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

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Math Expert
Joined: 02 Sep 2009
Posts: 55631
The sum of two integers is 27. The larger integer is 25% greater than  [#permalink]

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26 Jun 2018, 05:28
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15% (low)

Question Stats:

77% (01:35) correct 23% (01:48) wrong based on 66 sessions

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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

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Posts: 2888
Re: The sum of two integers is 27. The larger integer is 25% greater than  [#permalink]

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26 Jun 2018, 05:38

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.

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Re: The sum of two integers is 27. The larger integer is 25% greater than  [#permalink]

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26 Jun 2018, 05:55
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

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Re: The sum of two integers is 27. The larger integer is 25% greater than  [#permalink]

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26 Jun 2018, 09:13
Bunuel wrote:
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 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)
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Re: The sum of two integers is 27. The larger integer is 25% greater than  [#permalink]

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27 Jun 2018, 18:13
Bunuel wrote:
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

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.

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Re: The sum of two integers is 27. The larger integer is 25% greater than  [#permalink]

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21 Feb 2019, 16:05
Top Contributor
Bunuel wrote:
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
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Re: The sum of two integers is 27. The larger integer is 25% greater than   [#permalink] 21 Feb 2019, 16:05
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