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The sum of two integers is 27. The larger integer is 25% greater

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by BTGModeratorVI » Tue Mar 10, 2020 7:19 am
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The sum of two integers is 27. The larger integer is 25% greater than the smaller integer. What is the positive difference between the two integers?

A. 3
B. 6
C. 9
D. 12
E. 15

Answer: A
Source: Princeton Review
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Re: The sum of two integers is 27. The larger integer is 25% greater

by Jay@ManhattanReview » Thu Mar 12, 2020 12:50 am
BTGModeratorVI wrote: ↑
Tue Mar 10, 2020 7:19 am
 The sum of two integers is 27. The larger integer is 25% greater than the smaller integer. What is the positive difference between the two integers?

A. 3
B. 6
C. 9
D. 12
E. 15

Answer: A
Source: Princeton Review
Say the smaller integer is x; thus, the larger integer = 1.25x

=> x + 1.25x = 2.25x = 27

x = smaller integer = 12 and larger integer = 1.25x = 1.25*12 = 15

Thus, the positive difference between the two integers = |12 – 15| = 3

The correct answer: A

Hope this helps!

-Jay
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Re: The sum of two integers is 27. The larger integer is 25% greater

by Brent@GMATPrepNow » Thu Mar 12, 2020 5:43 am
BTGModeratorVI wrote: ↑
Tue Mar 10, 2020 7:19 am
 The sum of two integers is 27. The larger integer is 25% greater than the smaller integer. What is the positive difference between the two integers?

A. 3
B. 6
C. 9
D. 12
E. 15

Answer: A
Source: Princeton Review
Let x = the smaller integer
So, 1.25x = the larger integer (since the larger integer is 25% greater than the smaller integer)

The sum of two integers is 27.
We can write: x + 1.25x = 27
Simplify: 2.25x = 27
Solve: x = 27/2.25
IMPORTANT: What's a nice fast way to evaluate 27/2.25?
An easy way is to create an EQUIVALENT fraction that has a nice denominator.

Take: 27/2.25
Double the top and bottom to get: 54/4.5 (better)
Double the top and bottom again to get: 108/9 (aha!!!)
Evaluate: 108/9 = 12

So, x = 12
So, the smaller number is 12

1.25x = the larger integer
1.25(12) = 15

The positive difference = 15 - 12 = 3

Answer: A

Cheers,
Brent
Brent Hanneson - Creator of GMATPrepNow.com
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Re: The sum of two integers is 27. The larger integer is 25% greater

by Scott@TargetTestPrep » Thu Mar 12, 2020 6:31 am
BTGModeratorVI wrote: ↑
Tue Mar 10, 2020 7:19 am
 The sum of two integers is 27. The larger integer is 25% greater than the smaller integer. What is the positive difference between the two integers?

A. 3
B. 6
C. 9
D. 12
E. 15

Answer: A
Source: Princeton Review


We can let the smaller integer = n and the larger integer = 1.25n; thus:

n + 1.25n = 27

2.25n = 27

n = 12

Thus, the larger integer is 1.25 x 12 = 15, and the difference between the two integers is 15 - 12 = 3.

Answer: A

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