pemdas wrote:The ratio of two positive numbers is 3 to 4. If k is added to each number the new ratio will be 4 to 5, and the sum of the numbers will be 117. What is the value of k?
A. 1
B. 13
C. 14
D. 18
E. 21
source: Magoosh
OA later
Since a known value (117) is given for the second ratio of 4:5, draw a RATIO BOX for this ratio:
__________X____Y____Total
Ratio:_____4____5_____9
Multiplier:
Actual:_______________117
The multiplier for the box = 117/9 = 13, implying that X=52 and Y=65:
____________X_____Y______Total
Ratio:_______4_____5_______9
Multiplier:___13____13______13
Actual:_____52____65_____117
Now plug in the answer choices, which represent the value of k.
When the correct answer choice is subtracted from 52 and 65, the resulting ratio will be 3:4.
Only answer choice
B works: k=13.
(52-13) : (65-13) = 39:52 = 3:4.
The correct answer is
B.
Last edited by
GMATGuruNY on Thu Jan 26, 2012 3:53 am, edited 1 time in total.
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