GMAT Math : GMAT Quantitative Reasoning

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Example Questions

Example Question #32 : Solving Equations

$\frac{2}{(5^{-1})x+0.1}=5$

What is the value of ?

Possible Answers:

1.8

1.6

1.7

1.5

1.9

Correct answer:

1.5

Explanation:

To find the value of x we need to isolate x on one side of the equation and the rest of the numbers on the other side.

$\frac{2}{(5^{-1})x+0.1}=5$

First, we multiply what is in the denominator on the left had side by the numerators on both sides.

$2=5\times((5^{-1})x +0.1)$

Then we distribute the 5 to both terms in the binomial. Doing this we get a zero in the exponent.

$2=(5^{0})x+0.5$

Anything raised to the zero just becomes one.

2=x+0.5

From here we subtract 0.5 from each side to solve for x.

x=2-0.5

x=1.5

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Example Question #31 : Solving Equations

Define $f (x) = x \cdot |x |$ . Which of the following would be a valid alternative way of expressing the definition of ?

Possible Answers:

$f (x) = \left\{\begin{matrix} x^{2} & \textrm{ if } x < 0\\ -x^{2} & \textrm{ if } x \geq 0 \end{matrix}\right.$

$f (x) = -x^{2}$

$f (x) = \left\{\begin{matrix} -x^{2} & \textrm{ if } x < 0\\ x^{2} & \textrm{ if } x \geq 0 \end{matrix}\right.$

$f (x) = \left\{\begin{matrix}0 & \textrm{ if } x < 0\\ x^{2} & \textrm{ if } x \geq 0 \end{matrix}\right.$

$f (x) = \left\{\begin{matrix} 0 & \textrm{ if } x < 0\\ -x^{2} & \textrm{ if } x \geq 0 \end{matrix}\right.$

Correct answer:

$f (x) = \left\{\begin{matrix} -x^{2} & \textrm{ if } x < 0\\ x^{2} & \textrm{ if } x \geq 0 \end{matrix}\right.$

Explanation:

By definition:

If $x \geq 0$ , then |x| = x ,and subsequently, $f (x) = x \cdot |x | = x \cdot x= x^{2}$

If x < 0 , then |x| = -x ,and subsequently, $f (x) = x \cdot |x | = x \cdot \left (- x \right )= - x^{2}$

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Example Question #32 : Solving Equations

$125^{N} = x$

Which of the following expressions is equal to $\log_{25}x$ ?

Possible Answers:

$N \sqrt{N }$

$\frac{2}{3}N$

$\sqrt[3]{N^2}$

$N \ln 5$

$\frac{3}{2}N$

Correct answer:

$\frac{3}{2}N$

Explanation:

$5 ^{2} = 25$ , so $5 = \sqrt{25}$ , and $125 = 5 ^{3}= \left (\sqrt{25} \right )^{3} = 25^\frac{3}{2}$ .

$x= 125^{N} = \left ( 25^\frac{3}{2} \right )^{N} =25^{\frac{3}{2}N} \right$

$\log_{25} x = \frac{3}{2}N$

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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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GMAT Math : GMAT Quantitative Reasoning

Study concepts, example questions & explanations for GMAT Math

All GMAT Math Resources

Example Questions

Example Question #32 : Solving Equations

Example Question #31 : Solving Equations

Example Question #32 : Solving Equations

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

All GMAT Math Resources

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