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If 1/3 of the total number of marbles in the three bags listed in the

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If 1/3 of the total number of marbles in the three bags listed in the table above are blue, how many marbles are there in bag Q?

A) 5
B) 9
C) 12
D) 23
E) 46

[Reveal] Spoiler:
Attachment:
2016-06-17_1618.png
2016-06-17_1618.png [ 22.59 KiB | Viewed 11413 times ]
[Reveal] Spoiler: OA

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Re: If 1/3 of the total number of marbles in the three bags listed in the [#permalink]

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Bag P : 10.8% of 37 = 4
Bag Q : 66.7% of x = 2x/3
Bag R : 50% of 32 = 16.

Given, 4 + 2x/3 + 16 = 1/3 ( 37+x+32) => x = 9. Hence B.
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Re: If 1/3 of the total number of marbles in the three bags listed in the [#permalink]

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New post 20 Aug 2016, 09:37
FacelessMan wrote:
Bag P : 10.8% of 37 = 4
Bag Q : 66.7% of x = 2x/3
Bag R : 50% of 32 = 16.

Given, 4 + 2x/3 + 16 = 1/3 ( 37+x+32) => x = 9. Hence B.


I have approximated 10.8% as 1/9, which is 11.1%
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If 1/3 of the total number of marbles in the three bags listed in the [#permalink]

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This might look like it contains hard calculations, but the thing to notice here is that the number of balls are always going to be integers.

So, 10.8% of 37 will be 4, we know 50% of x is 32 and we can keep 66.7% as 2/3rds. Once you do this, the question can be solved to arrive at ~9 quickly.
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Re: If 1/3 of the total number of marbles in the three bags listed in the [#permalink]

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If 1/3 of the total number of marbles in the three bags listed in the table above are blue, how many marbles are there in bag Q?

A) 5
B) 9
C) 12
D) 23
E) 46

Total has to be multiple of 3 since 1/3rd of them are blue and 1st and 3rd bag have total 69 marbles so (69 + x)/3 is blue total hence x also must be divisible by 3

hence narrow down to B) 9 or C) 12

66.67 % is nothing but 2/3 rd (ie 33.33 * 2 ie 1/3 * 2)

so if x is 9 then blue marbles in 2nd bag is 6 (2/3rd of 9 = 6)
or if x is 12 then blue marbles in 3rd bag is 8 (2/3rd of 12 = 8)

do that math : if x = 9 then total = 69 + 9 = 78
and total blue = 16 + 4 + 6 = 26
26/78 = 1/3 -----> fits (most likely that B is the ans)

cross check
if x = 12 then total = 81
total blue = 28
28/81 != 1/3 hence (B)
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Re: If 1/3 of the total number of marbles in the three bags listed in the [#permalink]

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New post 13 Jun 2017, 04:45
manlog wrote:
I have approximated 10.8% as 1/9, which is 11.1%


10.8% of 37 -> 10% of 37 = 3.7.

3.7 is a little low and the number of balls must be an integer; can round up to 4.
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Re: If 1/3 of the total number of marbles in the three bags listed in the [#permalink]

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New post 19 Dec 2017, 07:42
Bunuel wrote:
Image
If 1/3 of the total number of marbles in the three bags listed in the table above are blue, how many marbles are there in bag Q?

A) 5
B) 9
C) 12
D) 23
E) 46

[Reveal] Spoiler:
Attachment:
2016-06-17_1618.png


We are given a table with the following information:

Bag P has 37 marbles and 10.8% of those marbles are blue. So there are 0.108(37) = 3.996, or 4, blue marbles in bag P.

Bag Q has X marble and 66.7% of those marbles are blue. Recall that the fraction 2/3 is approximately 66.7%, so there are (2/3)X blue marbles in bag Q.

Bag R has 32 marbles and 50% of those marbles are blue. So, there are 0.5(32) = 16 blue marbles in bag R.

We are also given that 1/3 of the total marbles in the 3 bags are blue. Thus, we can create the following equation:

1/3(37 + X + 32) = 4 + (2/3)X + 16

Multiplying the equation by 3, we have:

37 + X + 32 = 12 + 2X + 48

X + 69 = 2X + 60

X = 9

There are 9 marbles in bag Q.

Answer: B
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Re: If 1/3 of the total number of marbles in the three bags listed in the [#permalink]

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New post 22 Apr 2018, 10:44
Bunuel wrote:
Image
If 1/3 of the total number of marbles in the three bags listed in the table above are blue, how many marbles are there in bag Q?

A) 5
B) 9
C) 12
D) 23
E) 46

[Reveal] Spoiler:
Attachment:
2016-06-17_1618.png

No. of blue marbles in each bag is
Bag P: 10.8% of 37 = 4
Bag Q:66.7% of X = 2/3 X
Bag R: 50% of 32 = 16

Total Blue marbles = 4 + 2/3 X + 16 = 20 + 2/3 X

Also Total marbles count = 37 + X + 32 = 69 + X

So, 1/3 (69+ X ) = 20 + 2/3 X
23 + 1/3 X = 20 + 2/3 X
1/3 X = 3
X = 9

Answer B
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Re: If 1/3 of the total number of marbles in the three bags listed in the   [#permalink] 22 Apr 2018, 10:44
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