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

VERITAS PREP OFFICIAL SOLUTION

Correct Answer: D

Let S = Shannon's age and J = Josh's age. From the question stem we know that 2S = J. Statement (1) yields the following equation: (J - 6 )= (3) (S - 6). This becomes J - 6 = 3S - 18, which yields J = 3S - 12. When combined with the equation (2S = J) given in the question stem, we have two variables and two unique equations; therefore, statement (1) alone is sufficient. Statement 2 also provides a second unique equation: (J + 12) = (1.5) (S + 12), which becomes J = 1.5S + 6.

Thus, statement (2) alone is also sufficient. Since each statement alone is sufficient, the correct answer is D.

given 2s=j from stmt 1) j-6=3(s-6) find the values sufficient.
stmt 2) j+12=1.5(s+6) slove. Hence ans D

Target question: What is Shannon's age?

Given: Shannon's age is exactly half of Josh's age
In other words, Josh is CURRENTLY 2 times as old as Shannon.
So, if we let x = Shannon's CURRENT age,...
...then 2x = Josh's CURRENT age

Statement 1: Six years ago Josh's age was exactly three times Shannon's age.
x - 6 = Shannon's age SIX YEARS AGO
And 2x - 6 = Josh's age SIX YEARS AGO
SIX YEARS AGO, Josh's age was exactly three times Shannon's age
We can write: 2x - 6 = 3(x - 6)
Expand: 2x - 6 = 3x - 18
Solve..... x = 12
The target question is Shannon's CURRENT age is 12
Since we can answer the target question with certainty, statement 1 is SUFFICIENT

Statement 2: Twelve years from now, Josh's age will be exactly 1.5 times Shannon's age.
x + 12 = Shannon's age TWELVE YEARS FROM NOW
And 2x + 12 = Josh's age TWELVE YEARS FROM NOW
TWELVE YEARS FROM NOW, Josh's age will be exactly 1.5 times Shannon's age
We can write: 2x + 12 = 1.5(x + 12)
Expand: 2x + 12 = 1.5x + 18
Solve..... x = 12
The target question is Shannon's CURRENT age is 12
Since we can answer the target question with certainty, statement 2 is SUFFICIENT

Answer: D

Cheers,
Brent

Given: Shannon's age is exactly half of Josh's age,

Asked: What is Shannon's age?

Let Shannon's age be x => Josh's age = 2x

(1) Six years ago Josh's age was exactly three times Shannon's age.
2x - 6 = 3 (x-6) = 3x - 18
x = 12
Shannon's age is 12.
SUFFICIENT


(2) Twelve years from now, Josh's age will be exactly 1.5 times Shannon's age
2x+12 = 1.5 (x+12) = 1.5x + 18
.5x = 6
x = 12
Shannon's age is 12.
SUFFICIENT

IMO D

Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.