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Today, Anna is ten years older than Michelle. If fifteen years ago..
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bettatantalo
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Today, Anna is ten years older than Michelle. If fifteen years ago.. [#permalink] New post  20 Sep 2018, 07:32
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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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BrentGMATPrepNow
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Today, Anna is ten years older than Michelle. If fifteen years ago.. [#permalink] New post  20 Sep 2018, 07:46
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bettatantalo wrote:
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


There's also the option of testing 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
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Re: Today, Anna is ten years older than Michelle. If fifteen years ago.. [#permalink] New post  20 Sep 2018, 07:36
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bettatantalo wrote:
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 = 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)
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Re: Today, Anna is ten years older than Michelle. If fifteen years ago.. [#permalink] New post  13 Oct 2020, 11:51
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Pick a random option to get near to the answer. Let us will pick 30 just because the numbers we see in the questions are 2, 10, and 15.

Michelle today: 30 and Fifteen years ago: 30 - 15 = 15

Anna today: 30 + 10 = 40 and fifteen years ago: 40 - 15 = 25 [Anna not twice of michelle].

Let us pick Michelle today: 25 and fifteen years ago: 25 - 15 = 10

Anna today: 25 + 10 = 35 and fifteen years ago" 35 - 15 = 20 [Anna was twice of michelle]

Answer C
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Re: Today, Anna is ten years older than Michelle. If fifteen years ago.. [#permalink] New post  17 Oct 2020, 06:50
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bettatantalo wrote:
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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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
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Re: Today, Anna is ten years older than Michelle. If fifteen years ago.. [#permalink] New post  17 Oct 2020, 07:16
bettatantalo wrote:
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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Today, A = M + 10
15 years ago, A - 15 = 2(M-15)

M+10-15 = 2M-30
M-5 = 2M-30
M=25

Answer is C.
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Re: Today, Anna is ten years older than Michelle. If fifteen years ago.. [#permalink]
17 Oct 2020, 07:16
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