GRE Math : Algebra

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Example Questions

Example Question #5 : How To Find A Rational Number From An Exponent

Simplify

$2^{10}+2^9$

Possible Answers:

$2^9\cdot 3$

$2^{19}$

$2^{10}$

$2^{10}\cdot 3$

$2^{18}\cdot 3$

Correct answer:

$2^9\cdot 3$

Explanation:

Whenever you see lots of multiplication (e.g. exponents, which are notation for repetitive multiplication) separated by addition or subtraction, a common way to transform the expression is to factor out common terms on either side of the + or - sign. That allows you to create more multiplication, which is helpful in reducing fractions or in reducing the addition/subtraction to numbers you can quickly calculate by hand as you'll see here.

So let's factor a 2^9 .

We have 2^9(2+1) .

And you'll see that the addition inside parentheses becomes quite manageable, leading to the final answer of $2^9\cdot 3$ .

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Example Question #1 : How To Find Out When An Equation Has No Solution

y = 32

y = x^2 - 4

Quantity A: $\frac{y}{7}$

Quantity B:

Possible Answers:

The two quantities are equal.

The relationship cannot be determined from the information given.

Quantity B is greater.

Quantity A is greater.

Correct answer:

The relationship cannot be determined from the information given.

Explanation:

We are given that y = 32. Plug this value of y into the second equation.

32 = x² – 4

36 = x²

x = +/– 6.

Next find a value for Quantity A:

y/7 = 32/7

This number is less than +6, but more than –6. Thus, the relationship cannot be determined from the information given.

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Example Question #1 : Linear / Rational / Variable Equations

Column A: $\left | x \right |$

Column B: x^3

Possible Answers:

Column A is greater.

The relationship cannot be determined.

The values are equal.

Column B is greater.

Correct answer:

The relationship cannot be determined.

Explanation:

Column B is greater for positive numbers.

The columns are equal for 0.

Column A is greater for negative numbers.

Because our answer changes depending on the value inserted, we cannot determine the relationship.

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Example Question #1 : How To Find Out When An Equation Has No Solution

Find the solution to the following equation if x = 3:

y = (4x² - 2)/(9 - x²)

Possible Answers:

no possible solution

Correct answer:

no possible solution

Explanation:

Substituting 3 in for x, you will get 0 in the denominator of the fraction. It is not possible to have 0 be the denominator for a fraction so there is no possible solution to this equation.

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Example Question #2 : Linear / Rational / Variable Equations

Undefined_denom3

I. x = 0

II. x = –1

III. x = 1

Possible Answers:

I, II, and III

II only

III only

II and III only

I only

Correct answer:

I only

Explanation:

Undefined_denom2

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Example Question #1 : How To Find Out When An Equation Has No Solution

Nosol1

Possible Answers:

–1/2

There is no solution

–3

Correct answer:

There is no solution

Explanation:

Nosol2

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Example Question #3 : Linear / Rational / Variable Equations

$\small h\left ( x\right )=\frac{28}{x+4}$

$\small \textup{For which of the following values of}\,x\,\textup{is the above function undefined?}$

Possible Answers:

$\small 4$

$\small 0$

None of the other answers

$\small -4$

$\small 28$

Correct answer:

$\small -4$

Explanation:

A fraction is considered undefined when the denominator equals 0. Set the denominator equal to zero and solve for the variable.

$\small x+4=0$

$\small x=-4$

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Example Question #3 : How To Find Out When An Equation Has No Solution

Solve:

3(2x - 6) + 2x = 7x - 12

Possible Answers:

Correct answer:

Explanation:

First, distribute, making sure to watch for negatives.

3(2x - 6) + 2x = 7x - 12

6x - 18 + 2x = 7x - 12

Combine like terms.

8x - 18 = 7x - 12

Subtract 7x from both sides.

x - 18 = -12

Add 18 on both sides and be careful adding integers.

x = 6

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Example Question #411 : Algebra

Solve:

-3(2x - 5) = 9 - 6x

Possible Answers:

$\frac{15}{9}$

No Solution

Infinitely Many Solutions

Correct answer:

No Solution

Explanation:

First, distribute the to the terms inside the parentheses.

-3(2x - 5) = 9 - 6x

-6x + 15 = 9 - 6x

Add 6x to both sides.

15 = 9

This is false for any value of . Thus, there is no solution.

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Example Question #2 : How To Find Out When An Equation Has No Solution

Solve $\left | 3-4x\right |<0$ .

Possible Answers:

$x<\frac{4}{3}$

$x>\frac{3}{4}$

$x<\frac{3}{4}$

No solutions

$x>\frac{4}{3}$

Correct answer:

No solutions

Explanation:

By definition, the absolute value of an expression can never be less than 0. Therefore, there are no solutions to the above expression.

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GRE Math : Algebra

Study concepts, example questions & explanations for GRE Math

All GRE Math Resources

Example Questions

Example Question #5 : How To Find A Rational Number From An Exponent

Example Question #1 : How To Find Out When An Equation Has No Solution

Example Question #1 : Linear / Rational / Variable Equations

Example Question #1 : How To Find Out When An Equation Has No Solution

Example Question #2 : Linear / Rational / Variable Equations

Example Question #1 : How To Find Out When An Equation Has No Solution

Example Question #3 : Linear / Rational / Variable Equations

Example Question #3 : How To Find Out When An Equation Has No Solution

Example Question #411 : Algebra

Example Question #2 : How To Find Out When An Equation Has No Solution

All GRE Math Resources

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