GMAT Math : Algebra

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Example Question #351 : Algebra

A factory makes barrels of the same shape but different sizes; the amount of water they hold varies directly as the cube of their height. The four-foot-high barrel holds 20 gallons of water; how much water would the six-foot-high barrel hold?

Possible Answers:

$45\textrm{ gal}$

$67 \frac{1}{2}\textrm{ gal}$

$30\textrm{ gal}$

$64\textrm{ gal}$

$80\textrm{ gal}$

Correct answer:

$67 \frac{1}{2}\textrm{ gal}$

Explanation:

Let be the height of a barrel and be its volume. Since varies directly as the cube of , the variation equation is

$V = k h^{3}$

for some constant of variation .

We find by substituting V = 20, h= 4 from the smaller barrels:

$20 = k \cdot 4^{3}$

$20 = k \cdot 64$

$k = \frac{20 }{64}= \frac{5 }{16}$

Then the variation equation is:

$V = \frac{5 }{16} h^{3}$

Now we can substitute h = 6 to find the volume of the larger barrel:

$V = \frac{5 }{16} \cdot 6^{3} = \frac{5 }{16} \cdot 216 = \frac{5 }{16} \cdot \frac{216}{1} = \frac{5 }{2} \cdot \frac{27}{1} = \frac{135 }{2}= 67 \frac{1 }{2}$

The larger barrel holds $67 \frac{1 }{2}$ gallons.

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Example Question #352 : Algebra

Solve for .

-x-3xy+4>0

Possible Answers:

$x<\frac{-4}{1+3y}$

$x>\frac{-4}{1+3y}$

$x>\frac{4}{1+3y}$

$x<\frac{4}{1+3y}$

Correct answer:

$x<\frac{4}{1+3y}$

Explanation:

$-x-3xy+4>0\Rightarrow 4>x+3xy$

$4>x(1+3y) \Rightarrow \frac{4}{1+3y}>x$

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Example Question #353 : Algebra

To convert Celsius temperature to the equivalent in Fahrenheit temperature , use the formula

$F = \frac{9}{5}C + 32$

To the nearest tenth of a degree, convert $70^{\circ } C$ to degrees Fahrenheit.

Possible Answers:

$158.0 ^{\circ } F$

$94.0 ^{\circ } F$

$183.6 ^{\circ } F$

$68.4 ^{\circ } F$

$21.1 ^{\circ } F$

Correct answer:

$158.0 ^{\circ } F$

Explanation:

$F = \frac{9}{5}C + 32 = \frac{9}{5} \cdot 70 + 32 = 126 + 32 = 158$

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Example Question #351 : Algebra

Solve for :

13+X-Y=2Y

Possible Answers:

X=-16Y

X=10

X=-13+3Y

X=13+-3Y

X=16Y

Correct answer:

X=-13+3Y

Explanation:

13+X-Y=2Y

We need to isolate . Move all other terms to the right hand side of the equation:

13+X-Y-13+Y=2Y-13+Y

Combine like terms:

X=-13+3Y

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Example Question #354 : Algebra

Solve for the value of :

|x-4|=-3x+5

Possible Answers:

$(\frac{9}{4},\frac{1}{2})$

$(\frac{4}{9},\frac{1}{2})$

$(-\frac{9}{4},\frac{1}{2})$

$(\frac{5}{4},\frac{3}{2})$

$(-\frac{1}{2}, \frac{9}{4})$

Correct answer:

$(\frac{9}{4},\frac{1}{2})$

Explanation:

|x-4|=-3x+5

To solve this absolute value equation, we need to set the right side of the equation equal to a positive and negative version in order to calculate the two options for absolute value.

x-4=-3x+5 OR x-4=-(-3x+5)=3x-5

x+3x=5+4 OR x-3x=-5+4

4x=9 OR -2x=-1

$x=\frac{9}{4}$ OR $x=\frac{1}{2}$

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Example Question #355 : Algebra

4-n=5

5m-8=12+3m

You are given the equations above. What is m-n ?

Possible Answers:

Correct answer:

Explanation:

We first solve each of the equations to find and :

4-n=5

-n=5-4

n=-1

5m-8=12+3m

5m-3m=12+8

2m=20

m=10

m-n=10-(-1)=10+1=11

Therefore, m-n=11 .

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Example Question #356 : Algebra

You are given the following equation:

$x=\frac{x-6}{3+x}$

What is the value of $x^{2}+2x+3$ ?

Possible Answers:

Correct answer:

Explanation:

First, we need to solve the provided equation for .

$x=\frac{x-6}{3+x}$

x(3+x)=x-6

$3x+x^{2}=x-6$

$3x+x^{2}-x=-6$

$x^{2}+2x+6=0$

We want to find the value of $x^{2}+2x+3$ . We can put the equation in this form by subtracting from each side:

$x^{2}+2x+6-3=-3$

$x^{2}+2x+3=-3$

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Example Question #353 : Algebra

Solve $\left | 2x+12\right |=20$ .

Possible Answers:

x=8 or x=-16

x=4 or x=-16

x=-16

x=4

x=8

Correct answer:

x=4 or x=-16

Explanation:

Since we are solving an absolute value equation, $\left | 2x+12\right |=20$ , we must solve for both potential values of the equation:

1.) 2x+12=20

2.) 2x+12=-20

Solving Equation 1:

2x+12=20

2x=8

x=4

Solving Equation 2:

2x+12=-20

2x=-32

x=-16

Therefore, for $\left | 2x+12\right |=20$ , x=4 or x=-16 .

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Example Question #42 : Equations

Solve for : 3y-4x=7x+33

Possible Answers:

$y=-\frac{3}{11}x+11$

$y=-\frac{11}{3}x+11$

$y=\frac{3}{11}x+11$

Not enough information provided

$y=\frac{11}{3}x+11$

Correct answer:

$y=\frac{11}{3}x+11$

Explanation:

In order to solve 3y-4x=7x+33 for , we need to isolate on one side of the equation:

3y-4x=7x+33

3y=11x+33

$y=\frac{11}{3}x+11$

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Example Question #354 : Algebra

Which of the following is a solution to the equation 7x+3y=22 ?

Possible Answers:

x=1, y=5

Two of the other answers are correct.

x=5, y=1

x=4, y=2

x=2, y=3

Correct answer:

x=1, y=5

Explanation:

In order to find values of and for which 7x+3y=22 , we need to plug the values into the equation:

1.) x=1, y=5 : 7(1)+3(5)=7+15=22 Correct

2.) x=5, y=1 : 7(5)+3(1)=35+3=38 Incorrect

3.) x=2, y=3 : 7(2)+3(3)=14+9=23 Incorrect

4.) x=4, y=2 : 7(4)+3(2)=28+6=34 Incorrect

Therefore, the only correct answer is x=1, y=5 .

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GMAT Math : Algebra

Study concepts, example questions & explanations for GMAT Math

All GMAT Math Resources

Example Questions

Example Question #351 : Algebra

Example Question #352 : Algebra

Example Question #353 : Algebra

Example Question #351 : Algebra

Example Question #354 : Algebra

Example Question #355 : Algebra

Example Question #356 : Algebra

Example Question #353 : Algebra

Example Question #42 : Equations

Example Question #354 : Algebra

All GMAT Math Resources

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