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

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

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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D

unitary method
3/2 inch is raised by 12 marbles

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

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

Answer: D

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 .

MAGOOSH OFFICIAL SOLUTION:

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Answer = D = 22

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

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.

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:

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

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

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

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


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


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


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

Regards,
Fabio.
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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
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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