GRE Math : Algebra

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13 Diagnostic Tests 452 Practice Tests Question of the Day Flashcards Learn by Concept

Example Questions

Example Question #361 : Gre Quantitative Reasoning

x^2-7x=-6

Quantity A:

Quantity B:

Possible Answers:

Quantity A is greater.

Quantity B is greater.

The two quantities are equal.

The relationship cannot be determined.

Correct answer:

Quantity A is greater.

Explanation:

Since there is an x^2 term in the equation

x^2-7x=-6

We must acknowledge the possibility of multiple values that satisfy the equation.

Rewrite it so that it is set equal to zero:

x^2-7x+6

For an equation of the form

ax^2+bx+c=0

The solutions for can be found using the quadratic formula:

$x_{1,2}=\frac{-b \pm \sqrt{b^2-4ac}}{2a}$

$x_{1,2}=\frac{-(-7) \pm \sqrt{(-7)^2-4(1)(6)}}{2(1)}=\frac{7 \pm \sqrt{25}}{2(1)}=1,6$

Quantity A:

Since this is , it can have the values of or . Both are bigger than

Quantity A is greater.

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Example Question #361 : Gre Quantitative Reasoning

x^2+3x=10

Quantity A: x^2

Quantity B:

Possible Answers:

Quantity A is greater.

Quantity B is greater.

The two quantities are equal.

The relationship cannot be determined.

Correct answer:

The relationship cannot be determined.

Explanation:

Since there is an x^2 term in the equation

x^2+3x=10

We must acknowledge the possibility of multiple values that satisfy the equation.

Rewrite it so that it is set equal to zero:

x^2+3x-10=0

For an equation of the form

ax^2+bx+c=0

The solutions for can be found using the quadratic formula:

$x_{1,2}=\frac{-b \pm \sqrt{b^2-4ac}}{2a}$

$x_{1,2}=\frac{-3 \pm \sqrt{3^2-4(1)(-10)}}{2(1)}=\frac{-3 \pm \sqrt49}{2}=2,-5$

Quantity A:

The two possible values are $2^2,(-5)^2\rightarrow 4,25$ . Only one of them is greater than five.

The relationship cannot be determined.

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Example Question #362 : Gre Quantitative Reasoning

x^2+5x+6=0

Quantity A:

Quantity B: 1.5

Possible Answers:

The relationship cannot be determined.

Quantity A is greater.

Quantity B is greater.

The two quantities are equal.

Correct answer:

Quantity B is greater.

Explanation:

Since there is an x^2 term in the equation

x^2+5x+6=0

We must acknowledge the possibility of multiple values that satisfy the equation.

For an equation of the form

ax^2+bx+c=0

The solutions for can be found using the quadratic formula:

$x_{1,2}=\frac{-b \pm \sqrt{b^2-4ac}}{2a}$

$x_{1,2}=\frac{-5 \pm \sqrt{5^2-4(1)(6)}}{2(1)}=\frac{-5\pm \sqrt1}{2}=-2,-3$

Both roots are negative.

Quantity B is greater.

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Example Question #44 : How To Evaluate Algebraic Expressions

At a store, pasta is sold in three sizes. A large box costs the same as four medium boxes or eight small boxes. If James buys an equal amount of large and medium boxes of pasta for the price needed to buy one hundred small boxes, how many medium boxes of pasta does he buy?

Possible Answers:

Correct answer:

Explanation:

To approach this problem, assign variables. Since one large box equals four medium boxes or eight small boxes in price

L=4M

L=8S

From this we can say that

4M=8S

or that

M=2S

We're told that James buys an equal number of large and medium boxes, and that the total price is equal to that of 100 small boxes:

xL+xM=100S

x(L+M)=100S

Rewrite this equation in terms of just the price of small boxes:

x(8S+2S)=100S

x(10S)=100S

x=10

James buys ten medium and ten large boxes of large pasta.

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Example Question #363 : Gre Quantitative Reasoning

When the integer is multiplied by , the result is more than times the integer . What is a-3b ?

Possible Answers:

$-\frac{8}{5}$

$\frac{5}{8}$

$-\frac{5}{8}$

$\frac{8}{5}$

Correct answer:

$\frac{5}{8}$

Explanation:

The key is to write the problem into mathematical terms.

We're told

"When the integer is multiplied by , the result is more than times the integer ."

Breaking this down piece by piece:

When the integer is multiplied by :

When the integer is multiplied by , the result is :

8a=

When the integer is multiplied by , the result is more than:

8a=5+

When the integer is multiplied by , the result is more than times the integer :

8a=5+24b

Now, solve this for

$a=3b+\frac{5}{8}$

$a-3b=(3b+\frac{5}{8})-3b=\frac{5}{8}$

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Example Question #364 : Gre Quantitative Reasoning

x^2-7x=-12

Quantity A:

Quantity B:

Possible Answers:

The two quantities are equal.

The relationship cannot be determined.

Quantity B is greater.

Quantity A is greater.

Correct answer:

The relationship cannot be determined.

Explanation:

Since there is an x^2 term in the equation

x^2-7x=-12

We must acknowledge the possibility of multiple values that satisfy the equation.

Rewrite it so that it is set equal to zero:

x^2-7x+12=0

For an equation of the form

ax^2+bx+c=0

The solutions for can be found using the quadratic formula:

$x_{1,2}=\frac{-b \pm \sqrt{b^2-4ac}}{2a}$

$x_{1,2}=\frac{-(-7) \pm \sqrt{(-7)^2-4(1)(12)}}{2(1)}=\frac{7\pm \sqrt{1}}{2}=3,4$

Quantity A can be either three or four. Since one of these is equal to Quantity B while the other is greater, the relationship cannot be determined.

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Example Question #81 : Expressions

When the integer is multiplied by , the result is thrice the difference of and times the integer . What is the value of $\frac{1}{3}a+3b$ ?

Possible Answers:

Correct answer:

Explanation:

To approach this problem, write out the problem statement in mathematical terms.

We're told

"When the integer is multiplied by , the result is thrice the difference of and times the integer ."

Write this out step by step.

When the integer is multiplied by :

When the integer is multiplied by , the result is:

2a=

When the integer is multiplied by , the result is thrice:

2a=3()

When the integer is multiplied by , the result is thrice the difference:

2a=3(-)

When the integer is multiplied by , the result is thrice the difference of :

2a=3(4-)

When the integer is multiplied by , the result is thrice the difference of and times the integer :

2a=3(4-6b)

Now, solve for

a=6-9b

$\frac{1}{3}a+3b=\frac{1}{3}(6-9b)+3b=2-3b+3b=2$

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Example Question #47 : How To Evaluate Algebraic Expressions

x^2-8x=-12

Quantity A:

Quantity B:

Possible Answers:

Quantity A is greater.

Quantity B is greater.

The two quantities are equal.

The relationship cannot be determined.

Correct answer:

Quantity A is greater.

Explanation:

Since there is an x^2 term in the equation

x^2-8x=-12

We must acknowledge the possibility of multiple values that satisfy the equation.

Rewrite it so that it is set equal to zero:

x^2-8x+12=0

For an equation of the form

ax^2+bx+c=0

The solutions for can be found using the quadratic formula:

$x_{1,2}=\frac{-b \pm \sqrt{b^2-4ac}}{2a}$

$x_{1,2}=\frac{-(-8) \pm \sqrt{(-8)^2-4(1)(12)}}{2(1)}=\frac{8\pm \sqrt{16}}{2}=2,6$

Both possible values for Quantity A are greater than

Quantity A is greater.

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Example Question #365 : Gre Quantitative Reasoning

$x \neq 0, -1$

Take the expression x@y to be equivalent to $\frac{x}{y}+x$ . What is the expression x^3@x^2@x equivalent to?

Possible Answers:

$\frac{x^2+x +1}{x^3+1}$

$\frac{x^3+x^2+x}{x+1}$

$\frac{x^4+x^3+x^2}{x^3+1}$

$\frac{x^4+x^3+x^2}{x+1}$

$\frac{x^2+x+1}{x+1}$

Correct answer:

$\frac{x^4+x^3+x^2}{x+1}$

Explanation:

When considering x^3@x^2@x , begin at the right of the equation. Since

x@y is equivalent to $\frac{x}{y}+x$ , x^2@x must be equivalent to

$\frac{x^2}{x}+x^2=x+x^2$

Now we need only consider x^3@(x+x^2)

$\frac{x^3}{x+x^2}+x^3=\frac{x^2}{1+x}+x^3=\frac{x^2+x^3(1+x)}{1+x}$

$\frac{x^4+x^3+x^2}{x+1}$

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Example Question #366 : Gre Quantitative Reasoning

x^2-11x=-10

Quantity A: |x-5|

Quantity B:

Possible Answers:

The two quantities are equal.

The relationship cannot be determined.

Quantity A is greater.

Quantity B is greater.

Correct answer:

Quantity A is greater.

Explanation:

Since there is an x^2 term in the equation

x^2-11x=-10

We must acknowledge the possibility of multiple values that satisfy the equation.

Rewrite it so that it is set equal to zero:

x^2-11x+10=0

For an equation of the form

ax^2+bx+c=0

The solutions for can be found using the quadratic formula:

$x_{1,2}=\frac{-b \pm \sqrt{b^2-4ac}}{2a}$

$x_{1,2}=\frac{-(-11) \pm \sqrt{(-11)^2-4(1)(10)}}{2(1)}=\frac{11 \pm \sqrt{81}}{2}=1,10$

Since there are two roots for x, Quantity A has two possible values:

|1-5|=|-4|=4;|10-5|=|5|=5

Both of these are greater than .

Quantity A is greater.

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All GRE Math Resources

13 Diagnostic Tests 452 Practice Tests Question of the Day Flashcards Learn by Concept

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GRE Math : Algebra

Study concepts, example questions & explanations for GRE Math

All GRE Math Resources

Example Questions

Example Question #361 : Gre Quantitative Reasoning

Example Question #361 : Gre Quantitative Reasoning

Example Question #362 : Gre Quantitative Reasoning

Example Question #44 : How To Evaluate Algebraic Expressions

Example Question #363 : Gre Quantitative Reasoning

Example Question #364 : Gre Quantitative Reasoning

Example Question #81 : Expressions

Example Question #47 : How To Evaluate Algebraic Expressions

Example Question #365 : Gre Quantitative Reasoning

Example Question #366 : Gre Quantitative Reasoning

All GRE Math Resources

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