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

[BTGmoderatorLU]

Source: Princeton Review

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

The OA is A

[Brent@GMATPrepNow]

Source: Princeton Review

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

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

Cheers,
Brent

[GMATGuruNY]

Source: Princeton Review

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

25% greater = 1/4 greater.
If the smaller integer = 4, then the larger integer = 4 + (1/4)4 = 5.
The values in red imply that the two integers summing to 27 must be in a RATIO OF 4 TO 5:
4, 5
8, 10
12, 15
The case in blue sums to 27, with the result that larger-smaller = 15-12 = 3.

The correct answer is A.

[Scott@TargetTestPrep]

Source: Princeton Review

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

The OA is A

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