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20 Sep 2018, 08:32
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C
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Difficulty:
5%
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Question Stats:
90% (01:29) correct
10%
(02:17)
wrong
based on 698
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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
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a) 20
b) 22
c) 25
d) 28
e) 30
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20 Sep 2018, 08:36
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bettatantalo
A = 10 + M--------------------------------->(I)
A - 15 = 2(M - 15)------------------------->(II)
Substitute the value of A
10 + M - 15 = 2M - 30
M = 40 - 15
Thus, Michelle is 25 Years now, answer must be (C)
Updated on: 15 Apr 2022, 16:06
Originally posted by BrentGMATPrepNow on 20 Sep 2018, 08:46.
Last edited by BrentGMATPrepNow on 15 Apr 2022, 16:06, edited 1 time in total.
Last edited by BrentGMATPrepNow on 15 Apr 2022, 16:06, edited 1 time in total.
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bettatantalo
STRATEGY: Upon reading any GMAT Problem Solving question, we should always ask, Can I use the answer choices to my advantage?
In this case, we can easily test the answer choices.
Now let's give ourselves up to 20 seconds to identify a faster approach.
In this case, we can also solve the question algebraically.
I think testing the answer choices will be faster and less prone to errors. So let's test the answer choices.
It's typically best to start with choice C, the middle value, since we can often eliminate answer choices after testing that value.
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 meets the given condition that Anna was twice as old as Michelle 15 YEARS AGO
Answer: C
Plan B: The conventional (i.e., high school math) approach
Let M = Michelle's PRESENT age
So, M + 10 = Anna's PRESENT age (since she's 10 years older than Michelle)
This means M - 15 = Michelle's age 15 YEARS AGO
And (M + 10) - 15 = Anna's age 15 YEARS AGO
In other words, M - 5 = Anna's age 15 YEARS AGO
Given: fifteen years ago, Anna was twice as old as Michelle
So, we can write: M - 5 = 2(M - 15)
Expand the right side: M - 5 = 2M - 30
Add 30 both sides of the equation: M + 25 = 2M
Subtract M from both sides of the equation: 25 = M
Answer: C
