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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 #1 : Absolute Value Inequalities

$\left | x-5\right |\leq7$

Possible Answers:

$x\leq-12$ and $x \geq 2$

$x\geq12$ and $x\leq -2$

x<12 and x> -2

$x\leq12$ and $x\geq-2$

Correct answer:

$x\leq12$ and $x\geq-2$

Explanation:

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

$x-5 \leq 7$

$x-5 + 5 \leq 7 +5$

$x\leq 12$

$x-5 \geq -7$

$x-5 +5 \geq -7 +5$

$x\geq -2$

The correct answer is $x\leq12$ and $x\geq -2.$

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Example Question #3 : Absolute Value Inequalities

A type of cell phone must be less than 9 ounces with a tolerance of 0.4 ounces. Which of the following inequalities can be used to assess which cell phones are tolerable? (w refers to the weight).

Possible Answers:

$\left | w-0.4\right | \geq 9$

$\left | w-9\right | \leq 0.4$

$\left | w-9\right | \geq 0.4$

$\left | w-0.4\right | \leq 9$

Correct answer:

$\left | w-9\right | \leq 0.4$

Explanation:

The Absolute Value Inequality that can assess which cell phones are tolerable is:

$\left | w-0.4\right | \leq 9$

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Example Question #2 : Absolute Value Inequalities

Solve for x: $|x-1|\le 5$

Possible Answers:

$x \le 6$

$x \ge 6$

x < 6

x>6

Correct answer:

$x \le 6$

Explanation:

Step 1: Separate the equation into two equations:

First Equation: $|x-1|\le 6$
Second Equation: $-(x-1)\ge -5$

Step 2: Solve the first equation

$x-1\le 5$
$x-1+1\le 5+1$
$x \le 6$

Step 3: Solve the second equation

$-(x+1)\ge -5$
$-x+1\ge -5$
$-x+1-1\ge -5-1$

$-x \ge -6$

$\rightarrow x \le 6$

The solution is $x\le 6$

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Example Question #2 : Absolute Value Inequalities

Which of the following expresses the entire solution set of $\left | x-10\right |+ 3 < 12$ ?

Possible Answers:

1<x<19

x<1 and x>19

-5<x<19

x>19 and x< -5

Correct answer:

1<x<19

Explanation:

Before expanding the quantity within absolute value brackets, it is best to simplify the "actual values" in the problem. Thus $\left | x-10 \right |+3<12$ becomes:

$\left | x-10 \right |<9$

From there, note that the absolute value means that one of two things is true: x-10<9 or x-10>-9 . You can therefore solve for each possibility to get all possible solutions. Beginning with the first:

x-10<9 means that:

x<19

For the second:

x-10>-9 means that:

x>1

Note that the two solutions can be connected by putting the inequality signs in the same order:

1<x<19

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Example Question #61 : Algebra

$\frac{2}{3}\left | 9x+6\right | -2\geq 1$

Possible Answers:

$x\geq -\frac{1}{6}$ or $x\leq -\frac{7}{6}$

There is no solution.

$x\leq-\frac{1}{6}$ and $x\geq- \frac{1}{2}$

$x\geq \frac{1}{6}$ and $x\leq \frac{1}{2}$

Correct answer:

$x\geq -\frac{1}{6}$ or $x\leq -\frac{7}{6}$

Explanation:

$\frac{2}{3}\left | 9x+6\right | -2\geq 1$

$\frac{2}{3}\left | 9x+6 \right |\geq 3$

$\left | 9x+6 \right |\geq \frac{9}{2}$

At this point, you've isolated the absolute value and can solve this problems for both cases, $9x+6\geq \frac{9}{2}$ and $9x+6\leq -\frac{9}{2}$ . Beginning with the first case:

$9x+6\geq \frac{9}{2}$

$9x+\frac{12}{2}\geq\frac{9}{2}$

$9x\geq -\frac{3}{2}$

$x\geq -\frac{1}{6}$

Then for the second case:

$9x+6\leq -\frac{9}{2}$

$9x+\frac{12}{2}\leq -\frac{9}{2}$

$9x\leq -\frac{21}{2}$

$x\leq -\frac{7}{6}$

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Example Question #241 : Gre Subject Test: Math

$\left | -4x-5 \right |< 11$

Possible Answers:

$x< \frac{4}{5}$ or x>-2

x< -4

x> -4 and $x< \frac{3}{2}$

x>-11 or x<-6

x> 4

Correct answer:

x> -4 and $x< \frac{3}{2}$

Explanation:

Since the absolute value with x in it is alone on one side of the inequality, you set the expression inside the absolute value equal to both the positive and negative value of the other side, 11 and -11 in this case. For the negative value -11, you must also flip the inequality from less than to a greater than. You should have two inequalities looking like this.

-4x-5<11 and -4x-5>-11

Add 5 to both sides in each inequality.

-4x<16 and -4x>-6

Divide by -4 to both sides of the inequality. Remember, dividing by a negative will flip both inequality symbols and you should have this.

x>-4 and $x< \frac{3}{2}$

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Example Question #242 : Gre Subject Test: Math

Evaluate:

$\left (2 + 3i \right )^{3}$

Possible Answers:

-46 + 63 i

-4 6+ 9i

8 - 27i

-62 + 63 i

8 + 9i

Correct answer:

-4 6+ 9i

Explanation:

We can set A = 2, B = 3i in the cube of a binomial pattern:

$\left ( A + B\right ) ^{3} = A ^{3} + 3 A^{2 }B + 3AB^{2} + B^{3}$

$= 2 ^{3} + 3 \cdot 2 ^{2 } \cdot 3i + 3 \cdot 2 \cdot (3i)^{2} + (3i)^{3}$

$= 2^{3} + 3 \cdot 2^{2} \cdot 3i + 3 \cdot 2 \cdot 3 ^{2}\cdot i^{2} + 3^{3} \cdot i^{3}$

$= 8 + 36i + 54 i^{2} + 27 i^{3}$

= 8 + 36i + 54 (-1) + 27 (-i)

= 8 + 36i - 54 - 27 i

= -46 + 9i

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Example Question #4621 : Algebra Ii

Simplify the following product:

{} (5+3i)(-2+i)

Possible Answers:

{}-7-i

{} -13-i

{} -10+3i

{} -13+11i

Correct answer:

{} -13-i

Explanation:

Multiply these complex numbers out in the typical way:

${}(5+3i)(-2+i) = -10+5i-6i+3i^2$

and recall that i^2=-1 by definition. Then, grouping like terms we get

{} (-10-3)+(5i-6i) = -13-i

which is our final answer.

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Example Question #2 : Imaginary Roots Of Negative Numbers

Simplify:

(5+8i)(6-2i)

Possible Answers:

16+32i

46+38i

25+8i

7+16i

Correct answer:

46+38i

Explanation:

Start by using FOIL. Which means to multiply the first terms together then the outer terms followed by the inner terms and lastly, the last terms.

(5+8i)(6-2i)=30-10i+48i-16i^2

Remember that $i=\sqrt-1$ , so i^2=-1 .

Substitute in for i^2

30-10i+48i-16i^2=30+38i-16(-1)=30+38i+16=46+38i

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Example Question #3 : Imaginary Roots Of Negative Numbers

Simplify:

(2+5i)(-8-i)

Possible Answers:

-18-5i

12+6i

42+11i

-11-42i

Correct answer:

-11-42i

Explanation:

Start by using FOIL. Which means to multiply the first terms together then the outer terms followed by the inner terms and lastly, the last terms.

(2+5i)(-8-i)=-16-2i-40i-5i^2

Remember that $i=\sqrt-1$ , so i^2=-1 .

Substitute in for i^2

-16-2i-40i-5i^2=-16-42i-5(-1)=-16+5-42i=-11-42i

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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 #1 : Absolute Value Inequalities

Example Question #3 : Absolute Value Inequalities

Example Question #2 : Absolute Value Inequalities

Example Question #2 : Absolute Value Inequalities

Example Question #61 : Algebra

Example Question #241 : Gre Subject Test: Math

Example Question #242 : Gre Subject Test: Math

Example Question #4621 : Algebra Ii

Example Question #2 : Imaginary Roots Of Negative Numbers

Example Question #3 : Imaginary Roots Of Negative Numbers

All GRE Subject Test: Math Resources

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