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GRE Subject Test: Math : Algebra

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All GRE Subject Test: Math Resources

2 Diagnostic Tests 148 Practice Tests Question of the Day Flashcards Learn by Concept

Example Questions

Example Question #3 : Inequalities

$3\leq 9 +c$ $\displaystyle 3\leq 9 +c$

Possible Answers:

$c\leq -6$ $\displaystyle c\leq -6$

$c\leq 6$ $\displaystyle c\leq 6$

$c\geq -6$ $\displaystyle c\geq -6$

$c\geq 6$ $\displaystyle c\geq 6$

Correct answer:

$c\geq -6$ $\displaystyle c\geq -6$

Explanation:

$3\leq 9 +c$ $\displaystyle 3\leq 9 +c$

Subtract 9 from both sides of the inequality.

$3-9 \leq (9-9) + c$ $\displaystyle 3-9 \leq (9-9) + c$

$-6 \leq c$ $\displaystyle -6 \leq c$

Because the variable, in this case $\displaystyle c$ is to the right of the inequality sign, you switch the inequality sign to its opposite. The $\leq$ $\displaystyle \leq$ becomes a $\geq$ $\displaystyle \geq$ so that the variable is to the left of the inequality sign.

$c\geq -6$ $\displaystyle c\geq -6$

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Example Question #31 : Algebra

$y + \frac{2}{3} > 7$ $\displaystyle y + \frac{2}{3} > 7$

Possible Answers:

$y\geq 6 \frac{1}{3}$ $\displaystyle y\geq 6 \frac{1}{3}$

$y> 6\frac{1}{3}$ $\displaystyle y> 6\frac{1}{3}$

$y \geq 7\frac{2}{3}$ $\displaystyle y \geq 7\frac{2}{3}$

$y< 6\frac{1}{3}$ $\displaystyle y< 6\frac{1}{3}$

Correct answer:

$y> 6\frac{1}{3}$ $\displaystyle y> 6\frac{1}{3}$

Explanation:

$y + \frac{2}{3} > 7$ $\displaystyle y + \frac{2}{3} > 7$

Subtract $\frac{2}{3}$ $\displaystyle \frac{2}{3}$ from both sides of the inequality.

$y + \frac{2}{3} - \frac{2}{3} > 7 - \frac{2}{3}$ $\displaystyle y + \frac{2}{3} - \frac{2}{3} > 7 - \frac{2}{3}$

$y> 6\frac{1}{3}$ $\displaystyle y> 6\frac{1}{3}$

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Example Question #31 : Classifying Algebraic Functions

$\displaystyle -12 > z-4$

Possible Answers:

$z\leq -8$ $\displaystyle z\leq -8$

z< -8 $\displaystyle z< -8$

z> -8 $\displaystyle z> -8$

$z\geq -8$ $\displaystyle z\geq -8$

Correct answer:

z< -8 $\displaystyle z< -8$

Explanation:

$\displaystyle -12 > z-4$

Add 4 to both sides of the inequality.

$\displaystyle -12 + 4> z-4 + 4$

-8 > z $\displaystyle -8 > z$

Because the variable $\displaystyle z$ is to the right of the inequality, it needs to be placed to the left of the inequality. When this happens, the inequality sign needs to be switched to its opposite.

z < -8 $\displaystyle z < -8$

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Example Question #31 : Classifying Algebraic Functions

$3x +6\geq -2x + 8$ $\displaystyle 3x +6\geq -2x + 8$

Possible Answers:

$x\geq \frac{5}{2}$ $\displaystyle x\geq \frac{5}{2}$

$x\leq \frac{2}{5}$ $\displaystyle x\leq \frac{2}{5}$

$x\geq \frac{2}{5}$ $\displaystyle x\geq \frac{2}{5}$

$x\leq \frac{5}{2}$ $\displaystyle x\leq \frac{5}{2}$

Correct answer:

$x\geq \frac{2}{5}$ $\displaystyle x\geq \frac{2}{5}$

Explanation:

$3x + 6 \geq -2x + 8$ $\displaystyle 3x + 6 \geq -2x + 8$

Subtract 6 from both sides of the inequality.

$3x + 6 - 6\geq -2x + 8 - 6$ $\displaystyle 3x + 6 - 6\geq -2x + 8 - 6$

$3x\geq -2x + 2$ $\displaystyle 3x\geq -2x + 2$

Add $\displaystyle 2x$ to both sides of the inequality.

$3x + 2x\geq -2x + 2x + 2$ $\displaystyle 3x + 2x\geq -2x + 2x + 2$

$5x \geq 2$ $\displaystyle 5x \geq 2$

Divide both sides by $\displaystyle 5$.

$\frac{5x}{5} \geq \frac{2}{5}$ $\displaystyle \frac{5x}{5} \geq \frac{2}{5}$

$x\geq \frac{2}{5}$ $\displaystyle x\geq \frac{2}{5}$

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Example Question #31 : Algebra

The difference between a number and 6 is no more than 7. What would those numbers be?

Possible Answers:

$n\geq 13$ $\displaystyle n\geq 13$

$n\leq 13$ $\displaystyle n\leq 13$

$n\leq 7$ $\displaystyle n\leq 7$

$n\leq 6$ $\displaystyle n\leq 6$

Correct answer:

$n\leq 13$ $\displaystyle n\leq 13$

Explanation:

$n - 6\leq 7$ $\displaystyle n - 6\leq 7$

Would be the inequality that represents that statement.

Add $\displaystyle 6$ to both sides of that inequality.

$n - 6 + 6 \leq 13$ $\displaystyle n - 6 + 6 \leq 13$

$n\leq 13$ $\displaystyle n\leq 13$

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Example Question #32 : Algebra

$x^{2} -64< 0$ $\displaystyle x^{2} -64< 0$ Find the solution set.

Possible Answers:

x = 0 $\displaystyle x = 0$

x < 8 $\displaystyle x < 8$

-8<x< 8 $\displaystyle -8< x< 8$

8< x<8 $\displaystyle 8< x< 8$

Correct answer:

-8<x< 8 $\displaystyle -8< x< 8$

Explanation:

$x^{2} - 64< 0$ $\displaystyle x^{2} - 64< 0$

$x^{2} < 64$ $\displaystyle x^{2} < 64$

$\displaystyle -8 < x < 8$

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Example Question #13 : Inequalities

$\displaystyle 3 (x-3) > 4 (x+2)$

Possible Answers:

x< 17 $\displaystyle x< 17$

x < -17 $\displaystyle x < -17$

x< -1 $\displaystyle x< -1$

x> -1 $\displaystyle x> -1$

Correct answer:

x < -17 $\displaystyle x < -17$

Explanation:

$\displaystyle 3 (x-3) > 4(x+2)$

Begin by simplifying the inequality by using the distributive property.

$\displaystyle 3x - 9 > 4x +8$

Add $\displaystyle 9$ to both sides.

$\displaystyle 3x-9 + 9 > 4x + 8 + 9$

$\displaystyle 3x> 4x + 17$

Subtract $\displaystyle 4x$ from both sides.

$\displaystyle 3x-4x > 4x-4x+17$

-x > 17 $\displaystyle -x > 17$

Because there is a negative variable, multiply both sides by $\displaystyle -1$ and switch the inequality sign to its opposite.

x< -17 $\displaystyle x< -17$

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Example Question #33 : Algebra

$\displaystyle b - 6 > 13$

Possible Answers:

b > 19 $\displaystyle b > 19$

b< 19 $\displaystyle b< 19$

b> 7 $\displaystyle b> 7$

b<7 $\displaystyle b< 7$

Correct answer:

b > 19 $\displaystyle b > 19$

Explanation:

$\displaystyle b - 6 > 13$

Add 6 to both sides of the inequality.

$\displaystyle b-6 + 6> 13 + 6$

b> 19 $\displaystyle b> 19$

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Example Question #38 : Algebra

$\displaystyle -3x -12> 15$

Possible Answers:

x< 9 $\displaystyle x< 9$

$x\geq 9$ $\displaystyle x\geq 9$

x> -9 $\displaystyle x> -9$

x < -9 $\displaystyle x < -9$

Correct answer:

x < -9 $\displaystyle x < -9$

Explanation:

$\displaystyle -3x-12> 15$

To isolate the variable, add $\displaystyle 12$ to both sides of the inequality.

$\displaystyle -3x-12+12 > 15 + 12$

-3x >27 $\displaystyle -3x >27$

Divide both sides by -3. $\displaystyle -3.$ Because you are dividing by a negative integer, you have to flip or switch the inequality sign to its opposite.

x < -9 $\displaystyle x < -9$

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Example Question #34 : Algebra

Solve.

$12 + n \leq 4$ $\displaystyle 12 + n \leq 4$

Possible Answers:

$n \leq -12$ $\displaystyle n \leq -12$

$n\leq -8$ $\displaystyle n\leq -8$

$n\leq 8$ $\displaystyle n\leq 8$

$n\leq 12$ $\displaystyle n\leq 12$

Correct answer:

$n\leq -8$ $\displaystyle n\leq -8$

Explanation:

$12+n\leq 4$ $\displaystyle 12+n\leq 4$

To isolate the variable , subtract $\displaystyle 12$ from both sides of the inequality.

$(12-12) + n \leq4-12$ $\displaystyle (12-12) + n \leq4-12$

$n\leq -8$ $\displaystyle n\leq -8$

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GRE Subject Test: Math : Algebra

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

All GRE Subject Test: Math Resources

Example Questions

Example Question #3 : Inequalities

Example Question #31 : Algebra

Example Question #31 : Classifying Algebraic Functions

Example Question #31 : Classifying Algebraic Functions

Example Question #31 : Algebra

Example Question #32 : Algebra

Example Question #13 : Inequalities

Example Question #33 : Algebra

Example Question #38 : Algebra

Example Question #34 : Algebra

All GRE Subject Test: Math Resources

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