OG Marbles in Bags Q

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AbeNeedsAnswers: Master | Next Rank: 500 Posts; Posts: 394; Joined: Sun Jul 02, 2017 10:59 amFollowed by: 5 members; Thanked: 1 times

by AbeNeedsAnswers » Wed Jul 19, 2017 10:15 pm

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----------# 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

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Source: Beat The GMAT — Problem Solving | Wed Jul 19, 2017 10:15 pm

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Jay@ManhattanReview: GMAT Instructor; Posts: 3008; Joined: Mon Aug 22, 2016 6:19 amFollowed by: 34 members; Location: Grand Central / New York; Thanked: 470 times

by Jay@ManhattanReview » Wed Jul 19, 2017 11:37 pm

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

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.

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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by [email protected] » Thu Jul 20, 2017 11:47 am

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

Contact Rich at [email protected]

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Matt@VeritasPrep: GMAT Instructor; Posts: 2630; Joined: Wed Sep 12, 2012 3:32 pmFollowed by: 119 members; Location: East Bay all the way; Thanked: 625 times; GMAT Score:780

by Matt@VeritasPrep » Sun Jul 23, 2017 4:03 pm

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

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Jeff@TargetTestPrep: GMAT Instructor; Posts: 1462; Joined: Thu Apr 09, 2015 9:34 amFollowed by: 22 members; Location: New York, NY; Thanked: 39 times

by Jeff@TargetTestPrep » Tue Jul 25, 2017 11:03 am

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

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

Jeffrey Miller
Head of GMAT Instruction
[email protected]

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