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Alice is twice as old as Brian and Cathy is 6 years

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by Gmat_mission » Sat Apr 06, 2019 4:45 am
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Alice is twice as old as Brian and Cathy is 6 years younger than Brian. If Alice is "a" years old, how old is Cathy in terms of "a"?

A. a + 6
B. a − 6
C. (a - 12)/2
D. (a + 12)/2
E. 2a − 6

[spoiler]OA=C[/spoiler]

Source: Princeton Review
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by Brent@GMATPrepNow » Sat Apr 06, 2019 6:57 am
Gmat_mission wrote:Alice is twice as old as Brian and Cathy is 6 years younger than Brian. If Alice is "a" years old, how old is Cathy in terms of "a"?

A. a + 6
B. a − 6
C. (a - 12)/2
D. (a + 12)/2
E. 2a − 6

[spoiler]OA=C[/spoiler]

Source: Princeton Review
GIVEN: Alice is a years old

Alice is twice as old as Brian
This also means Brian is HALF as old as Alice
So, Brian's age = a/2

Cathy is 6 years younger than Brian
So, Cathy's age = (Brian's age) - 6
So, Cathy's age = (a/2) - 6

How old is Cathy in terms of a ?
Cathy's age = (a/2) - 6
= a/2 - 12/2
= (a - 12)/2

Answer: C

Cheers,
Brent
Brent Hanneson - Creator of GMATPrepNow.com
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by swerve » Sat Apr 06, 2019 10:00 am
Make \(B=X\), so
\(A=2X\)
\(C=X-6\)

Make \(A=2X\), so \(X=\frac{A}{2}\).

\(C=\frac{A}{2}-6 = \frac{A-12}{2}\)

Hence, __C__ is the correct option.
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