GRE Math : Linear / Rational / Variable Equations

Study concepts, example questions & explanations for GRE Math

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Example Questions

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Example Question #111 : Linear / Rational / Variable Equations

Ben is walking three dogs that weigh an average of 75 pounds each. Ben begins to walk a fourth dog, and the average weight of the dogs decreases to 70 pounds. What is the weight in pounds of the fourth dog?

Possible Answers:

60

40

55

45

50

Correct answer:

55

Explanation:

The total weight of the first three dogs is 225 pounds. This amount, plus the weight of the fourth dog, divided by total number of dogs, is the new average weight:

\frac{d + 225}{4} = 70

d + 225 = 280

d = 55 lbs

Example Question #112 : Linear / Rational / Variable Equations

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.

What is the monthly break-even point at Pets Plus?

Possible Answers:

30

35

50

40

25

Correct answer:

30

Explanation:

Let x= the number of bird houses sold each month.

Revenue = 40x

Costs=15x+750

The break-even point is where the revenue is the same as the costs:

Revenue=Costs 

40x=15x+750 

Solve for x:

x=30

Therefore, Pets Plus must sell 30 bird houses to break-even.

Example Question #113 : Linear / Rational / Variable Equations

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:

\$300

\$500

\$250

\$625

\$750

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.

Example Question #114 : Linear / Rational / Variable Equations

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 .

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

Example Question #115 : Linear / Rational / Variable Equations

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

Possible Answers:

16

12

18

14

10

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.

Example Question #116 : Linear / Rational / Variable Equations

Consider the following equation:

Which of the following must be true?

Possible Answers:

Correct answer:

Explanation:

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

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

Subtract  from both sides:

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

Add 9 to both sides:

Add  to both sides:

Divide both sides by 3:

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  always holds because 4 and 6 are both even. 

Example Question #117 : Linear / Rational / Variable Equations

If

,

then 

Possible Answers:

Correct answer:

Explanation:

Divide both sides by 300 to get .  Subtract 7 and divide by two to get .

Example Question #118 : Linear / Rational / Variable Equations

If b – 3 = a, then (a – b)2 =

Possible Answers:

The answer cannot be determined from the given information.

–9

3

–3

9

Correct answer:

9

Explanation:

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

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