BTGmoderatorLU wrote:Source: e-GMAT
If the ratio of the present age of Anna and Paula is 1:2, what could be the ratio of their respective ages 8 years ago??
A. 3 : 8
B. 4 : 7
C. 3 : 5
D. 2 : 3
E. 4 : 5
The OA is A
Some possible ratios of ages are:
A/P = 8/16, 9/18, 10/20, 11/22, 12/24, 13/26, 14/28, 15/30, 16/32, 17/34, 18/36, 19/38, 20/40
So 8 years ago, these ratios would be:
A/P = 0/8, 1/10, 2/12, 3/14, 4/16, 5/18, 6/20, 7/22, 8/24, 9/26, 10/28, 11/30, 12/32.
We see that if Anna is 20 and Paula is 40, the ratio of their ages 8 years ago is 12/32 = 3/8.
Alternate Solution:
Let x = Ann's present age. Since the ratio of Ann's present age to Paula's present age is 1:2, Paula's present age must be 2x.
8 years ago, Ann's age was (x - 8), and Paula's age was (2x - 8); therefore, the ratio of their ages was (x - 8)/(2x - 8). Let's set this expression equal to each answer choice and see which one gives a positive integer value for x:
A) 3:8
(x - 8)/(2x - 8) = 3/8
8x - 64 = 6x -24
2x = 40
x = 20
We see that answer choice A gives us a positive integer value for x, so it must be the correct answer choice. Indeed, the ratio of Ann's present age to Paula's present age is 20/40, and the ratio of Ann's age 8 years ago to Paula's age 8 years ago is 12/32 = 3/8.
Answer: A
