GRE Math : How to find the solution to an equation

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Example Questions

Example Question #91 : How To Find The Solution To An Equation

Pets Plus makes bird houses. Their monthly fixed expenses are $750. The cost for each bird house is $15. The bird houses sell for $40.

If Pets Plus sells 50 bird houses, what is the profit?

Possible Answers:

$\$625$

$\$300$

$\$500$

$\$750$

$\$250$

Correct answer:

$\$500$

Explanation:

Let $x$ = the number of birdhouses sold each month.

$Revenue=40x$

$Costs=15x+750$

$Profit = Revenue-Costs$

$=40x-15x-750$

$=25x-750$

Substituting in 50 for $x$ gives an answer of 500, so the profit on 50 birdhouses is $500.

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Example Question #52 : Algebra

George is three times older than Joey. The sum of their ages is 16. What is the product of their ages?

Possible Answers:

Correct answer:

Explanation:

Let = Joey's age and = George's age.

Then the equation to solve becomes x + 3x = 16 .

4x=16

x=4

Therefore, Joey is 4 years old and George is 12 years old, so the product of their ages is 48.

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Example Question #53 : Algebra

Three consecutive even numbers add to 42. What is the middle number?

Possible Answers:

$18$

$16$

$14$

$10$

$12$

Correct answer:

$14$

Explanation:

Let $x$ = 1st even number, $x+2$ = 2nd even number, and $x+4$ = 3rd even number.

Then the equation to solve becomes $x+(x+2)+(x+4)=42$ .

$3x+6=42$

Thus $x=12,x+2=14,\ and\ x+4=16$ , so the middle number is 14.

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Example Question #51 : Equations / Inequalities

Consider the following equation:

$\left | 2x-9 \right | = x-3$

Which of the following must be true?

$I) \quad x=6$

$II) \quad x \mbox{ is positive }$

$III) \quad x \mbox{ is even }$

Possible Answers:

$II \mbox{ only }$

$\mbox{ none of these }$

$II \mbox{ and } III \mbox{ only }$

$III \mbox{ only }$

$I, II \mbox{ and } III$

Correct answer:

$II \mbox{ and } III \mbox{ only }$

Explanation:

The quantity inside the absolute value brackets must equal either x-3 or -(x-3) , depending on whether the quantity inside the brackets is positive or negative. We therefore have two seperate equations:

2x-9 = x-3

2x-9 =-(x-3)

To solve the first equation, add 9 to both sides:

2x = x+6

Subtract from both sides:

x=6

This is the first solution. Now let's look at the second equation. The distributive law gives us:

2x-9 =-x+3

Add 9 to both sides:

2x =-x+12

Add to both sides:

3x = 12

Divide both sides by 3:

x=4

Therefore, is either 4 or 6.

Statement does NOT have to be true because can also equal 4.

Statement must be true because both 4 and 6 are positive .

Finally, statement III always holds because 4 and 6 are both even.

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Example Question #51 : Algebra

$5\textup{,}100 = 300(2v + 7)$ ,

then v =

Possible Answers:

500

$\frac{1}{5}$

Correct answer:

Explanation:

Divide both sides by 300 to get 17 = 2v + 7 . Subtract 7 and divide by two to get v = 5 .

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Example Question #151 : Gre Quantitative Reasoning

If b – 3 = a, then (a – b)² =

Possible Answers:

–9

–3

The answer cannot be determined from the given information.

Correct answer:

Explanation:

The quantity can be regrouped to be –3 = a – b. Thus, (a – b)² = (–3)² = 9.

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GRE Math : How to find the solution to an equation

Study concepts, example questions & explanations for GRE Math

All GRE Math Resources

Example Questions

Example Question #91 : How To Find The Solution To An Equation

Example Question #52 : Algebra

Example Question #53 : Algebra

Example Question #51 : Equations / Inequalities

Example Question #51 : Algebra

Example Question #151 : Gre Quantitative Reasoning

All GRE Math Resources

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