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What number is 72 more than three-fourth of itself?

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by Max@Math Revolution » Thu Jul 14, 2016 12:13 am
What number is 72 more than three-fourth of itself?
A. 138
B. 225
C. 288
D. 324
E. 336

*An answer will be posted in 2 days.
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by Brent@GMATPrepNow » Sat Jul 16, 2016 1:53 pm
Max@Math Revolution wrote:What number is 72 more than three-fourth of itself?
A. 138
B. 225
C. 288
D. 324
E. 336

*An answer will be posted in 2 days.
One approach is to TEST each answer choice.

A) 138
Does 138 = 72 more than 3/4 of itself?
(3/4)(138) + 72 = 175.5 NOPE

B) 225
Does 225 = 72 more than 3/4 of itself?
(3/4)(225) + 72 = some non-integer NOPE

C) 288
Does 288 = 72 more than 3/4 of itself?
(3/4)(288) + 72 = 288
BINGO!!!

Answer: C
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by Brent@GMATPrepNow » Sat Jul 16, 2016 1:54 pm
Max@Math Revolution wrote:What number is 72 more than three-fourth of itself?
A. 138
B. 225
C. 288
D. 324
E. 336
Here's an algebraic solution:

A number is 72 more than three-fourth of itself
Let x be the number
So, we get: x = (3/4)x + 72
Subtract (3/4)x from both sides to get: (1/4)x = 72
Multiply both sides by 4 to get: x = 288

Answer: C
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by Brent@GMATPrepNow » Sat Jul 16, 2016 1:57 pm
Max@Math Revolution wrote:What number is 72 more than three-fourth of itself?
A. 138
B. 225
C. 288
D. 324
E. 336

*An answer will be posted in 2 days.
Once we have the equation, we can also start by eliminating the fraction.
x = (3/4)x + 72
Multiply both sides by 4 to get: 4x = 3x + 288
Subtract 3x from both sides: x = 288

Answer: C

VIDEO about eliminating fractions from an equation: https://www.gmatprepnow.com/module/gmat ... /video/963
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by Max@Math Revolution » Mon Jul 18, 2016 3:03 am
From n=72+(3n/4), n/4=72, n=72(4)=288
Hence, the correct answer is C.
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