GMATPrepNow wrote:

A ball is randomly selected from a box containing white balls and black balls only. If the probability of randomly selecting a white ball is 4/5, how many white balls must be added to the box so that the probability of randomly drawing a white ball is 7/8?

(1) The ratio of white balls to black balls is 4:1

(2) There are 27 more white balls than black balls

Target question: How many white balls must be added to the box so that the probability of randomly drawing a white ball is 7/8? Given: The probability of randomly selecting a white ball is 4/5 Let W = number of white balls in the box

Let B = number of black balls in the box

So, the TOTAL number of balls = W+B

If the probability of selecting a white ball = 4/5, then we can write: W/(W+B) = 4/5

Cross multiply to get: 4(W+B) = 5W

Expand: 4W + 4B = 5W

Simplify:

4B = W Statement 1: The ratio of white balls to black balls is 4:1 In other words: W/B = 4/1

Cross multiply to get 4B = W

This MATCHES the given information. In other words, statement 1 provides no new information.

As such, statement 1 is NOT SUFFICIENT

Statement 2: There are 27 more white balls than black balls In other words, W = B + 27

Now take

4B = W and replace W with B+27, to get: 4B = B + 27

Solve to get: B = 9

So, there are presently 9 blacks in the box, which means there are 36 white balls in the box.

Now that we know exactly how many white and black balls are in the box, we can just keep add white balls to the box until P(selecting a white ball) = 7/8

So, we COULD answer the t

arget question with certainty.

As such, statement 2 is SUFFICIENT

ASIDE: For "fun," let's determine how many white balls we need to add.

We presenty have 36 white balls and 9 black balls for a total of 45 balls.

Let's add x white balls to the box

So, 36+x = the new number of white balls in the box

And 45+x = TOTAL number of balls in the box

We want P(white ball) = 7/8

We can write: (36+x)/(45+x) = 7/8

Cross multiply to get: 8(36+x) = 7(45+x)

Expand: 288 + 8x = 315 + 7x

Solve: x = 27

So, we must add 27 white balls to the box so that P(white ball) = 7/8

Answer: B

Cheers,

Brent

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Brent Hanneson – Founder of gmatprepnow.com