Each of the 256 solid-colored marbles in a box is either blue, green,

B= blue, G= green, P= purple

B+G+P = 256

Statement 1: G=4B
B+4B+P = 256 ---->P = 256-5B
\(\frac{B}{256-5B}\) Not sufficient

Statement 2: G =192
B+P = 64
\(\frac{64-P}{P}\) Not sufficient

Together,
P = 256-5B ---> Equation 1
B = 64-P ---> Equation 2
Two equations and two unknowns ---> Sufficient

Answer: Option C

Video solution by GMATinsight

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

Video solution from Quant Reasoning:
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GMAT Data Sufficiency - Marbles and Ratios

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