### All GRE Math Resources

## Example Questions

### Example Question #31 : How To Evaluate Algebraic Expressions

Compare and determine which number is larger.

: Number of minutes in a week.

: Number of hours in a leap year.

**Possible Answers:**

**Correct answer:**

To solve this problem, we must figure out the values of .

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.

.

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.

Because is larger than , is larger.

### Example Question #32 : How To Evaluate Algebraic Expressions

Compare the two quantities and determine which are larger.

: The distance between and

: The distance between and

**Possible Answers:**

**Correct answer:**

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

is the distance between the points and . The two points are separated by units horizontally and units vertically.

Using the quadratic formula we find that the distance between the two points of is

Quantity B is the distance between the points and .

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

Using the quadratic formula we find that the distance between the two points of Quantity B is

Comparing the two distances,, therefore Quantity A is larger than Quantity B.

### Example Question #33 : How To Evaluate Algebraic Expressions

Compare and determine which is larger.

: The sum of the factors of

: The sum of the factors of

**Possible Answers:**

**Correct answer:**

To solve this problem we must solve for .

Quantity A is the sum of the factors of .

Quantity B is the sum of the factors of .

will always be greater than . Therefore Quantity B is larger than Quantity A.

### Example Question #34 : How To Evaluate Algebraic Expressions

Determine whether is larger.

**Possible Answers:**

**Correct answer:**

To solve this we must solve for .

is equivalent to . Because is larger than , .

### Example Question #35 : How To Evaluate Algebraic Expressions

A candle that burns for is now long.

Compare and determine which is greater.

: The number of minutes it would take the entire candle to burn.

:

**Possible Answers:**

**Correct answer:**

Because it took for the candle to decrease in size by , in order for the entire candle to burn out, we divide the total size of the candle by and multiply by .

. Therefore Quantity B is larger than Quantity A.

### Example Question #36 : How To Evaluate Algebraic Expressions

Compare the two quantities and determine which is larger.

**Possible Answers:**

**Correct answer:**

The equation can be factored down to . Therefore the roots of the equation are . Twice the sum of these roots is equal to , therefore the two quantities are equivalent.

### Example Question #37 : How To Evaluate Algebraic Expressions

A convinence store purchases coke cans at each and sells them for above cost.

Compare the two quantities are determine which is greater.

**Possible Answers:**

**Correct answer:**

is simply . is the profit the store makes on each can. Because the store buys the cans for and sells them for above cost, this means the can sells the . Therefore the store profits per can, meaning that Quantity B is larger than Quantity A.

### Example Question #38 : How To Evaluate Algebraic Expressions

Determine which quantity is larger.

**Possible Answers:**

**Correct answer:**

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

. etc....

Therefore Quantity A is larger than Quantity B when

### Example Question #39 : How To Evaluate Algebraic Expressions

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

Determine which quantity is larger.

**Possible Answers:**

**Correct answer:**

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 each and the last two hosues cost the remaining combined. This would make the standard deviation huge. The houses could also have been priced 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.

### Example Question #40 : How To Evaluate Algebraic Expressions

Quantity A:

Quantity B:

**Possible Answers:**

The relationship cannot be determined.

Quantity A is greater.

Quantity B is greater.

The two quantities are equal.

**Correct answer:**

The relationship cannot be determined.

Since there is an term in the equation

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

Rewrite it so that it is set equal to zero:

For an equation of the form

The solutions for can be found using the quadratic formula:

Quantity A:

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