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# When 12 marbles are added to a rectangular aquarium, the water in the

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Math Expert
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When 12 marbles are added to a rectangular aquarium, the water in the [#permalink]

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20 Mar 2015, 06:18
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Question Stats:

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When 12 marbles are added to a rectangular aquarium, the water in the aquarium rises 1 1/2 inches. In total, how many marbles must be added to the aquarium to raise the water 2 3/4 inches?

A. 16
B. 18
C. 20
D. 22
E. 24

Kudos for a correct solution.
[Reveal] Spoiler: OA

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Manager
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Re: When 12 marbles are added to a rectangular aquarium, the water in the [#permalink]

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20 Mar 2015, 07:38
1
KUDOS
We know that it takes 12 marbles to gain 1.5 inches. Now we need to find out how many marbles we need to gain 2.75 inches.

$$\frac{12 marbles}{1.5 inches} = \frac{x marbles}{2.75 inches}$$

$$x = \frac{12 * 2.75}{1.5} = \frac{12*\frac{11}{4}}{\frac{3}{2}} = \frac{3*11}{\frac{3}{2}} = \frac{33*2}{3} = 11*2 = 22.$$

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Math Expert
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Re: When 12 marbles are added to a rectangular aquarium, the water in the [#permalink]

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20 Mar 2015, 08:08
1
KUDOS
Expert's post
Bunuel wrote:
When 12 marbles are added to a rectangular aquarium, the water in the aquarium rises 1 1/2 inches. In total, how many marbles must be added to the aquarium to raise the water 2 3/4 inches?

A. 16
B. 18
C. 20
D. 22
E. 24

Kudos for a correct solution.

apart from mathematical equation, the other way is by elimination and estimation...

12marbles-----1 1/2 in...... 24 marbles----3 in

12=4*3marbles-----1 1/2 in=1/2*3
4 marbles----1/2 in...
4*5 marbles----1/2*5=2 1/2..
so ans more than 20 and less than 24...

so ans 22 D..
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Re: When 12 marbles are added to a rectangular aquarium, the water in the [#permalink]

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20 Mar 2015, 11:10
1
KUDOS
D

unitary method
3/2 inch is raised by 12 marbles

so 11/4 inch is raised by 12*(2/3)*(11/4)=22

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Re: When 12 marbles are added to a rectangular aquarium, the water in the [#permalink]

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20 Mar 2015, 19:41
Bunuel wrote:
When 12 marbles are added to a rectangular aquarium, the water in the aquarium rises 1 1/2 inches. In total, how many marbles must be added to the aquarium to raise the water 2 3/4 inches?

A. 16
B. 18
C. 20
D. 22
E. 24

Kudos for a correct solution.

use the ratio method
(12)/(3/2) = x/(11/4)
x=22

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Director
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GMAT 1: 630 Q49 V27
When 12 marbles are added to a rectangular aquarium, the water in the [#permalink]

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20 Mar 2015, 22:10
Bunuel wrote:
When 12 marbles are added to a rectangular aquarium, the water in the aquarium rises 1 1/2 inches. In total, how many marbles must be added to the aquarium to raise the water 2 3/4 inches?

A. 16
B. 18
C. 20
D. 22
E. 24

Kudos for a correct solution.

easy question for a kudo
As the aquarium is rectangular , the rise per marble will be same at each point.
so ,
$$\frac{12 * 2}{3} = \frac{4*X}{11}$$
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Re: When 12 marbles are added to a rectangular aquarium, the water in the [#permalink]

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23 Mar 2015, 04:27
Bunuel wrote:
When 12 marbles are added to a rectangular aquarium, the water in the aquarium rises 1 1/2 inches. In total, how many marbles must be added to the aquarium to raise the water 2 3/4 inches?

A. 16
B. 18
C. 20
D. 22
E. 24

Kudos for a correct solution.

MAGOOSH OFFICIAL SOLUTION:
Attachment:

Aqua_Marbles.png [ 20.21 KiB | Viewed 1722 times ]

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Re: When 12 marbles are added to a rectangular aquarium, the water in the [#permalink]

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25 Mar 2015, 02:28

Marbles required $$= \frac{11}{4} * 12 * \frac{2}{3} = 22$$
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Re: When 12 marbles are added to a rectangular aquarium, the water in the [#permalink]

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01 Apr 2015, 06:12
12 marbles = 1 1/2, 1 1/2 = 3/2

Raise to; 2 3/4 = 11 / 4

3/2 = 6/4

You need to go from 6 / 4 to 11 / 4, which is 5 / 4.

12 marbles = 6 / 4
2 marbles = 1 / 4

you need 5 / 4, 5*marbles is 10 marbles.

10 + 12 marbles = 22 marbles.

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Re: When 12 marbles are added to a rectangular aquarium, the water in the [#permalink]

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22 Dec 2017, 17:55
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Re: When 12 marbles are added to a rectangular aquarium, the water in the   [#permalink] 22 Dec 2017, 17:55
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