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GRE Subject Test: Math : GRE Subject Test: Math

Study concepts, example questions & explanations for GRE Subject Test: Math

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All GRE Subject Test: Math Resources

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Example Questions

Example Question #44 : Algebra

31>7x+3>2x+6

4>x>3/5

Possible Answers:

x<4

4>x>5/3

3/2>x>1/2

x>3/5

Unsolvable

Correct answer:

3/2>x>1/2

Explanation:

To solve this inequality you must first break apart the inequality into two seperate inequalities.

31>7x+3

subtract the three from both sides

28>7x

divide seven on both sides

4>x

7x+3>2x+6

subtract 2x from both sides

5x+3>6

Subtract 3 from both sides

5x>3

Divide by 5 on both sides

5x>3

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Example Question #42 : Algebra

$Solve\ for\ x: 3x-12>-9$

Possible Answers:

x<1

x<-7

x>1

x>-7

Correct answer:

x>1

Explanation:

$3x-12>-9\ Add\ 12\ to\ both\ sides\\ \\$

$3x>3\ divide\ both\ sides\ by\ 3$

x>1

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Example Question #24 : Solving Inequalities

$Solve\ for\ x:\\$

5-2x>13

Possible Answers:

x>-4

x<-4

x>-9

x<-9

Correct answer:

x<-4

Explanation:

$5-2x>13\ subtract\ 5\ from\ both\ sides$

$-2x>8\ divide\ both\ sides\ by\ (-2)$

$x<-4\ when\ dividing\ by\ a\ negative\ make\ sure\ you\ flip\ the\ inequality\ sign$

$We\ flip\ the\ inequality\ sign\ because\ the\ sign\ on\ both\ sides\ changed.$

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Example Question #27 : Solving Inequalities

4x + 12 < x + 21

Possible Answers:

all values of where $x\geq 3$

all values of where x< 3

all values of where x> 3

all values of where $x\leq 3$

Correct answer:

all values of where x< 3

Explanation:

4x + 12 < x + 21

Subtract 12 from both sides of the inequality.

4x + 12 - 12< x + 21 - 12

4x < x + 9

Subtract from both sides of the inequality.

4x - x< x-x -9

3x < 9

Divide both sides by 3.

$\frac{3x}{3} < \frac{9}{3}$

x < 3

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Example Question #231 : Gre Subject Test: Math

$5\left | x-7\right |+14<39$

Possible Answers:

x> 12 or x< 2

x<12

2< x<12

2< x

Correct answer:

2< x<12

Explanation:

The first thing we must do is get the absolute value alone: $5\left | x-7\right |+14<39$

$5\left | x-7\right |<25$

$\left | x-7\right |<5$

When we're working with absolute values, we are actually solving two equations:

x-7<5 and x-7> -5

Fortunately, these can be written as one equation:

-5< x-7<5

If you feel more comfortable solving the equations separately then go ahead and do so.

2< x<12

To get alone, we added on both sides of the inequality sign

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Example Question #1 : Absolute Value Inequalities

$\left | y\right | + 18 \leq 11.3$

Possible Answers:

$y\leq 29.3$

There is no solution.

$y\geq 6.7$

$y\leq -6.7$

Correct answer:

There is no solution.

Explanation:

$\left | y\right | + 18 \leq 11.3$

$\left | y\right |\leq -6.7$

Because Absolute Value must be a non-negative number, there is no solution to this Absolute Value inequality.

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Example Question #2 : Absolute Value Inequalities

The weight of the bowling balls manufactured at the factory must be lbs. with a tolerance of lbs. Which of the following absolute value inequalities can be used to assess which bowling balls are tolerable?

Possible Answers:

$\left | w-8\right | \geq 3$

$\left | w-3 \right | \leq 8$

$\left | w-3 \right |\geq 8$

$\left | w-8\right | \leq 3$

Correct answer:

$\left | w-8\right | \geq 3$

Explanation:

The following absolute value inequality can be used to assess the bowling balls that are tolerable:

$\left | w-8\right |\geq3$

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Example Question #52 : Algebra

$4\left |(x+0.3)\right | - 3 < 11$

Possible Answers:

x<3.2 and x> -2.3

x<-3.2 and x> -2.3

x> 3.2 and x< -2.3

There is no solution.

Correct answer:

x<3.2 and x> -2.3

Explanation:

$4\left |(x+0.3) \right | - 3< 11$

4x + 1.2 - 3 < 11

4x -1.8<11

4x -1.8 +1.8<11 + 1.8

4x< 12.8

$\frac{4x}{4} < \frac{12.8}{4}$

x<3.2

4x + 1.2 - 3> -11

4x - 1.8> -11

4x - 1.8 + 1.8> -11 + 1.8

4x > -9.2

$\frac{4x}{4}>\frac{-9.2}{4}$

x> -2.3

The correct answer is x<3.2 and x>2.3

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Example Question #2 : Absolute Value Inequalities

$\left | 6+x\right |-4 < 0$

Possible Answers:

x<2 and x>10

x>-2 and x< -10

x<-2 and x> -10

x< 2 and x > 10

Correct answer:

x<-2 and x> -10

Explanation:

$\left | 6+x\right | -4 < 0$

6 + x -4 < 0

6 + x < 4

6-6 + x < 4-6

x< -2

6 + x > -4

6-6 + x > -6-4

x>-10

The correct answer is x< -2 and x>-10.

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Example Question #1 : Absolute Value Inequalities

$\left | \frac{x-6}{2} \right |\leq 3$

Possible Answers:

$x\geq 0$ and $x\leq 12$

There is no solution.

$x\geq 0$ and $x\leq 12$

$x\leq 0$ and $x\geq12$

Correct answer:

$x\geq 0$ and $x\leq 12$

Explanation:

$\left | \frac{x-6}{2} \right |\leq3$

$\frac{2}{1} \left | \frac{x-6}{2} \right | \leq 2\times3$

$x-6 \leq 6$

$x\leq 12$

$\frac{2}{1} \left | \frac{x-6}{2} \right | \geq 2 \times -3$

$x-6 \geq -6$

$x\geq 0$

The correct answer is $x\leq12$ and $x\geq 0.$

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All GRE Subject Test: Math Resources

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GRE Subject Test: Math : GRE Subject Test: Math

Study concepts, example questions & explanations for GRE Subject Test: Math

All GRE Subject Test: Math Resources

Example Questions

Example Question #44 : Algebra

Example Question #42 : Algebra

Example Question #24 : Solving Inequalities

Example Question #27 : Solving Inequalities

Example Question #231 : Gre Subject Test: Math

Example Question #1 : Absolute Value Inequalities

Example Question #2 : Absolute Value Inequalities

Example Question #52 : Algebra

Example Question #2 : Absolute Value Inequalities

Example Question #1 : Absolute Value Inequalities

All GRE Subject Test: Math Resources

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