GMAT Math : Algebra

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Example Questions

Example Question #1391 : Problem Solving Questions

Find the value of g(z) when z=-144

$g(z)=\frac{x}{4}+65$

Possible Answers:

Correct answer:

Explanation:

Find the value of g(z) when z=-144

$g(z)=\frac{x}{4}+65$

To solve this equation, we need to substitute the given value of z into our function and simplify. Let's begin!

$g(z)=\frac{-144}{4}+65=-36+65=29$

So, our answer is 29

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Example Question #33 : Solving Linear Equations With One Unknown

Solve 2a+4b=12 and 6a-b=3 .

Possible Answers:

a=1, b=1

a=3, b=3

a=2, b=2

a=1, b=3

a=3, b=1

Correct answer:

a=1, b=3

Explanation:

Stack the two equations on top of each other. The easiest method to solving two equations for two unknowns is to manipulate one of the equations, so that the leading coefficient in front of the variable matches the other equation. Then, you can simply add or subtract the equation, solve for one variable, and plug that answer into the other equation.

3(2a+4b=12)=6a+12b=36

6a-b=2

(6a+12b=36)-(6a-b=2)=11b=33. b=3

6a-3=3. a=1

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Example Question #311 : Algebra

Solve for :

5z+9=10

Possible Answers:

$\frac{-1}{5}$

$\frac{1}{5}$

Correct answer:

$\frac{1}{5}$

Explanation:

5z+9=10

5z=10-9

5z=1

$z=\frac{1}{5}$

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Example Question #1 : Solving Equations

If $\dpi{100} \small 5x+4=19$ , what is the value of $\dpi{100} \small 4x^{2}-5$ ?

Possible Answers:

$\dpi{100} \small 139$

$\dpi{100} \small 19$

$\dpi{100} \small 31$

$\dpi{100} \small 10$

$\dpi{100} \small 3$

Correct answer:

$\dpi{100} \small 31$

Explanation:

First, we need to solve for $\dpi{100} \small x$ from the first equation in order to calculate the second quadratic function. To solve for $\dpi{100} \small x$ , we need to subtract four on each side of the equation, then we will get

$\dpi{100} \small 5x=15$

The answer for $\dpi{100} \small x$ would be $\dpi{100} \small \frac{15}{5}$ , which is $\dpi{100} \small 3$ .

So now we can calculate the function by plugging in $\dpi{100} \small x=3$ .

$\dpi{100} \small 3^{2}=9$ , and $\dpi{100} \small 9\times 4=36$ .

$\dpi{100} \small 36-5=31$

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Example Question #2 : Solving Equations

A tractor spends 5 days plowing $\dpi{100} \small x$ number of fields. How many days will it take to plow $\dpi{100} \small y$ number of fields at the same rate?

Possible Answers:

$\frac{xy}{5}$

$\frac{5x}{y}$

$\frac{y}{5x}$

$\frac{5y}{x}$

$\frac{5}{xy}$

Correct answer:

$\frac{5y}{x}$

Explanation:

The equation that will be used is (rate * number of days = number of fields plowed). From the first part of the question, number of fields plowed $\dpi{100} \small (x)$ is calculated as:

$rate \cdot 5 = x$

To solve for rate both sides are divided by 5.

$rate = \frac{x}{5}$

This rate is used for the second part of the problem. $\frac{x}{5} * days = y$ . To solve for days, both sides are divided by $\frac{x}{5}$ , which is the same as multiplying by $\frac{5}{x}$ , cancelling out the $\frac{x}{5}$ and giving the answer of $days = \frac{5y}{x}$ .

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Example Question #3 : Solving Equations

A 70 ft long board is sawed into two planks. One plank is 30 ft longer than the other, how long (in feet) is the shorter plank?

Possible Answers:

$\dpi{100} \small 40$

$\dpi{100} \small 50$

$\dpi{100} \small 20$

$\dpi{100} \small 15$

$\dpi{100} \small 30$

Correct answer:

$\dpi{100} \small 20$

Explanation:

Let $\dpi{100} \small x$ = length of the short plank and $\dpi{100} \small x+30$ = length of the long plank.

$\dpi{100} \small x+x+30=70$ is the length of the pre-cut board, or combined length of both planks.

$\dpi{100} \small 2x+30=70$

$\dpi{100} \small 2x=40$

$\dpi{100} \small x=20$

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Example Question #4 : Solving Equations

Solve $2x^{2} - 8x - 24 = 0.$

Possible Answers:

$\dpi{100} \small x=-12\ or\ x=-4$

$\dpi{100} \small x=6\ or\ x=-2$

$\dpi{100} \small x=2\ or\ x=-2$

$\dpi{100} \small x=-6\ or\ x=2$

$\dpi{100} \small x=6\ or\ x=-6$

Correct answer:

$\dpi{100} \small x=6\ or\ x=-2$

Explanation:

$2x^{2} - 8x - 24 = 2(x^{2}-4x-12)=0$

Divide both sides by 2: $x^{2}-4x-12=0$ . We need to find two numbers that multiply to $\dpi{100} \small -12$ and sum to $\dpi{100} \small -4$ . The numbers $\dpi{100} \small -6$ and $\dpi{100} \small 2$ work.

$x^{2}-4x-12= (x-6)(x+2)=0$

$\dpi{100} \small x-6=0$

$\dpi{100} \small x=6$

$\dpi{100} \small or\ x+2=0$

$\dpi{100} \small x=-2$

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Example Question #5 : Solving Equations

If $1-\frac{4}{a}=2-\frac{7}{a}$ then $a=$

Possible Answers:

$2$

$\frac{2}{3}$

$\frac{1}{3}$

$3$

$-1$

Correct answer:

$3$

Explanation:

Multiply both sides of the equation by a: $a-4=2a-7$

Then, solve for $a$ .

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Example Question #6 : Solving Equations

$\dpi{100} \small 4y+7=3x+5$

Solve for x.

Possible Answers:

$x = \frac{4}{3}y - \frac{2}{3}$

$y = x + \frac{2}{3}$

not enough information

$y = \frac{4}{3}x + \frac{2}{3}$

$x = \frac{4}{3}y + \frac{2}{3}$

Correct answer:

$x = \frac{4}{3}y + \frac{2}{3}$

Explanation:

We need to solve for x in terms of y by isolating x.

3x=4y+2

$x = \frac{4}{3}y + \frac{2}{3}$

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Example Question #7 : Solving Equations

Which of the following is a solution to the equation x+2y-3z=4 ?

Possible Answers:

x=1,y=2,z=3

x=2,y=-1,z=5

x=8,y=1,z=2

x=3,y=2,z=1

two of the answer choices are correct

Correct answer:

two of the answer choices are correct

Explanation:

We need to plug in the answer choices and see which produce the value 4.

1. x=3,y=2,z=1:3+2(2)-3(1)=3+4-3=4 , correct

2. x=1,y=2,z=3:1+2(2)-3(3)=1+4-9=-4 , incorrect

3. x=8,y=1,z=2:8+2(1)-3(2)=8+2-6=4 , correct

4. x=2,y=-1,z=5:2+2(-1)-3(5)=2-2-15=-15 , incorrect

Therefore two of the answer choices are correct.

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GMAT Math : Algebra

Study concepts, example questions & explanations for GMAT Math

All GMAT Math Resources

Example Questions

Example Question #1391 : Problem Solving Questions

Example Question #33 : Solving Linear Equations With One Unknown

Example Question #311 : Algebra

Example Question #1 : Solving Equations

Example Question #2 : Solving Equations

Example Question #3 : Solving Equations

Example Question #4 : Solving Equations

Example Question #5 : Solving Equations

Example Question #6 : Solving Equations

Example Question #7 : Solving Equations

All GMAT Math Resources

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