# GRE Math : How to evaluate algebraic expressions

## 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.

Explanation:

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

Explanation:

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

Explanation:

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.

Explanation:

To solve this we must solve for .

is equivalent to .  Because  is larger than , .

### Example Question #351 : Algebra

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.

Explanation:

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.

Explanation:

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.

Explanation:

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.

Explanation:

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.

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  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:

The relationship cannot be determined.

The two quantities are equal.

Quantity A is greater.

Quantity B is greater.

The relationship cannot be determined.

Explanation:

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.

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