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If Shannon's age is exactly half of Josh's age, what is. . .

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If Shannon's age is exactly half of Josh's age, what is. . .

by M7MBA » Sun Jan 07, 2018 11:20 am
If Shannon's age is exactly half of Josh's age, what is Shannon's age?

(1) Six years ago Josh's age was exactly three times Shannon's age.
(2) Twelve years from now, Josh's age will be exactly 1.5 times Shannon's age

The OA is the option D.

Experts, I don't know how to prove that the statement (1) is sufficient. Can you help me here? Thanks in advanced.
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by Jay@ManhattanReview » Mon Jan 08, 2018 2:56 am
M7MBA wrote:If Shannon's age is exactly half of Josh's age, what is Shannon's age?

(1) Six years ago Josh's age was exactly three times Shannon's age.
(2) Twelve years from now, Josh's age will be exactly 1.5 times Shannon's age

The OA is the option D.

Experts, I don't know how to prove that the statement (1) is sufficient. Can you help me here? Thanks in advanced.
Say Shannon's age is given by S and Josh's age is given by J. We have S = J/2. We have to find out the value of S.

(1) Six years ago Josh's age was exactly three times Shannon's age.

=> J - 6 = 3(S - 6) => J = 3S - 12.

Plugging in the value of S = J/2 in J = 3S - 12, we get J = 3J/2 - 12 => J = 24 and S = 24/2 = 12. Sufficient.

(2) Twelve years from now, Josh's age will be exactly 1.5 times Shannon's age.

=> J + 12 = 1.5*(S + 12) => J = 1.5S + 6.

Plugging in the value of S = J/2 in 1.5S + 6, we get J = 1.5J/2 + 6 => J = 24 and S = 24/2 = 12. Sufficient.

The correct answer: D

Hope this helps!

-Jay
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