All GMAT Math Resources
Example Question #1 : Understanding Real Numbers
Solve for x.
Add 3 to both sides:
Divide both sides by 2:
Example Question #2 : Understanding 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?
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 : Understanding Real Numbers
Which of the following expressions is equal to
Example Question #4 : Understanding Real Numbers
Given that , , and , evaluate .
Not enough information is given to answer the question
To find :
and we choose the positive square root
Example Question #5 : Understanding 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?
Today, . In 3 years, .
Example Question #6 : Real Numbers
Given that and , what is the range of possible values for ?
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 #6 : Understanding Real Numbers
If and are composite integers, which of the following can be prime?
None of these can be prime.
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.
So the answer is
Example Question #7 : Understanding Real Numbers
If is a real number, which of the following CANNOT be a value for x?
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 : Understanding Real Numbers
Let be the product of integers from 18 to 33, inclusive. If , how many more unique prime factors does have than ?
Not enough information given.
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 #10 : Real Numbers
If are both negative, then could NOT be equal to....
is negative and is positive
Therefore, the solution cannot be negative.