# GMAT Math : Understanding real numbers

## Example Questions

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### Example Question #1 : Real Numbers

Solve  for x.

Explanation:

Divide both sides by 2:

### Example Question #1 : Real Numbers

Of 200 students, 80 take biology, 40 take chemistry, 60 take physics, 13 take two science courses, and no one takes three science courses. How many students are not taking a science course?

Explanation:

To calculate the number of students taking at least 1 science course, add the number of students who are taking each course and subtract the number of students who are taking 2 (to ensure they're not counting twice).

To calculate the number of students NOT taking a class, subtract this number by the total number of students.

### Example Question #3 : Real Numbers

Which of the following expressions is equal to

Explanation:

### Example Question #4 : Real Numbers

Given that , and , evaluate .

Not enough information is given to answer the question

Explanation:

To find :

,

so

Since

and we choose the positive square root

### Example Question #5 : Real Numbers

Today, Becky's age (B) is 3 times Charlie's age. In 3 years, what will Charlie's age be in terms of B?

Explanation:

Today, . In 3 years, .

### Example Question #6 : Real Numbers

Given that  and , what is the range of possible values for  ?

Explanation:

The lowest possible value of  is the lowest possible value of  divided by the highest possible value of

The highest possible value of  is the highest possible value of  divided by the lowest possible value of

### Example Question #7 : Real Numbers

If and  are composite integers, which of the following can be prime?

None of these can be prime.

Explanation:

so this is a composite number for all  and .

is by definition a composite number.

the product of 2 numbers.

This leaves just .  For a number to be prime, it must be odd (except for 2) so we need to have either or be odd (but not both).  The first composite odd number is 9.  .  The smallest composite number is 4. .

is a prime number.

### Example Question #1 : Real Numbers

If  is a real number, which of the following CANNOT be a value for x?

122

-122

125

-3

3

3

Explanation:

The definition of the set of real numbers is the set of all numbers that can fit into a/b where a and b are both integers and b does not equal 0.

So, since we see a fraction here, we know a non-real number occurs if the denominator is 0. Therefore we can find where the denominator is 0 by setting x-3 =0 and solving for x. In this case, x=3 would create a non-real number. Thus our answer is that x CANNOT be 3 for our expression to be a real number.

### Example Question #8 : Real Numbers

Let  be the product of integers from 18 to 33, inclusive. If , how many more unique prime factors does  have than ?

Greater than

Not enough information given.

Explanation:

This question does not require any calculation. Given that 32 (an even number) is a factor of , then 2 must be a prime factor. If  is then multiplied by 2 (to get ) then  has no additional unique prime factors (its only additional prime factor, 2, is NOT unique).

### Example Question #1 : Real Numbers

If  are both negative, then  could NOT be equal to....