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

Question

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.

NEW question from GMAT® Official Guide 2019 
(DS07822)

GURUCHANAKYA · Accepted Answer

B+G+P = 256 
to find B/P = ??

Stat 1 : G/B=4/1 
Insufficient

Stat 2: G=192 ,
therefore B+P = 256-192 = 64,

Combining Stat 1 & 2 ,

we get b= 192/4 = 48 ,
and therefore P = 64-48 = 16

B/P = 48/16 = 3:1

Answer Choice C .

EgmatQuantExpert · Answer

Solution

Given:  
 • Each of the 256 solid-colored marbles in a box is either blue, green, or purple

To find:  
 • The ratio of the number of blue marbles to the number of purple marbles in the box

Analysing Statement 1  
 • As per the information given in statement 1, the number of green marbles in the box is 4 time the number of blue marbles in the box
 o Hence, if blue marbles are x, then green marbles will be 4x
o We do not have any information about the number of marbles of any color

Hence, statement 1 is not sufficient to answer

Analysing Statement 2  
 • As per the information given in statement 2, there are 192 green marbles in the box
 o From this statement, we can say the total number of purple and blue marbles is  (256 – 192) = 64 
o But we can’t find out the individual number of purple and blue marbles

Hence, statement 2 is not sufficient to answer

Combining Both Statements  
If we combine both the statements, we can say:
 • Number of green marbles is 192
• Green marbles are 4 times the number of blue marbles
 o Hence, number of blue marbles =  \frac{192}{4} = 48 
o Therefore, number of purple marbles =  64 – 48 = 16  
• As we know the number of marbles of each color, we can find out the required ratio

Hence, the correct answer is option C.

Answer: C

michael30 · Answer

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

GMATinsight · Answer

Answer: Option C

Video solution by  GMATinsight

https://www.youtube.com/watch?v=U9FpqAw2bxQ

ScottTargetTestPrep · Answer

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

avigutman · Answer

Video solution from Quant Reasoning: Subscribe for more: https://www.youtube.com/QuantReasoning? ... irmation=1 https://www.youtube.com/watch?v=pGDG0B2dRqc

GmatKnightTutor · Answer

GMAT Data Sufficiency - Marbles and Ratios

https://www.youtube.com/watch?v=Q2f1t35B9Ro

bumpbot · Answer

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

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