A jar contains only marbles of three different colors: red, green, and

Question

A jar contains only marbles of three different colors: red, green, and yellow. The red and green marbles are in a ratio of 2:5, and the yellow and red marbles are in a ratio of 5:6. Which of the following could be the total number of marbles?

I. 24
II. 52
III. 182

A. I only
B. II only
C. III only
D. II and III only
E. I, II and III

Show Answer

Official Answer

D

I. 24
II. 52
III. 182

A. I only
B. II only
C. III only
D. II and III only
E. I, II and III

eswarchethu135 · Answer

R:G:Y = 6:15:5

Total marbles are 26x.

52 and 182 can be the only possibilities. As 'x' should be an integer 24 cannot be the total number of marbles.

OPTION:  D

Pooja132 · Answer

any other explanation?

rajatchopra1994 · Answer

Explanation: As we know R/G=2/5 ; Y/R=5/6 From above we know: 6Y=5R=2G=X (Let) X/2 + X/5 + X/6 = (should be eqaul to Option A,B,C . So that X value should be integer) 26X/30= 24 X Not having Integer Value (not Possible) 26X/30=52 Possible. X is integer. 26X/30=182 Possible, X is integer. IMO-D

Please give kudos, if you find my explanation Good Enough

Ratanp · Answer

hi Im having difficulty understnading, i did it this way

Y : R : G
 2 : 5
5 : 6

and its coming 52, but are are we getting both 52 and 182?

avungp · Answer

Since Red is the common marble, I took LCM of 2 and 6 = 12

Therefore, R/G = 2x6/5x6 and Y/R = 5x2/6x2 (Multiply to get the LCM)

After Multiplication, Red = 12, Yellow = 10 and Green = 30

(12+10+30) = 52 (II is Possible)
(12+10+30) x 3.5 = 182 (III is Possible)

I is not possible because no multiple of the Ratio is equal to 24

Answer: D

suntnon · Answer

This is how I did it.

R/G = 2/5 and Y/R = 5/6

Cross multiplying, 5R + 2G + 6Y = 13X (X being a new common variable).

13X = 52
X = 4 (Satisfies)

13X = 182
X = 14 (Satisfies)

Answer D. II and III

luisdicampo · Answer

Deconstructing the Question  
We have marbles: Red (R), Green (G), Yellow (Y).
Given:
 R:G = 2:5 
The statement "yellow and red marbles are in ratio 5:6" as written means:
  Y:R = 5:6  
(Note: if it was meant to be the opposite,  R:Y=5:6 , the result changes.)

We need which totals could work:
I. 24 II. 52 III. 182

Step-by-step  
 Using the ratio as written:    Y:R=5:6

From  R:G=2:5 , let:
 R=2k,\ G=5k

From  Y:R=5:6 :
 Y=\frac{5}{6}R=\frac{5}{6}(2k)=\frac{5}{3}k 
So  k  must be a multiple of 3:  k=3t .

Then:
 R=6t,\ G=15t,\ Y=5t 
Total:
 T=6t+15t+5t=26t 
So  T  must be a multiple of  26 .

Check options:
24 = not multiple of 26 
52 =  26\cdot 2  ✓ 
182 =  26\cdot 7  ✓

Answer: D (II and III only)

If the ratio was actually reversed (R:Y=5:6):  
Then total would be  47t , and none of 24, 52, 182 is a multiple of 47.

A jar contains only marbles of three different colors: red, green, and

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