Today, Anna is 10 years older than Michelle. If fifteen years ago, Anna was twice as old as Michelle, how old is Michell

[M7MBA]

Today, Anna is 10 years older than Michelle. If fifteen years ago, Anna was twice as old as Michelle, how old is Michelle today?

a) 20
b) 22
c) 25
d) 28
e) 30

Answer: C

Source: Official Guide

[Brent@GMATPrepNow]

Today, Anna is 10 years older than Michelle. If fifteen years ago, Anna was twice as old as Michelle, how old is Michelle today?

a) 20
b) 22
c) 25
d) 28
e) 30

Answer: C

Source: Official Guide

One option is to test the answer choices. In many cases, it can be the fastest approach.

A) 20
If Michelle is 20 years old TODAY, then Anna is 30 years old TODAY (since she's 10 years older than Michelle)
So, 15 YEARS AGO, Michelle was 5 years old and Anna was 15 years old
This does NOT meet the given condition that Anna was twice as old as Michelle 15 YEARS AGO
Eliminate A

B) 22
If Michelle is 22 years old TODAY, then Anna is 32 years old TODAY (since she's 10 years older than Michelle)
So, 15 YEARS AGO, Michelle was 7 years old and Anna was 17 years old
This does NOT meet the given condition that Anna was twice as old as Michelle 15 YEARS AGO
Eliminate B

C) 25
If Michelle is 25 years old TODAY, then Anna is 35 years old TODAY (since she's 10 years older than Michelle)
So, 15 YEARS AGO, Michelle was 10 years old and Anna was 20 years old
This DOES meet the given condition that Anna was twice as old as Michelle 15 YEARS AGO

Answer: C

[Scott@TargetTestPrep]

Today, Anna is 10 years older than Michelle. If fifteen years ago, Anna was twice as old as Michelle, how old is Michelle today?

a) 20
b) 22
c) 25
d) 28
e) 30

Answer: C

Source: Official Guide

Solution:

We can let A = Anna’s current age and M = Michelle’s current age. We can create the equations:

A = M + 10

and

A - 15 = 2(M - 15)

Substituting M + 10 for A in the second equation, we have:

M + 10 - 15 = 2(M - 15)

M - 5 = 2M - 30

25 = M

Answer: C