Brent@GMATPrepNow wrote:A box contains black balls and white balls only. If a ball is randomly selected from the box, what is the probability that the selected ball is black?
(1) There are 31 more black balls than white balls in the box
(2) If 19 black balls were removed from the box, the probability of selecting a black ball would be 0.6
Target question: What is the probability that the selected ball is black?
Given: A box contains black balls and white balls only.
Let B = number of black balls in the box
Let W = number of white balls in the box
This means B+W = TOTAL number of balls in the box
So, P(selected ball is black) =
B/(B+W)
Statement 1: There are 31 more black balls than white balls in the box
We can write: B = W + 31
Is this enough information to determine the value of
B/(B+W)?
No.
Replace B with W + 31 to get:
B/(B+W) = (W + 31)/(W + 31 + W)
= (W + 31)/(2W + 31)
Notice that, as we change the value of W, the probability changes.
For example, when W = 1, we get: (W + 31)/(2W + 31) = 32/33
When W = 2, we get: (W + 31)/(2W + 31) = 33/35
etc.
Since we cannot answer the
target question with certainty, statement 1 is NOT SUFFICIENT
Statement 2: If 19 black balls were removed from the box, the probability of selecting a black ball would be 0.6
If 19 black balls were removed from the box, then B - 19 = new number of black balls
And the TOTAL number of balls would be B + W - 19
So, we can write: (B - 19)/(B + W - 19) = 0.6
Or we can write: we can write: (B - 19)/(B + W - 19) = 3/5
Is this enough information to determine the value of
B/(B+W)?
No.
Cross multiply to get: 5(B - 19) = 3(B + W - 19)
Expand: 5B - 95 = 3B + 3W - 57
Rearrange to get: 2B - 3W = 38
As you might see, we cannot use this information to determine the value of
B/(B+W)
Since we cannot answer the
target question with certainty, statement 2 is NOT SUFFICIENT
Statements 1 and 2 combined
Statement 1 tells us that B = W + 31
Statement 2 tells us that 2B - 3W = 38
So, we have two different equations with 2 variables.
Since we COULD solve this system of equations for B and W, we COULD determine the value of
B/(B+W)
Since we COULD answer the
target question with certainty, the combined statements are SUFFICIENT
Answer:
C
Cheers,
Brent
