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

Question

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

EgmatQuantExpert · Answer

Solution

Given:  
 • The sum of two integers is 27
• The larger integer is 25% greater than the smaller integer

To find:  
 • The positive difference between the two integers

Approach and Working:  
If we assume the smaller integer to be n, then
 • The larger integer =  n + \frac{n}{4} = \frac{5n}{4}

As their sum is 27, we can write
 •  n + \frac{5n}{4} = 27 
Or,  \frac{9n}{4} = 27 
Or, n =  \frac{27*4}{9} = 12

The smaller integer = 12

Therefore, the larger integer =  12 + \frac{12}{4} = 12 + 3 = 15

• positive difference = 15 – 12 = 3

Hence, the correct answer is option A.

Answer: A

pikolo2510 · Answer

Let the smaller integer be x
therefore, the larger integer will be 1.25x

Given that, x+1.25x = 27
2.25x = 27
x = 12

larger integer = 15

difference between larger and smaller integer = 15-12
=3

Answer is A

Abhishek009 · Answer

Let the larger Integer be 4k
So, Smaller Integer is 5k ( 125% of 4k)

Now, we have  ( 4k + 5k) = 27

Or,  9k = 27

So,  k = 3

Thus, the positive integer between the two Integers is  k( 5 - 4) = 3 , Answer must be (A)

JeffTargetTestPrep · Answer

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

BrentGMATPrepNow · Answer

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

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