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A jar contains marbles of 3 colors
[#permalink]
Updated on: 28 Dec 2017, 10:45

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Question Stats:

A jar contains only marbles of three different colors : red,green and yellow.The red and green marbles are in the 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?

- (A). 13

- (B). 24

- (C). 52

- (D). 90

- (E). 134

- (F). 182

Show: :: OA

C,F

Re: A jar contains marbles of 3 colors
[#permalink]
27 Aug 2016, 01:26

2

Suppose:

R = Red marbles in jar

G = Green marbles in jar

Y = Yellow marbles in jar

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

=> (R/G) * (Y/R) = (2/5) *(5/6)

=> Y/G = 1/3

We can write above ratios as

G:R = 5:2 => G:R = 15:6 ... 1

R:Y = 6:5 ... 2

=> G:R:Y = 15:6:5

Now Total number of marbles = T = Gx+Rx+Yx = 15x+6x+5x = 26x

So total number of marbles in the jar should be any multiple of 26.In given options C and F are the values which are factors of 26.

So answers are C and F

R = Red marbles in jar

G = Green marbles in jar

Y = Yellow marbles in jar

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

=> (R/G) * (Y/R) = (2/5) *(5/6)

=> Y/G = 1/3

We can write above ratios as

G:R = 5:2 => G:R = 15:6 ... 1

R:Y = 6:5 ... 2

=> G:R:Y = 15:6:5

Now Total number of marbles = T = Gx+Rx+Yx = 15x+6x+5x = 26x

So total number of marbles in the jar should be any multiple of 26.In given options C and F are the values which are factors of 26.

So answers are C and F

A jar contains marbles of 3 colors
[#permalink]
29 Aug 2016, 14:48

3

Expert Reply

yasir9909 wrote:

A jar contains only marbles of three different colors : red,green and yellow.The red and green marbles are in the 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?

- (A). 13

- (B). 24

- (C). 52

- (D). 90

- (E). 134

- (F). 182

Show: :: OA

C,F

Our goal here is to COMBINE both ratios: R:G = 2:5 and Y:R = 5:6

Since both ratios have a number of RED marbles, we'll use this value to combine the ratios.

To do so, we need to rewrite one ratio (or possibly both ratios) as an equivalent ratio, so that the resulting ratio shares a RED value with the other given ratio.

So, take the first ratio of R:G (2:5) and multiply both quantities by 3 to get: R:G = 6:15

So, we now have the ratios Y:R = 5:6 AND R:G = 6:15

We can COMBINE them to get Y:R:G = 5:6:15

So, we could have 5 yellows, 6 reds, and 15 greens for a total of 26 marbles

Or, we could have 10 yellows, 12 reds, and 30 greens for a total of 52 marbles

Or we could have 15 yellows, 18 reds, and 45 greens for a total of 78 marbles

etc.

As you can see, the totals are all multiples of 26.

Since answer choices A and F are the ONLY multiples of 26, they are the correct answers.

Answer: A, F

_________________

Re: A jar contains marbles of 3 colors
[#permalink]
06 Sep 2017, 05:36

I think your answers should be combined. Given the fact that the ratio is 5:6:15, the sum of 5+6+15 = 26. Thus, we should look for multiples of 26 that are 13 = 26*1/2, 52 = 26*2 and 182 = 26*7. To conclude the answers are A, C and F.

Am I right?

Am I right?

Re: A jar contains marbles of 3 colors
[#permalink]
18 Sep 2017, 02:01

IlCreatore wrote:

I think your answers should be combined. Given the fact that the ratio is 5:6:15, the sum of 5+6+15 = 26. Thus, we should look for multiples of 26 that are 13 = 26*1/2, 52 = 26*2 and 182 = 26*7. To conclude the answers are A, C and F.

Am I right?

Am I right?

Thinking about this question again, I found out that the right answers are those of yasir because 13 is not a multiple of 26 since a multiple is defined as an integer number that is product of two integers and 1/2 is not an integer.

Re: A jar contains marbles of 3 colors
[#permalink]
18 Sep 2017, 14:00

1

Expert Reply

IlCreatore wrote:

I think your answers should be combined. Given the fact that the ratio is 5:6:15, the sum of 5+6+15 = 26. Thus, we should look for multiples of 26 that are 13 = 26*1/2, 52 = 26*2 and 182 = 26*7. To conclude the answers are A, C and F.

Am I right?

Am I right?

Answer choice A is not correct.

13 is not a multiple of 26.

Multiples of 26 are in the form 26k, where k is an INTEGER

So, the multiples of 26 are as follows: {. . ., -78, -52, -26, 0, 26, 52, 78, 104, . . . }

Cheers,

Brent

_________________

Re: A jar contains marbles of 3 colors
[#permalink]
25 Sep 2017, 04:37

GreenlightTestPrep wrote:

IlCreatore wrote:

Am I right?

Answer choice A is not correct.

13 is not a multiple of 26.

Multiples of 26 are in the form 26k, where k is an INTEGER

So, the multiples of 26 are as follows: {. . ., -78, -52, -26, 0, 26, 52, 78, 104, . . . }

Cheers,

Brent

Exactly as I wrote in my second comment. Your previous answer was wrong, yasir was right.

Re: A jar contains marbles of 3 colors
[#permalink]
04 Sep 2018, 18:40

1

here it is given - red : green => 2:5 ---(i)

Yellow : red => 5:6 ---(ii)

from (i) we get => red : green => 2:5 => 6:15

so green:red:yellow => 15:6:5

we get total number = 15x + 6x + 5x = 26x

so the answer will be multiple of 26. ans : C, F

Yellow : red => 5:6 ---(ii)

from (i) we get => red : green => 2:5 => 6:15

so green:red:yellow => 15:6:5

we get total number = 15x + 6x + 5x = 26x

so the answer will be multiple of 26. ans : C, F

Re: A jar contains marbles of 3 colors
[#permalink]
16 Feb 2021, 06:18

Hello from the GRE Prep Club BumpBot!

Thanks to another GRE Prep Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

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Thanks to another GRE Prep Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.

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