GRE Math : Expressions

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Example Question #31 : How To Evaluate Algebraic Expressions

Compare $\textup{Quantity A and B}$ and determine which number is larger.

$\textup{Quantity A}$ : Number of minutes in a week.

$\textup{Quantity B}$ : Number of hours in a leap year.

Possible Answers:

$\textup{Can't be determined by the information provided.}$

$\textup{The two quantities are equal.}$

$\textup{Quantity B}$

$\textup{Quantity A}$

Correct answer:

$\textup{Quantity A}$

Explanation:

To solve this problem, we must figure out the values of $\textup{Quantity A and B}$ .

Quantity A is equivalent to the number of minutes in a week. There are 7 days in a week, 24 hours in a day, and 60 mins to an hour.

$1\textup{ week}*7\frac{\textup{days}}{\textup{week}}*24\frac{\textup{hours}}{\textup{day}}*60\frac{\textup{mins}}{\textup{hour}}=10\textup{,}080$ .

Quantity B is equivalent to the number of horus in a leap year. There are 366 days in a leap year and 24 hours a day.

$1\textup{ year}*366\frac{\textup{days}}{\textup{year}}*24\frac{\textup{hours}}{\textup{day}}=8784$

Because $\textup{10,080}$ is larger than 8784 , $\textup{Quantity A}$ is larger.

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Example Question #31 : Evaluating Expressions

Compare the two quantities and determine which are larger.

$\textup{Quantity A}$ : The distance between $(4\textup{,}2)$ and $(6\textup{,}8)$

$\textup{Quantity B}$ : The distance between $(-5\textup{,}-2)$ and $(-3\textup{,}0)$

Possible Answers:

$\textup{Quantity B is larger.}$

$\textup{Quantity A is larger.}$

$\textup{The two quantities are equal.}$

$\textup{Can't be determined by the information provided.}$

Correct answer:

$\textup{Quantity A is larger.}$

Explanation:

To solve this problem we must make use of the quadratic formula.

$\textup{Quantity A}$ is the distance between the points $\left ( 4\textup{,}2\right )$ and $\left ( 6\textup{,}8\right )$ . The two points are separated by units horizontally and units vertically.

Using the quadratic formula x^2+y^2=z^2 we find that the distance between the two points of $\textup{Quantity A}$ is

2^2+6^2=z^2

z^2=40

$z=\sqrt{40}=2\sqrt{10}$

Quantity B is the distance between the points $\textup{(-5,-2)}$ and $(-3\textup{,}0)$ .

The two points of Quantity B are seperated by 2 units horizontally and 2 units vertically.

Using the quadratic formula x^2+y^2=z^2 we find that the distance between the two points of Quantity B is

2^2+2^2=z^2

z^2=8

$z=\sqrt{8}=2\sqrt{2}$

Comparing the two distances, $2\sqrt{10}>2\sqrt{2}$ , therefore Quantity A is larger than Quantity B.

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Example Question #31 : How To Evaluate Algebraic Expressions

Compare $\textup{Quantity A and B}$ and determine which is larger.

$\textup{Quantity A}$ : The sum of the factors of x^2+3x-4

$\textup{Quantity B}$ : The sum of the factors of x^2+4x+4

Possible Answers:

$\textup{Can't be determined by the information provided.}$

$\textup{Quantity A is larger.}$

$\textup{The two quantities are equal.}$

$\textup{Quantity B is larger.}$

Correct answer:

$\textup{Quantity B is larger.}$

Explanation:

To solve this problem we must solve for $\textup{Quantity A and B}$ .

Quantity A is the sum of the factors of x^2+3x-4 .

x^2+3x-4=(x+4)(x-1)

(x+4)+(x-1)=2x+3

Quantity B is the sum of the factors of x^2+4x+4 .

x^2+4x+4=(x+2)(x+2)

(x+2)+(x+2)=2x+4

2x+4 will always be greater than 2x+3 . Therefore Quantity B is larger than Quantity A.

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Example Question #71 : Expressions

Determine whether $\textup{Quantity A or B}$ is larger.

$\textup{Quantity A: 30\% of 7}$

$\textup{Quantity B: 2.5}$

Possible Answers:

$\textup{Can't be determined by the information provided.}$

$\textup{Both quantities are equal.}$

$\textup{Quantity B is larger.}$

$\textup{Quantity A is larger.}$

Correct answer:

$\textup{Quantity B is larger.}$

Explanation:

To solve this we must solve for $\textup{Quantity A}$ .

$\textup{30\% of 7}$ is equivalent to 2.1 . Because 2.5 is larger than 2.1 , $\textup{Quantity B is larger than Quantity A}$ .

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Example Question #31 : How To Evaluate Algebraic Expressions

A $\textup{20 inch}$ candle that burns for $\textup{5 minutes}$ is now $\textup{12 inches}$ long.

Compare $\textup{Quantity A and Quantity B}$ and determine which is greater.

$\textup{Quantity A}$ : The number of minutes it would take the entire candle to burn.

$\textup{Quantity B}$ : $\textup{13 minutes}$

Possible Answers:

$\textup{The two quantities are equal.}$

$\textup{Quantity B is larger.}$

$\textup{Quantity A is larger.}$

$\textup{Can't be determined by the information given.}$

Correct answer:

$\textup{Quantity B is larger.}$

Explanation:

Because it took $\textup{5 minutes}$ for the candle to decrease in size by $\textup{8 inches}$ , in order for the entire candle to burn out, we divide the total size of the candle by $\textup{8 inches}$ and multiply by $\textup{5 minutes}$ .

$\frac{20 \textup{ inches}}{8\textup{ inches}}*5\textup{ minutes}=12.5\textup{ minutes}$ . Therefore Quantity B is larger than Quantity A.

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Example Question #36 : How To Evaluate Algebraic Expressions

Compare the two quantities and determine which is larger.

x^2-6x+8

$\textup{Quantity A: Twice the sum of the roots of the equation.}$

$\textup{Quantity B: 12}$

Possible Answers:

$\textup{The two quantities are equal.}$

$\textup{Quantity A is larger.}$

$\textup{Quantity B is larger.}$

$\textup{Can't be determined by the information provided.}$

Correct answer:

$\textup{The two quantities are equal.}$

Explanation:

The equation x^2-6x+8 can be factored down to (x-4)(x-2) . Therefore the roots of the equation are $\textup{4 and 2}$ . Twice the sum of these roots is equal to , therefore the two quantities are equivalent.

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Example Question #37 : How To Evaluate Algebraic Expressions

A convinence store purchases coke cans at $\textup{50 cents}$ each and sells them for $50\%$ above cost.

Compare the two quantities are determine which is greater.

$\textup{Quantity A: 15 cents}$

$\textup{Quantity B: Profit the store makes on each can.}$

Possible Answers:

$\textup{Quantity A is larger.}$

$\textup{Can't be determined by the information provided.}$

$\textup{Quantity B is larger.}$

$\textup{The two quantities are equivalent.}$

Correct answer:

$\textup{Quantity B is larger.}$

Explanation:

$\textup{Quantity A}$ is simply $\textup{15 cents}$ . $\textup{Quantity B}$ is the profit the store makes on each can. Because the store buys the cans for $\textup{50 cents}$ and sells them for $50\%$ above cost, this means the can sells the $50\textup{ cents}*150\%=75\textup{ cents}$ . Therefore the store profits $\textup{25 cents}$ per can, meaning that Quantity B is larger than Quantity A.

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Example Question #31 : How To Evaluate Algebraic Expressions

0<x<1

Determine which quantity is larger.

$\textup{Quantity A: }x$

$\textup{Quantity B: }x^2$

Possible Answers:

$\textup{The quantities are equivalent.}$

$\textup{Quantity A is larger.}$

$\textup{Can't be determined by the information provided.}$

$\textup{Quantity B is larger.}$

Correct answer:

$\textup{Quantity A is larger.}$

Explanation:

A cruious thing happens with you try to square numbers less than but greater than . The numbers actually become smaller!

0.5^2=0.25 . etc....

Therefore Quantity A is larger than Quantity B when 0<x<1

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Example Question #39 : How To Evaluate Algebraic Expressions

houses have a total valuation of $\$750,000$ in 2014. In 2015, two of the houses decreased in value by $\$50,000$ , one of the houses increased in value by $\$100,000$ and the rest of the houses remained the same price.

Determine which quantity is larger.

$\textup{Quantity A: The change in the standard deviation of price of the 5 houses from 2014-2015}$

$\textup{Quantity B: \$40000}$

Possible Answers:

$\textup{Quantity A is larger.}$

$\textup{The two quantities are equivalent.}$

$\textup{Can't be determined by the information provided.}$

$\textup{Quantity B is larger.}$

Correct answer:

$\textup{Can't be determined by the information provided.}$

Explanation:

Standard deviation for the house prices is the is the amount of variance for the houses. Because we aren't given the prices of the houses, we have no idea what the standard deviation could be. The houses could have been priced so that of the houses cost $\$1$ each and the last two hosues cost the remaining $\$749,997$ combined. This would make the standard deviation huge. The houses could also have been priced $\$150,000$ each, meaning that the standard deviation for that year would be . It is impossible to determine which quantity is larger based on the information provided.

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Example Question #71 : Expressions

x^2+x=2

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:

The relationship cannot be determined.

Explanation:

Since there is an x^2 term in the equation

x^2+x=2

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

Rewrite it so that it is set equal to zero:

x^2+x-2=0

For an equation of the form

ax^2+bx+c=0

The solutions for can be found using the quadratic formula:

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

Quantity A:

$x_{1,2}=\frac{-1 \pm \sqrt{1^2-4(1)(-2)}}{2(1)}=\frac{-1 \pm \sqrt9}{2}=1,-2$

Since could be positive or negative, the relationship cannot be determined.

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GRE Math : Expressions

Study concepts, example questions & explanations for GRE Math

All GRE Math Resources

Example Questions

Example Question #31 : How To Evaluate Algebraic Expressions

Example Question #31 : Evaluating Expressions

Example Question #31 : How To Evaluate Algebraic Expressions

Example Question #71 : Expressions

Example Question #31 : How To Evaluate Algebraic Expressions

Example Question #36 : How To Evaluate Algebraic Expressions

Example Question #37 : How To Evaluate Algebraic Expressions

Example Question #31 : How To Evaluate Algebraic Expressions

Example Question #39 : How To Evaluate Algebraic Expressions

Example Question #71 : Expressions

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