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

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

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New post 20 Mar 2015, 07:38
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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.

\(\frac{12 marbles}{1.5 inches} = \frac{x marbles}{2.75 inches}\)

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

Answer: D

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New post 20 Mar 2015, 08:08
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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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New post 20 Mar 2015, 11:10
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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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New post 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

Answer: D

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

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New post 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 ,
\(\frac{12 * 2}{3} = \frac{4*X}{11}\)
Answer 22 .
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Re: When 12 marbles are added to a rectangular aquarium, the water in the [#permalink]

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New post 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
Aqua_Marbles.png [ 20.21 KiB | Viewed 1722 times ]

_________________

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Collection of Questions:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


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

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New post 25 Mar 2015, 02:28
Answer = D = 22

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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New post 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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