simultaneous eq can give you the value of x and y. I did the problem myself and realised that I must keep the values in fraction. So dont simplify it further.
Then substituting the value of x and y in each equation should get you the answer.

x + y = 24 and 2x-7y=15.... (1)
x = 183/9
y = 33/9

Just a glance through the options should suggest that C should be the answer. Substitute the values and confirm the result.
Important points in my opinion are
1. Leave the values of x and y as fraction
2. Substitue the values after going through the options.
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by Anju@Gurome » Sat Apr 13, 2013 12:02 pm
bryan22583 wrote:If x + y = 24 and 2x-7y=15, which of the following is equal to 13?
We have to make 13 from 24 and 15.
Note that (24 + 15) = 39 = 3*13

Hence, if we add multiply each of the given equation by 1/3 and add them, we will get the correct answer.

So, (x + y)/3 + (2x - 7y)/3 = 13
--> (x/3 + 2x/3) + (y/3 - 7y/3) = 13
--> x - 2y = 13

The correct answer is C.
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by GMATGuruNY » Sat Apr 13, 2013 2:08 pm
bryan22583 wrote:If x + y = 24 and 2x-7y=15, which of the following is equal to 13?

A. x-y
B. x+y
C. x-2y
D. 2x + y
E. 2x-y
Adding together x+y = 24 and 2x-7y = 15, we get:
(x+y) + (2x-7y) = 24+15
3x - 6y = 39.

Dividing each side by 3, we get:
x - 2y = 13.

The correct answer is C.
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