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Macey is three times as old as Mike. In eight years, she will be twice

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Macey is three times as old as Mike. In eight years, she will be twice [#permalink]

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New post 17 Jan 2016, 10:21
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Macey is three times as old as Mike. In eight years, she will be twice as old as Mike. How old was Macey three years ago?

A. 5
B. 8
C. 21
D. 24
E. 30
[Reveal] Spoiler: OA

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Re: Macey is three times as old as Mike. In eight years, she will be twice [#permalink]

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New post 17 Jan 2016, 10:28
Let's Macey's present age be x, and Mike's present age be y. Now lets formulate equations based on the given information.
1. x = 3y
2. (x+8)=2(y+8) => x-2y = 8

Solving these equations, we get x= 24, and y = 8.

Macey's age 3 years ago = 24 - 3 = 21. Hence C.
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Re: Macey is three times as old as Mike. In eight years, she will be twice [#permalink]

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New post 18 Jan 2016, 12:26
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Hi All,

This question can be solved by TESTing THE ANSWERS.

We're told that Macey is THREE TIMES as old as Mike. We're then told that, in 8 years, Macey will be TWICE as old as Mike. We're asked how old Macey was 3 YEARS AGO.

The answer choices to this question are all INTEGERS. Since Macey is NOW three times as old as Mike, her age is almost certainly going to be a multiple of 3. We're asked for her ago 3 YEARS AGO and THAT number will also be a multiple of 3 (since subtracting a multiple of 3 from another multiple of 3 will give us a multiple of 3). This is all meant to say that the correct answer is probably Answer C, D or E.

Let's TEST Answer D: 24

IF... Macey was 24 3 years ago....
Macey is now 27
Mike is now 9
In 8 years....
Macey will be 35
Mike will be 17
While that's fairly 'close' to what we're looking for, it is NOT correct (Macey is supposed to be TWICE Mike's age). Since we're close though, the correct answer is probably close to 24....

Let's TEST Answer C: 21

IF... Macey was 21 3 years ago....
Macey is now 24
Mike is now 8
In 8 years....
Macey will be 32
Mike will be 16
Since 32 is twice 16, this is a MATCH for what we were looking for, so this MUST be the correct answer.

Final Answer:
[Reveal] Spoiler:
C


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Re: Macey is three times as old as Mike. In eight years, she will be twice [#permalink]

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New post 18 Jan 2016, 13:11
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If anyone is interested, we have a free video lesson on how to solve past/present/future ages questions: http://www.gmatprepnow.com/module/gmat-word-problems?id=908
Once you've watched that video, you can try answering this question: http://www.gmatprepnow.com/module/gmat-word-problems?id=909

Cheers,
Brent
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Re: Macey is three times as old as Mike. In eight years, she will be twice [#permalink]

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New post 26 Dec 2017, 00:12
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Re: Macey is three times as old as Mike. In eight years, she will be twice   [#permalink] 26 Dec 2017, 00:12
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