GRE Math : Inequalities

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Example Question #1 :How To Find The Solution To An Inequality With Subtraction

Find the slope of the inequality equation $y-7< x+2y-14$

Possible Answers:

–7

Correct answer:

Explanation:

The answer is:

$y-7< x+2y-14$

$-y-7< x-14$

$-1(-y< x-7)$

$y > -x+7$

From the equation we can see that the slope is –1.

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Example Question #1 :How To Find The Solution To An Inequality With Subtraction

andare both integers.

If y-3x>21 , y>1 , and y<4 , which of the following is a possible value of?

Possible Answers:

Correct answer:

Explanation:

y的值是可能的,即23, and plug them into the first inequality. First, plug in 2. 2 – 3x > 21. Subtract 2 from both sides, and then divide by –3. Don't forget that when you divide or multiply by a negative number in an inequality you must flip the inequality sign. Thus, x < –19/3. Now plug in 3. We find, following the same steps, that when y=3, x < –6. Thus –7 is the correct answer.

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Example Question #3 :How To Find The Solution To An Inequality With Subtraction

Quantity A:

The value(s) for which the following function is undefined:

$f(x)=\sqrt{5x-135}$

Quantity B:

Which of the following is true?

Possible Answers:

Quantity B is larger.

Quantity A is larger.

A comparison cannot be detemined from the given information.

The two quantities are equal.

Correct answer:

Quantity B is larger.

Explanation:

This question is not as hard as it seems. Remember that for real numbers, square roots cannot be taken of negative numbers. Therefore, we know that this function is undefined for:

5x-135 < 0

This is simple to solve. Merely add 135 to both sides:

5x<135

Then, divide by:

x < 27

Therefore, quantity A islessthan quantity B. This means that quantity B is greater than it.

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Example Question #4 :How To Find The Solution To An Inequality With Subtraction

|x+12|<42

Quantity A:

Quantity B:

Which of the following is true?

Possible Answers:

The two quantities are equal.

Quantity A is larger.

A comparison cannot be detemined from the given information.

Quantity B is larger.

Correct answer:

A comparison cannot be detemined from the given information.

Explanation:

Recall that when you have an absolute value and an inequality like

|x+12|<42 ,

this is the same as saying that x+12 must be betweenand. You can rewrite it:

-42 < x+12<42

To solve this, you merely need to subtractfrom all three values:

-54 < x <30

Sinceis betweenand, it could be both larger or smaller than. Therefore, you cannot determine the relationship based on the given information.

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Example Question #1 :How To Find The Solution To An Inequality With Multiplication

Quantitative Comparison

x > 0

Column A:

Column B: $\frac{5}{x}$

Possible Answers:

Quantity B is greater.

Quantity A is greater.

The quantities are equal.

The relationship cannot be determined from the information provided.

Correct answer:

The relationship cannot be determined from the information provided.

Explanation:

For quantitative comparison questions involving a shared variable between quantities, the best approach is to test a positive integer, a negative integer, and a fraction. Half of our work is eliminated, however, because the question stipulates that x > 0. We only need to check a positive integer and a positive fraction between 0 and 1. Plugging in 2, we see that quantity A is greater than quantity B. Checking 1/2, however, we find that quantity B is greater than quantity A. Thus the relationship cannot be determined.

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Example Question #2 :How To Find The Solution To An Inequality With Multiplication

If –1 <n< 1, all of the following could be true EXCEPT:

Possible Answers:

n²< n

n²< 2n

16n²- 1 = 0

(n-1)²> n

|n²- 1| > 1

Correct answer:

|n²- 1| > 1

Explanation:

N_part_1

N_part_2

N_part_3

N_part_4

N_part_5

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Example Question #3 :How To Find The Solution To An Inequality With Multiplication

(√(8) / -x ) < 2. Which of the following values could be x?

Possible Answers:

-1

-2

All of the answers choices are valid.

-4

-3

Correct answer:

-1

Explanation:

The equation simplifies to x > -1.41. -1 is the answer.

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Example Question #4 :How To Find The Solution To An Inequality With Multiplication

Solve forx

$\small 3x+7 \geq -2x+4$

Possible Answers:

$\small x \geq \frac{3}{5}$

$\small x \leq -\frac{3}{5}$

$\small x \geq -\frac{3}{5}$

$\small x \leq \frac{3}{5}$

Correct answer:

$\small x \geq -\frac{3}{5}$

Explanation:

$\small 3x+7 \geq -2x+4$

$\small 3x \geq -2x-3$

$\small 5x \geq -3$

$\small x\geq -\frac{3}{5}$

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Example Question #5 :How To Find The Solution To An Inequality With Multiplication

We have x^2-4<0 , find the solution set for this inequality.

Possible Answers:

x>2, x<-2

-2<x<2

x>-2

x=0

x<2

Correct answer:

-2<x<2

Explanation:

$x^2-4<0 \Rightarrow x^2<4 \Rightarrow -2<x<2$

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Example Question #6 :How To Find The Solution To An Inequality With Multiplication

Fill in the circle with either $<$ , $>$ , or $=$ symbols:

$(x-3)\circ\frac{x^2-9}{x+3}$ for $x\geq 3$ .

Possible Answers:

The rational expression is undefined.

$(x-3)> \frac{x^2-9}{x+3}$

$(x-3)< \frac{x^2-9}{x+3}$

$(x-3)=\frac{x^2-9}{x+3}$

None of the other answers are correct.

Correct answer:

$(x-3)=\frac{x^2-9}{x+3}$

Explanation:

$(x-3)\circ\frac{x^2-9}{x+3}$

Let us simplify the second expression. We know that:

$(x^2-9)=(x+3)(x-3)$

So we can cancel out as follows:

$\frac{x^2-9}{x+3}=\frac{(x+3)(x-3)}{(x+3)}=x-3$

$(x-3)=\frac{x^2-9}{x+3}$

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GRE Math : Inequalities

Study concepts, example questions & explanations for GRE Math

All GRE Math Resources

Example Questions

Example Question #1 :How To Find The Solution To An Inequality With Subtraction

Example Question #1 :How To Find The Solution To An Inequality With Subtraction

Example Question #3 :How To Find The Solution To An Inequality With Subtraction

Example Question #4 :How To Find The Solution To An Inequality With Subtraction

Example Question #1 :How To Find The Solution To An Inequality With Multiplication

Example Question #2 :How To Find The Solution To An Inequality With Multiplication

Example Question #3 :How To Find The Solution To An Inequality With Multiplication

Example Question #4 :How To Find The Solution To An Inequality With Multiplication

Example Question #5 :How To Find The Solution To An Inequality With Multiplication

Example Question #6 :How To Find The Solution To An Inequality With Multiplication

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