Data Sufficiency

BTGmoderatorDC wrote:Brady, Charlie, and Daryl play on the same baseball team. The number of home runs hit by Brady in a particular season is what fraction of the total home runs hit by the three players in that season?

(1) Brady hit 12 home runs in that season.
(2) In that season, the number of home runs hit by Brady was twice the number hit by Charlie and Daryl combined.

OA B

Source: Princeton Review

Given: Brady, Charlie, and Daryl play on the same baseball team.

Target question: The number of home runs hit by Brady in a particular season is what fraction of the total home runs hit by the three players in that season?
This is a good candidate for rephrasing the target question.

Let B = number of home runs that Brady hit
Let C = number of home runs that Charlie hit
Let D = number of home runs that Daryl hit

So, B + C + D = the TOTAL number of home runs hit
So, the fraction of the total home runs that Brady hit = B/(B + C + D)

REPHRASED target question: What is the value of B/(B + C + D)?

Aside: Here's a video with tips on rephrasing the target question: https://www.gmatprepnow.com/module/gmat- ... cy?id=1100

Statement 1: Brady hit 12 home runs in that season.
Since we have no information about the number of home runs that Charlie (C), and Daryl (D) hit, there's no way to answer the REPHRASED target question with certainty.
So, statement 1 is NOT SUFFICIENT

Statement 2: In that season, the number of home runs hit by Brady was twice the number hit by Charlie and Daryl combined.
So, we can write: B = 2(C + D) = 2C + 2d

Now take B/(B + C + D) and replace B with 2C + 2d to get: (2C + 2D)/(2C + 2D + C + D)
Simplify to get: (2C + 2D)/(3C + 3D)
Factor top and bottom to get: 2(C + D)/3(C + D)
Simplify to get: 2/3
So, the answer to the REPHRASED target question is B/(B + C + D) = 2/3
Since we can answer the REPHRASED target question with certainty, statement 2 is SUFFICIENT

Answer: B

Cheers,
Brent