GMAT Focus Question -- Any Simpler Methods?

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bryan22583: Newbie | Next Rank: 10 Posts; Posts: 7; Joined: Thu Mar 14, 2013 7:23 am

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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Source: Beat The GMAT — Problem Solving | Sat Apr 13, 2013 10:35 am

rintoo22: Senior | Next Rank: 100 Posts; Posts: 73; Joined: Sun May 06, 2012 2:19 am; Location: Cape Town; Thanked: 6 times

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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Anju@Gurome: GMAT Instructor; Posts: 511; Joined: Wed Aug 11, 2010 9:47 amFollowed by: 86 members; Location: Delhi, India; Thanked: 344 times

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.

Anju Agarwal
Quant Expert, Gurome

Backup Methods : General guide on plugging, estimation etc.
Wavy Curve Method : Solving complex inequalities in a matter of seconds.

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GMATGuruNY: GMAT Instructor; Posts: 15539; Joined: Tue May 25, 2010 12:04 pmFollowed by: 1906 members; Location: New York, NY; Thanked: 13060 times; GMAT Score:790

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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