# GRE Math : GRE Quantitative Reasoning

## Example Questions

### Example Question #1 : How To Use Scientific Notation

The speed of light is approximately .

In scientific notation how many kilometers per hour is the speed of light?

Explanation:

For this problem we need to convert meters into kilometers and seconds into hours. Therefore we get,

Multiplying this out we get

### Example Question #11 : Gre Quantitative Reasoning

If one mile is equal to 5,280 feet, how many feet are 100 miles equal to in scientific notation?

Explanation:

100 miles = 528,000 feet. To put a number in scientific notation, we put a decimal point to the right of our first number, giving us 5.28. We then multiply by 10 to whatever power necessary to make our decimal equal the value we are looking for. For 5.28 to equal 528,000 we must multiply by 10^5.

### Example Question #12 : Gre Quantitative Reasoning

Explanation:

This question requires you to have an understanding of scientific notation. Begin by multiplying the two numbers:

To use scientific notation, the number to the left of the decimal has to be between 1 and 10. In this case, we are looking to move the decimal place until we are left with 9 on the left of the decimal. Count the number of places that the decimal will have to move. In this case, it is five. Therefore:

Note: The notation is raised to a negative power because we moved the decimal from left to right.

### Example Question #1 : How To Find Compound Interest

A five-year bond is opened with  in it and an interest rate of %, compounded annually. This account is allowed to compound for five years. Which of the following most closely approximates the total amount in the account after that period of time?

Explanation:

Each year, you can calculate your interest by multiplying the principle () by . For one year, this would be:

For two years, it would be:

, which is the same as

Therefore, you can solve for a five year period by doing:

Using your calculator, you can expand the  into a series of multiplications. This gives you , which is closest to

### Example Question #2 : How To Find Compound Interest

Jack has , to invest. If he invests two-thirds of it into a high-yield savings account with an annual interest rate of , compounded quarterly, and the other third in a regular savings account at  simple interest, how much does Jack earn after one year?

Explanation:

First, break the problem into two segments: the amount Jack invests in the high-yield savings, and the amount Jack invests in the simple interest account (10,000 and 5,000 respectively).

Now let's work with the high-yield savings account. $10,000 is invested at an annual rate of 8%, compounded quarterly. We can use the compound interest formula to solve: Plug in the values given: Therefore, Jack makes$824.32 off his high-yield savings account. Now let's calculate the other interest:

Add the two together, and we see that Jack makes a total of,  off of his investments.

### Example Question #1 : How To Find Compound Interest

If a cash deposit account is opened with  for a three year period at % interest compounded once annually, which of the following is closest to the positive difference between the interest accrued in the third year and the interest accrued in the second year?

Explanation:

It is easiest to break this down into steps. For each year, you will multiply by  to calculate the new value. Therefore, let's make a chart:

After year 1: ; Total interest:

After year 2: ; Let us round this to ; Total interest:

After year 3: ; Let us round this to ; Total interest:

Thus, the positive difference of the interest from the last period and the interest from the first period is:

### Example Question #11 : Algebra

Quantitative Comparison

Quantity A: x2

Quantity B: x3

The relationship cannot be determined from the information given.

Quantity A is greater.

The two quantities are equal.

Quantity B is greater.

The relationship cannot be determined from the information given.

Explanation:

Let's pick numbers. For quantitative comparisons with exponents, it's good to try 0, a negative number, and a fraction.

0: 02 = 0, 03 = 0, so the two quantities are equal.

–1: (–1)2 = 1, (–1)3 = –1, so Quantity A is greater.

### Example Question #12 : Algebra

If , then which of the following must also be true?

Explanation:

We know that the expression must be negative. Therefore one or all of the terms x7, y8 and z10 must be negative; however, even powers always produce positive numbers, so y8 and z10 will both be positive. Odd powers can produce both negative and positive numbers, depending on whether the base term is negative or positive. In this case, x7 must be negative, so x must be negative. Thus, the answer is x < 0.

### Example Question #1 : How To Find Patterns In Exponents

Which quantity is the greatest?

Quantity A

Quantity B

The realationship cannot be determined from the information given.

Quantity B is greater.

Quantity A is greater.

The two quantities are equal.

Quantity A is greater.

Explanation:

First rewrite quantity B so that it has the same base as quantity A.

can be rewriten as , which is equivalent to .

Now we can compare the two quantities.

is greater than .

### Example Question #4 : How To Find Patterns In Exponents

Simplify the following:

Explanation:

With problems like this, it is always best to break apart your values into their prime factors. Let's look at the numerator and the denominator separately:

Numerator

Continuing the simplification:

Now, these factors have in common a . Factor this out:

Denominator

This is much simpler: