GMAT Official Guide 2019 Each of the 256 solid-colored

[BTGmoderatorDC]

Each of the 256 solid-colored marbles in a box is either blue, green, or purple. What is the ratio of the number of blue marbles to the number of purple marbles in the box?

(1) The number of green marbles in the box is 4 times the number of blue marbles in the box.
(2) There are 192 green marbles in the box.

[Jay@ManhattanReview]

Each of the 256 solid-colored marbles in a box is either blue, green, or purple. What is the ratio of the number of blue marbles to the number of purple marbles in the box?

(1) The number of green marbles in the box is 4 times the number of blue marbles in the box.
(2) There are 192 green marbles in the box.

Given: There are a total of 256 blue, green, or purple marbles.

Say the number of blue marbles = b, the number of green marbles = g, and the number of purple marbles = p.

We have to determine the ratio of the value of b/p.

Let's take each statement one by one.

(1) The number of green marbles in the box is 4 times the number of blue marbles in the box.

=> g = 4b. Can't get the value of b/p. Insufficient.

(2) There are 192 green marbles in the box.

=> g = 192. Can't get the value of b/p. Insufficient.

(1) and (2) together

We know that g = 192 and g = 4b; thus, b = g/4 = 192/4 = 48

Since g + p + b = 256, we get p = 256 - 92 - 48 = 16

Thus, b/p = 48/16 = 3 : 1. Sufficient.

The correct answer: C

Hope this helps!

-Jay
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[Scott@TargetTestPrep]

Each of the 256 solid-colored marbles in a box is either blue, green, or purple. What is the ratio of the number of blue marbles to the number of purple marbles in the box?

(1) The number of green marbles in the box is 4 times the number of blue marbles in the box.
(2) There are 192 green marbles in the box.

Solution:

Question Stem Analysis:

We need to determine the ratio of the number of blue marbles to the number of purple marbles in a box, given that the box contains 256 solid-colored marbles that are either blue, green, or purple. We can let the number of blue, green, and purple marbles be b, g, and p, respectively. So we can create the equation b + g + p = 256, and we need to determine the value of b/p.

Statement One Alone:

With the information in statement one, we can create the equation:

g = 4b

Recall that we also have the equation b + g + p = 256. Substituting 4b for g, we have:

b + 4b + p = 256

5b + p = 256

We see that we can’t determine the value of either b or p; thus, we can’t determine the value of b/p. Statement one alone is not sufficient.

Statement Two Alone:

With the information in statement two, we can create the equation:

g = 192

Recall that we also have the equation b + g + p = 256. Substituting 4b for g, we have:

b + 192 + p = 256

b + p = 64

Again, we see that we can’t determine the value of either b or p; thus, we can’t determine the value of b/p. Statement two alone is not sufficient.


Statements One and Two Together:

With the two statements, we see that:

5b + p = 256

and

b + p = 64

With both equations, we see that we can determine both values of b and p and hence the value of b/p. Both statements together are sufficient.

Answer: C