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Manager Joined: 13 Aug 2016
Posts: 77
GRE 1: Q158 V154 Followers: 0

Kudos [?]: 39 , given: 21

A jar contains marbles of 3 colors [#permalink] 00:00

Question Stats: 42% (01:39) correct 57% (01:37) wrong based on 21 sessions
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

[Reveal] Spoiler: OA
C,F
[Reveal] Spoiler: OA

Last edited by Carcass on 28 Dec 2017, 10:45, edited 3 times in total.
Edited by Carcass Manager Joined: 13 Aug 2016
Posts: 77
GRE 1: Q158 V154 Followers: 0

Kudos [?]: 39  , given: 21

Re: A jar contains marbles of 3 colors [#permalink]
2
KUDOS
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 GRE Instructor Joined: 10 Apr 2015
Posts: 1995
Followers: 60

Kudos [?]: 1811  , given: 9

Re: A jar contains marbles of 3 colors [#permalink]
1
KUDOS
Expert's post
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

[Reveal] Spoiler: 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.

[Reveal] Spoiler:
A, F

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_________________

Brent Hanneson – Creator of greenlighttestprep.com Director Joined: 03 Sep 2017
Posts: 520
Followers: 1

Kudos [?]: 356 , given: 66

Re: A jar contains marbles of 3 colors [#permalink]
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?
Director Joined: 03 Sep 2017
Posts: 520
Followers: 1

Kudos [?]: 356 , given: 66

Re: A jar contains marbles of 3 colors [#permalink]
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?

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. GRE Instructor Joined: 10 Apr 2015
Posts: 1995
Followers: 60

Kudos [?]: 1811  , given: 9

Re: A jar contains marbles of 3 colors [#permalink]
1
KUDOS
Expert's post
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?

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
_________________

Brent Hanneson – Creator of greenlighttestprep.com Director Joined: 03 Sep 2017
Posts: 520
Followers: 1

Kudos [?]: 356 , given: 66

Re: A jar contains marbles of 3 colors [#permalink]
GreenlightTestPrep wrote:
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?

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. Intern Joined: 10 Jun 2018
Posts: 32
Followers: 0

Kudos [?]: 16  , given: 4

Re: A jar contains marbles of 3 colors [#permalink]
1
KUDOS
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 Re: A jar contains marbles of 3 colors   [#permalink] 04 Sep 2018, 18:40
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