GMAT Math : GMAT Quantitative Reasoning

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Example Questions

Example Question #308 : Algebra

Solve for :

-4a+8=4

Possible Answers:

$\frac{1}{4}$

$\frac{1}{2}$

$-\frac{1}{2}$

Correct answer:

Explanation:

To solve for a we need to isolate a on one side of the equation and all other numbers on the other side of the equation.

Inorder to do this we first subtract 8 from both sides.

-4a+8=4

Now, we divide by -4 to finish isolating a.

-4a=-4

a=1

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Example Question #309 : Algebra

Solve for .

-2(x+5)-7(8-x)=14-(2+x)

Possible Answers:

x=11.14

x=13

x=-13

x=-4.25

Correct answer:

x=13

Explanation:

-2(x+5)-7(8-x)=14-(2+x)

-2x-10-56+7x=14-2-x

-10-56+6x=12

6x=78

x=13

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Example Question #31 : Solving Linear Equations With One Unknown

A number, when added to the product of and , yields . What is the number?

Possible Answers:

160

12.6

Correct answer:

Explanation:

The first step in solving this problem is to write out an equation with the information provided:

$n+12\cdot6=88$

where represents the number we are seeking.

We then solve for our number:

n+72=88

n=88-72

n=16

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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 #1391 : Gmat Quantitative Reasoning

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:

$\dpi{100} \small 3$

$\dpi{100} \small 19$

$\dpi{100} \small 10$

$\dpi{100} \small 139$

$\dpi{100} \small 31$

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 #1 : 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:

$\frac{xy}{5}$

$\frac{5x}{y}$

$\frac{5}{xy}$

$\frac{5y}{x}$

$\frac{y}{5x}$

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 #2 : 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:

$\dpi{100} \small 40$

$\dpi{100} \small 20$

$\dpi{100} \small 30$

$\dpi{100} \small 50$

$\dpi{100} \small 15$

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 #3 : Equations

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

Possible Answers:

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

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

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

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

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

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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GMAT Math : GMAT Quantitative Reasoning

Study concepts, example questions & explanations for GMAT Math

All GMAT Math Resources

Example Questions

Example Question #308 : Algebra

Example Question #309 : Algebra

Example Question #31 : Solving Linear Equations With One Unknown

Example Question #1391 : Problem Solving Questions

Example Question #33 : Solving Linear Equations With One Unknown

Example Question #1391 : Gmat Quantitative Reasoning

Example Question #1 : Solving Equations

Example Question #1 : Equations

Example Question #2 : Equations

Example Question #3 : Equations

All GMAT Math Resources

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