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

Question

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 .

GSBae · Answer

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

chetan2u · Answer

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..

hsbinfy · Answer

D

unitary method
3/2 inch is raised by 12 marbles

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

peachfuzz · Answer

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

Answer: D

Lucky2783 · Answer

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 .

Bunuel · Answer

MAGOOSH OFFICIAL SOLUTION: Aqua_Marbles.png

PareshGmat · Answer

Answer = D = 22

Marbles required  = \frac{11}{4} * 12 * \frac{2}{3} = 22

SavageBrother · Answer

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.

EMPOWERgmatRichC · Answer

Hi All,

We're told that when 12 marbles are added to a rectangular aquarium, the water in the aquarium rises 1 1/2 inches. We're asked how many marbles must be added to the aquarium in total to raise the water 2 3/4 inches. This question is ultimately about ratios, so you can approach the math in a variety of different ways.

To start, I'm going to convert the mixed fractions into decimals: 
12 marbles --> raises the water 1.5 inches 
X marbles --> raises the water 2.75 inches

2.75 - 1.5 = 1.25 additional inches needed to be raised

We know that 12 marbles raises the water 1.5 inches, so we can set up a ratio to determine how many marbles would be needed to raise the water an additional 1.25 inches...

1.5/12 = 1.25/X 
1.5X = 15 
X = 15/1.5 = 10 additional marbles needed.

Thus, we need 12+10 = 22 total marbles.

Final Answer:  D

GMAT assassins aren't born, they're made, 
Rich

fskilnik · Answer

{\rm{aqua}}\,\,{\rm{dimensions}}\,\,{\rm{:}}\,\,a,b,h\,\,\,\, \Rightarrow \,\,\,\,\,{\rm{Volume}}\left( {{\rm{aqua}}} \right) = abh

M = {\rm{Volume}}\left( {{\rm{marble}}} \right)

? = x\,\,\,\,\left( {\# \,\,{\rm{marbles}}} \right)

\left\{ \matrix{
 abh\,\,{\rm{ + }}\,\,{\rm{12}} \cdot M = \underbrace {ab}_{{\rm{i}}{{\rm{n}}^2}}\,\, \cdot \,\,\underbrace {\,\left( {{\rm{h}} + 1{1 \over 2}} \right)}_{{\rm{in}}}\,\,\,\,\, \Rightarrow \,\,\,\,\,12M = {3 \over 2}abh \hfill \cr 
 abh\,\,{\rm{ + }}\,\,x \cdot M = \underbrace {ab}_{{\rm{i}}{{\rm{n}}^2}}\,\, \cdot \,\,\underbrace {\,\left( {{\rm{h}} + 2{3 \over 4}} \right)}_{{\rm{in}}}\,\,\,\,\, \Rightarrow \,\,\,\,\,xM = {{11} \over 4}abh \hfill \cr} \right.

xM = \left  = {{11} \over 4}\left( {{2 \over 3} \cdot 12M} \right)\,\,\,\,\,\, \Rightarrow \,\,\,\,\,? = x = 22

We follow the notations and rationale taught in the  GMATH  method.

Regards, 
Fabio.

ScottTargetTestPrep · Answer

We can create the proportion:

12/(3/2) = x/(11/4)

24/3 = 4x/11

24(11) = 12x

2(11) = x

22 = x

Alternate Solution:

We observe that the addition of each marble raises the water (1 1/2)/12 = (3/2)/12 = 1/8 inches. Thus, to raise the water 2 3/4 = 11/4 inches, we need (11/4)/(1/8) = (11/4) x (8/1) = 11 x 2 = 22 marbles.

Answer: D

BrentGMATPrepNow · Answer

We can solve this question using  equivalent ratios

We'll use the ratio:  #of marbles / rise (in inches)

Let  x  = the number of marbles required to raise the water 2 3/4 inches (aka 2.75 inches).

We can write:  12 / 1.5  =  x / 2.75

Cross multiply to get: (1.5)(x) = (12)(2.75) 
Simplify: 1.5x = 33
Solve: x = 33/1.5 = 22

Answer: D

Cheers,
Brent

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