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
The sum of two integers is 27. The larger integer is 25%
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Let x = the smaller integerBTGmoderatorLU wrote: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
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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25% greater = 1/4 greater.BTGmoderatorLU wrote: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
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.
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We can let the smaller integer = n and the larger integer = 1.25n; thus:BTGmoderatorLU wrote: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
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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