----------# of --------% blue
---------marbles
Bag P 37 10.8%
Bag Q X 66.7%
Bag R 32 50.0%
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
B
OG Marbles in Bags Q
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There are a total of 37 + X + 32 = 69 + X number of marbles; and out of them 1/3 of (69 + X) = (69 + X)/3 are blue.AbeNeedsAnswers wrote:----------# of --------% blue
---------marbles
Bag P 37 10.8%
Bag Q X 66.7%
Bag R 32 50.0%
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
B
Individually, the number of blue marbles in each bag is given by...
Bag P: 37 x 10.8%.
It' calculation is challenging without a calculator; however, we can get this.
We see that 10% of 37 = 3.7 and 11% of 37 = 3.7 + 0.37 = 4.07; also 10.8% lies between 10% and 11%, thus the value of 10.8% of 37 would lie between 3.7 and 4.07. Since the number of blue marbles is a positive integer and only one integer, 4, lies between 3.7 and 4.07, the avlue of 10.8% of 37 = 4.
Bag Q: X x 66.7% = X*(2/3) = 2X/3; 66.67% is a popular figure and one must remember that it is equal to 2/3.
Bag R : 32 x 50.0% = 32*1/2 = 16
Thus, we have,
4 + 2X/3 + 16 = (69 + X)/3
2X/3 + 20 = 69/3 + X/3
2X/3 - X/3 = 23 - 20
X/3 = 3
[spoiler]X = 9.[/spoiler]
The correct answer: B
Hope this helps!
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Hi Abe Needs Answers,
This question involves a particular Number Property that you can use to eliminate Answers; combined with TESTing THE ANSWERS, you can solve this problem with just a bit of arithmetic.
From the table, we know that the total number of marbles is 37 + X + 32 = (69 + X) marbles. The prompt tells us that exactly 1/3 of the total marbles are blue, so (69+X) MUST be a multiple of 3.
69 is a multiple of 3; since we're adding X to 69 and ending up with a multiple of 3, then X must ALSO be a multiple of 3. Eliminate Answer A, D and E.
From here, we can TEST THE ANSWERS. Let's TEST...
Answer B: 9
IF... X = 9
Bag P = (about 10.8%) of 37 = 4 blue marbles
Bag Q = (about 66.7%) of 9 = 6 blue marbles
Bag R = (50%) of 32 = 16 blue marbles
Total Blues = 26
Total Marbles = 78
26/78 = 1/3. This is an exact match for what we were told, so this MUST be the answer.
Final Answer: B
GMAT assassins aren't born, they're made,
Rich
This question involves a particular Number Property that you can use to eliminate Answers; combined with TESTing THE ANSWERS, you can solve this problem with just a bit of arithmetic.
From the table, we know that the total number of marbles is 37 + X + 32 = (69 + X) marbles. The prompt tells us that exactly 1/3 of the total marbles are blue, so (69+X) MUST be a multiple of 3.
69 is a multiple of 3; since we're adding X to 69 and ending up with a multiple of 3, then X must ALSO be a multiple of 3. Eliminate Answer A, D and E.
From here, we can TEST THE ANSWERS. Let's TEST...
Answer B: 9
IF... X = 9
Bag P = (about 10.8%) of 37 = 4 blue marbles
Bag Q = (about 66.7%) of 9 = 6 blue marbles
Bag R = (50%) of 32 = 16 blue marbles
Total Blues = 26
Total Marbles = 78
26/78 = 1/3. This is an exact match for what we were told, so this MUST be the answer.
Final Answer: B
GMAT assassins aren't born, they're made,
Rich
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We know that
(.108*37 + (2/3)x + .5*32)/ (37 + 32 + x) = 1/3
Assuming that .108 is rounded and treating .108*37 as 4, this gives us
(4 + (2/3)x + 16)/(69 + x) = 1/3
From here, crossmultiply and solve:
3 * (20 + (2/3)x) = 69 + x
60 + 2x = 69 + x
x = 9
(.108*37 + (2/3)x + .5*32)/ (37 + 32 + x) = 1/3
Assuming that .108 is rounded and treating .108*37 as 4, this gives us
(4 + (2/3)x + 16)/(69 + x) = 1/3
From here, crossmultiply and solve:
3 * (20 + (2/3)x) = 69 + x
60 + 2x = 69 + x
x = 9
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We are given a table with the following information:AbeNeedsAnswers wrote:----------# of --------% blue
---------marbles
Bag P 37 10.8%
Bag Q X 66.7%
Bag R 32 50.0%
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
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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