GMAT Math : GMAT Quantitative Reasoning

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Example Questions

Example Question #42 : Simplifying Algebraic Expressions

If you were to write $(x-3)^{10}$ in expanded form in descending order of degree, what would the third term be?

Possible Answers:

$810x^{8}$

$405x^{8}$

$45x^{8}$

$243x^{8}$

$945x^{8}$

Correct answer:

$405x^{8}$

Explanation:

By the Binomial Theorem, if you expand $(A+B)^{n}$ , writing the result in standard form, the $r \mathrm{th}$ term (with the terms being numbered from 0 to ) is

$C(n,r)A^{n-r}B^{r}$

Set A=x , B=-3 , n=10 , and r=2 (again, the terms are numbered 0 through , so the third term is numbered 2) to get

$C(10,2)\cdot x^{10-2}\cdot (-3)^{2}$

$=\frac{10!}{8! 2!}\cdot x^{8}\cdot 9$

$=45\cdot x^{8}\cdot 9$

$=405x^{8}$

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Example Question #51 : Simplifying Algebraic Expressions

Assume that $x,y \neq 0$ .

Which of the following expressions is equal to the following expression?

$\frac{(x+y)^{2} +(x - y)^{2}}{x^{2}y^{2}}$

Possible Answers:

$\frac{2 }{x^{2}y} + \frac{2 }{xy^{2}}$

$4x^{2}y^{2}$

$\frac{2 }{x^{2}} + \frac{2 }{y^{2}}$

$\frac{2 }{x} + \frac{2 }{y}$

Correct answer:

$\frac{2 }{x^{2}} + \frac{2 }{y^{2}}$

Explanation:

$\frac{(x+y)^{2} +(x - y)^{2}}{x^{2}y^{2}}$

$=\frac{(x^{2}+2xy+y^{2}) + (x^{2}-2xy+y^{2}) }{x^{2}y^{2}}$

$=\frac{x^{2}+x^{2}+2xy-2xy+y^{2}+y^{2} }{x^{2}y^{2}}$

$=\frac{2x^{2}+2y^{2} }{x^{2}y^{2}}$

$=\frac{2x^{2} }{x^{2}y^{2}} + \frac{2y^{2} }{x^{2}y^{2}}$

$=\frac{2 }{y^{2}} + \frac{2 }{x^{2}} = \frac{2 }{x^{2}} + \frac{2 }{y^{2}}$

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Example Question #1 : Linear Equations, One Unknown

For what value of $\small N$ would the following equation have no solution?

$\small \small 3 (4x - 7) + 12 = 2 (5x - 3) + N (x - 3)$

Possible Answers:

$\small \small N= 1$

The equation must always have at least one solution regardless of the value of $\small N$ .

$\small N= -2$

$\small \small N= -1$

$\small N= 2$

Correct answer:

$\small N= 2$

Explanation:

Simplify both sides of the equation as much as possible, and solve for $\small x$ in the equation in terms of $\small N$ :

$\small \small \small 3 (4x - 7) + 12 = 2 (5x - 3) + N (x - 3)$

$\small 3 \cdot 4x - 3 \cdot 7 + 12 = 2 \cdot 5x - 2 \cdot 3 + N \cdot x - N \cdot 3$

$\small 12x - 21 + 12 = 10x - 6 + Nx - 3N$

$\small 12x - 9 = (10+N)x + (- 6 - 3N)$

$\small \small 12x - (10+N)x = (- 6 - 3N) + 9$

$\small (2-N)x = 3 - 3N$

$\small x = \frac{3 - 3N}{2 -N}$

$\small x$ has exactly one solution unless the denominator is 0 - that is, $\small N = 2$ . We make sure that this value renders no solution by substituting:

$\small \small \small 3 (4x - 7) + 12 = 2 (5x - 3) + N (x - 3)$

$\small \small \small \small 3 (4x - 7) + 12 = 2 (5x - 3) + 2 (x - 3)$

$\small 12x - 21 + 12 = 10x - 6 + 2x - 6$

$\small 12x - 9 = 12x - 12$

$\small - 9 = - 12$

The equation has no solution, and $\small N = 2$ is the correct answer.

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Example Question #1 : Linear Equations, One Unknown

Solve for :

n+2=-14-n

Possible Answers:

Correct answer:

Explanation:

n+2=-14-n

n+n=-14-2

2n=-16

n=-8

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Example Question #2 : Linear Equations, One Unknown

Solve for :

-6x-20=-2x+4(1-3x)

Possible Answers:

Correct answer:

Explanation:

-6x-20=-2x+4(1-3x)

-6x-20=-2x+4-12x

-6x-20=-14x+4

-6x+14x=4+20

8x=24

x=3

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Example Question #1 : Solving Linear Equations With One Unknown

Solve for :

-14+6b+7-2b=1+5b

Possible Answers:

Correct answer:

Explanation:

-14+6b+7-2b=1+5b

-7+4b=1+5b

4b-5b=1+7

-b=8

b=-8

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Example Question #1 : Linear Equations, One Unknown

What is the midpoint coordinate of (1,4) and (7,10) ?

Possible Answers:

(6,6)

(3,3)

(7,4)

(4,7)

Correct answer:

(4,7)

Explanation:

Midpoint formula:

$\left(\frac{x_{1}+x_{2}}{2},\frac{y_{1}+y_{2}}{2}\right)$

$(1,4)\ and\ (7,10)$

$\left(\frac{1+7}{2},\frac{4+10}{2}\right)$

$\left(\frac{8}{2},\frac{14}{2}\right)$

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Example Question #1364 : Problem Solving Questions

What is the midpoint coordinate of (1,2) and (5,2) ?

Possible Answers:

(3,2)

(2,0)

(2,3)

(6,4)

Correct answer:

(3,2)

Explanation:

Midpoint formula:

$\left(\frac{x_{1}+x_{2}}{2},\frac{y_{1}+y_{2}}{2}\right)$

$(1,2)\ and\ (5,2)$

$\left(\frac{1+5}{2},\frac{2+2}{2}\right)$

$\left(\frac{6}{2},\frac{4}{2}\right)$

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Example Question #1 : Solving Linear Equations With One Unknown

What is the midpoint coordinate of (-2,-1) and (-8,7) ?

Possible Answers:

(5,3)

(3,5)

(-5,3)

(3,-5)

Correct answer:

(-5,3)

Explanation:

Midpoint formula:

$\left(\frac{x_{1}+x_{2}}{2},\frac{y_{1}+y_{2}}{2}\right)$

$(-2,-1)\ and\ (-8,7)$

$\left(\frac{-2+-8}{2},\frac{-1+7}{2}\right)$

$\left(\frac{-10}{2},\frac{6}{2}\right)$

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Example Question #1 : Solving Linear Equations With One Unknown

Solve the following equation:

$2\left | x-5\right |+16=30$ .

Possible Answers:

x = {-9 : 16}

x = {0 ; 10}

x = {-7 ; 7}

x = {-2 ; 12}

x = 2

Correct answer:

x = {-2 ; 12}

Explanation:

We start by isolating the absolute value expression:

This gives us two cases when we remove the absolute value:

x - 5 = 7 and x - 5 = -7

Then we solve for each case:

$x - 5 = 7 \Rightarrow x = 7 + 5 \Rightarrow x= 12$

$x - 5 = -7 \Rightarrow x = -7 + 5\Rightarrow x= -2$

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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 #42 : Simplifying Algebraic Expressions

Example Question #51 : Simplifying Algebraic Expressions

Example Question #1 : Linear Equations, One Unknown

Example Question #1 : Linear Equations, One Unknown

Example Question #2 : Linear Equations, One Unknown

Example Question #1 : Solving Linear Equations With One Unknown

Example Question #1 : Linear Equations, One Unknown

Example Question #1364 : Problem Solving Questions

Example Question #1 : Solving Linear Equations With One Unknown

Example Question #1 : Solving Linear Equations With One Unknown

All GMAT Math Resources

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