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 #71 : Evaluating Expressions

For any integer $x \neq 4$ , x@=x-4

Quantity A: $\frac{10@}{5@}$

Quantity B: $(\frac{10}{5})@$

Possible Answers:

Quantity A is greater.

The relationship cannot be determined.

The two quantities are equal.

Quantity B is greater.

Correct answer:

Quantity A is greater.

Explanation:

To solve this problem, use the property x@=x-4 to evaluate each quantity:

Quantity A:

$\frac{10@}{5@}=\frac{10-4}{5-4}=\frac{6}{1}=6$

Quantity B:

$(\frac{10}{5})@=2@=2-4=-2$

Quantity A is greater.

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Example Question #72 : How To Evaluate Algebraic Expressions

Jason can run miles in hours. How many miles will Jason run in minutes?

Possible Answers:

$\frac{9s}{8r}$

$\frac{120s}{r}$

$\frac{r}{2s}$

$\frac{2s}{r}$

$\frac{8r}{9s}$

Correct answer:

$\frac{2s}{r}$

Explanation:

First, create an expression for Jason's running speed. If he runs miles in hours, his speed is

$\frac{3s}{2r}\frac{miles}{hour}$

Now convert the time spent running to hours minutes:

$80minutes\frac{1hour}{60minutes}=\frac{80}{60}hour=\frac{4}{3}hour$

Now to find the distance travelled, mutiply his speed by the time spent running:

$\frac{3s}{2r}\frac{miles}{hour}(\frac{4}{3}hour)=\frac{2s}{r}$

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Example Question #72 : Evaluating Expressions

For any pair of numbers and , a@b=a^2b-b .

What is (3@2)@4 ?

Possible Answers:

716

1020

804

320

Correct answer:

1020

Explanation:

To solve this problem, utilize the property a@b=a^2b-b , starting with the terms in the parenthesis:

(3@2)=3^2(2)-2=18-2=16

(3@2)@4=16@4=16^2(4)-4=1024-4=1020

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Example Question #112 : Expressions

For two numbers and $a@b=b-\frac{b}{a}$ . What is 3@(4@8) ?

Possible Answers:

Correct answer:

Explanation:

To solve this problem, use the $a@b=b-\frac{b}{a}$ starting with the term in the parenthesis:

$(4@8)=8-\frac{8}{4}=8-2=6$

$3@(4@8)=3@6=6-\frac{6}{3}=6-2=4$

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Example Question #112 : Expressions

xy^2z>0

xyz^2<0

Quantity A:

Quantity B:

Possible Answers:

The two quantities are equal.

Quantity B is greater.

Quantity A is greater.

The relationship cannot be determined.

Correct answer:

The relationship cannot be determined.

Explanation:

Consider the condtions we're given:

xy^2z>0

xyz^2<0

Because neither of these are zero, $x,y,z \neq 0$

Now we must consider the signs of each variable.

Looking at

xy^2z>0

We know that as a square, y^2>0 , even if the sign of is unknown.

This means that xz>0 as well. Although the signs of and are unknown, we know that they must share the same sign.

Now consider xyz^2<0

z^2>0

So xy<0 , meaning and have opposite signs. However, since we cannot make a definite statement about either, the signs remain unknown.

The relationship cannot be determined.

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Example Question #392 : Gre Quantitative Reasoning

xy^2z^2>0

xy^2z<0

Quantity A:

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:

Consider the parameters

xy^2z^2>0

xy^2z<0

Since these are not zero, $x,y,z \neq 0$

Looking at xy^2z^2>0

Squares of non-zero real values are positive, so

y^2,z^2>0

This means that x>0

Now consider xy^2z<0

Again, y^2>0

This means that

xz<0

Since x>0

It must mean that

z<0

Quantity A is greater.

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Example Question #77 : How To Evaluate Algebraic Expressions

x=3y+4

x+y=-8

Quantity A:

Quantity B:

Possible Answers:

Quantity B is greater.

Quantity A is greater.

The two quantities are equal.

The relationship cannot be determined.

Correct answer:

Quantity A is greater.

Explanation:

To solve this problem, solve for and

We have the system of equations

x=3y+4

x+y=-8

Rewrite them so that the variables are on one side of the equation and the numbers are on the other:

x-3y=4

x+y=-8

Now, subtract the bottom equation from the top equation:

(x-3y)-(x+y)=4-(-8)

-4y=12

y=-3

Plut this value back into the bottom equation:

x-3=-8

x=-5

Now consider the quantities:

Quantity A: x=-5

Quantity B: 2y=2(-3)=-6

Quantity A is greater.

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Example Question #392 : Gre Quantitative Reasoning

xy=15

Quantity A: (4x)(2y)

Quantity B: 110

Possible Answers:

Quantity B is greater.

The two quantities are equal.

The relationship cannot be determined.

Quantity A is greater.

Correct answer:

Quantity A is greater.

Explanation:

This problem essentially requires finding the value of Quantity A.

Do not trouble yourself with finding the individual values of and .

Rather, multiply out the terms:

(4x)(2y)=8xy

We're told that xy=15 , therefore

8xy=8(xy)=8(15)=120

Quantity A is greater.

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Example Question #75 : Evaluating Expressions

Take the expression x@y to be equivalent to the expression x(x-2y) . What does the expression $x\ @\left ( y\ @\ x\right)$ represent?

Possible Answers:

x-y-xy

xy-2x^2

x^2-2xy^2+4x^2y

2x^2-2xy^2+2x^2y

2x^2+2xy^2-2x^2y

Correct answer:

x^2-2xy^2+4x^2y

Explanation:

To approach tihs problem, note that if x@y is equivalent to the expression x(x-2y) , then y@x=y(y-2x)

Let's replace that complex function with a single variable:

y@x=y(y-2x)=q

Now we can rewrite x@y@x as x@q=x(x-2q)

Now plug in the value for

x@y@x=x(x-2y(y-2x))=x(x-2y^2+4xy)=x^2-2xy^2+4x^2y

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Example Question #391 : Algebra

If the sum of two consecutive even integers is and the difference of their squares is 188 , what is the smaller integer?

Possible Answers:

Correct answer:

Explanation:

In this problem we're given two pieces of information; however, consider how much we need to utilize.

We're told that the sum of two consecutive even integers is . Writing that in mathematical terms:

x+(x+2)=94

2x+2=94

2x=92

x=46

The two integers are and .

Note that we could confirm this with the other piece of information regarding the difference of squares:

(x+2)^2-x^2=188

x^2+4x+4-x^2=188

4x+4=188

4x=184

x=46

However, there is no need to do this; it's better to save time by only utilizing as much information is needed.

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GRE Math : Algebra

Study concepts, example questions & explanations for GRE Math

All GRE Math Resources

Example Questions

Example Question #71 : Evaluating Expressions

Example Question #72 : How To Evaluate Algebraic Expressions

Example Question #72 : Evaluating Expressions

Example Question #112 : Expressions

Example Question #112 : Expressions

Example Question #392 : Gre Quantitative Reasoning

Example Question #77 : How To Evaluate Algebraic Expressions

Example Question #392 : Gre Quantitative Reasoning

Example Question #75 : Evaluating Expressions

Example Question #391 : Algebra

All GRE Math Resources

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