Problem Solving

BTGmoderatorLU wrote:If the ratio of the present age of Anna and Paula is 3 : 4, what could be the ratio of their respective ages after 8 years?

A. 1 : 2
B. 3 : 8
C. 3 : 5
D. 2 : 3
E. 4 : 5

The OA is E.

Source: e-GMAT

Here's a nice property of fractions: If a, b and k are positive, then (a + k)/(b + k) approaches 1 as k gets bigger.
For example, the fraction (2+11)/(3+11) is closer to 1 than 2/3 is.
Likewise, the fraction (1+7)/(2+7) is closer to 1 than 1/2 is.

Let A = Anna's present age
Let P = Paula's present age
So, A/P = 3/4

In EIGHT YEARS, we can conclude that:
Let A + 8= Anna's future age
Let P + 8 = Paula's future age
So, in EIGHT YEARS, the ratio of their ages = (A + 8)/(P + 8)

By the above rule, we know that (A + 8)/(P + 8) is closer to 1 than is A/P is.
In other words, (A + 8)/(P + 8) is closer to 1 than 3/4 is.

Check the answer choices.....
Only answer choice E (aka 4/5) is closer to 1 than 3/4 is.

Answer: E

Cheers,
Brent

BTGmoderatorLU wrote:If the ratio of the present age of Anna and Paula is 3:4, what could be the ratio of their respective ages after 8 years?

A. 1 : 2
B. 3 : 8
C. 3 : 5
D. 2 : 3
E. 4 : 5

The OA is E.

Source: e-GMAT

Some possible ratios of their current ages are:

A/P = 3/4, 6/8, 9/12, 12/15, 15/20, 18/24, 21/28, 24/32...

So after 8 years, these ratios, would be:

11/12, 14/16 = 7/8, 17/20, 20/23, 23/28, 26/32 = 13/16, 29/36, 32/40 = 4/5, ...
We see that if Anna is 24 and Paula is 32, the ratio of their ages 8 years later is 32/40 = 4/5, or 4 : 5.

Answer: E