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There are 4 bottles with the same number balls

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by VJesus12 » Tue Jul 17, 2018 1:12 am
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There are 4 bottles with the same number balls m respectively. If balls from only the 1-st bottle are moved to the other 3 bottles and finally the ratio of the numbers of balls in the bottles is 1 : 6 : 5 : 4, what fraction does the moved balls represent in terms of m?

A. m/4
B. m/2
C. 3m/4
D. m
E. 4m/5

The OA is the option C.

I am really confused with this PS question. I would like to see how to solve it. Please, anyone, help me here. Thanks in advance.
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by GMATGuruNY » Tue Jul 17, 2018 1:46 am
VJesus12 wrote:There are 4 bottles with the same number balls m respectively. If balls from only the 1-st bottle are moved to the other 3 bottles and finally the ratio of the numbers of balls in the bottles is 1 : 6 : 5 : 4, what fraction does the moved balls represent in terms of m?

A. m/4
B. m/2
C. 3m/4
D. m
E. 4m/5
Let the total number of balls = the sum of the parts of the final ratio = 1+6+5+4 = 16.
Since there are 16 balls in total, and each of the 4 bottles begins with m balls, m=4.

Since the number of balls in the first bottle decreases from 4 to 1, the number of balls moved from the first bottle = 4-1 = 3.
Of these 3 balls, 2 are moved to second bottle (increasing the total number of balls in the second bottle to 6), and 1 is moved to the third bottle (increasing the total number of balls in the third bottle to 5).

The question stem asks for the number of moved balls: 3.
The correct answer must yield a value of 3 when m=4.
Only C works:
(3m)/4 = (3*4)/4 = 4.

The correct answer is C.
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by regor60 » Tue Jul 17, 2018 5:20 am
VJesus12 wrote:There are 4 bottles with the same number balls m respectively. If balls from only the 1-st bottle are moved to the other 3 bottles and finally the ratio of the numbers of balls in the bottles is 1 : 6 : 5 : 4, what fraction does the moved balls represent in terms of m?

A. m/4
B. m/2
C. 3m/4
D. m
E. 4m/5

The OA is the option C.

I am really confused with this PS question. I would like to see how to solve it. Please, anyone, help me here. Thanks in advance.
Since each bottle held m balls, there are 4m balls in total.

The first bottle, after moving balls, now holds 1/(1+6+5+4) of all the balls or 1/16 of 4m balls, equals

4m/16 = m/4.

Since the first bottle originally held m balls, the number moved is m-m/4 = [spoiler]C, 3m/4[/spoiler]
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by Scott@TargetTestPrep » Thu Jul 19, 2018 4:21 pm
VJesus12 wrote:There are 4 bottles with the same number balls m respectively. If balls from only the 1-st bottle are moved to the other 3 bottles and finally the ratio of the numbers of balls in the bottles is 1 : 6 : 5 : 4, what fraction does the moved balls represent in terms of m?

A. m/4
B. m/2
C. 3m/4
D. m
E. 4m/5
After the balls have been moved, we can let the balls in the bottles be x, 6x, 5x and 4x, respectively. So there are a total 16x balls. However, originally, each bottle has m balls, so the total number of balls is also 4m. Therefore, we have:

16x = 4m

4x = m

So originally, the 1st bottle had 4x balls. But after balls were removed from it, it has x balls. So 3x balls must have been removed from it. Since m = 4x and the moved balls = 3x, then the moved balls = (3/4)m or 3m/4.

Answer: C

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