GMAT Math : Understanding real numbers

Study concepts, example questions & explanations for GMAT Math

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Example Questions

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Example Question #1 : Understanding Real Numbers

Solve \dpi{100} \small 2x-3> 0 for x.

Possible Answers:

\dpi{100} \small x< \frac{3}{2}

\dpi{100} \small x\leq \frac{3}{2}

\dpi{100} \small x\geq \frac{3}{2}

\dpi{100} \small x> \frac{-3}{2}

\dpi{100} \small x> \frac{3}{2}

Correct answer:

\dpi{100} \small x> \frac{3}{2}

Explanation:

\dpi{100} \small 2x-3> 0

Add 3 to both sides: \dpi{100} \small 2x> 3

Divide both sides by 2: \dpi{100} \small x> \frac{3}{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?

Possible Answers:

Correct answer:

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).

\small 80\ +\ 40\ +\ 60\ -\ 13\ =167

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

\small 200\ -\ 167\ =\ 33

Example Question #3 : Understanding Real Numbers

Which of the following expressions is equal to 

Possible Answers:

Correct answer:

Explanation:

 

Example Question #4 : Understanding Real Numbers

Given that , and , evaluate .

Possible Answers:

Not enough information is given to answer the question

Correct answer:

Explanation:

To find :

 ,

so 

Since 

and we choose the positive square root

Example Question #4 : 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?

Possible Answers:

\small 3(B+3)

\small 3B+3

\small \frac{B+3}{3}

\small 3(B+3)

\small \frac{B}{3}+3

\small 3B+3

Correct answer:

\small \frac{B}{3}+3

Explanation:

Today, \small C=\frac{B}{3}. In 3 years, \small C=\frac{B}{3}+3.

Example Question #5 : Understanding Real Numbers

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

Possible Answers:

Correct answer:

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 : Understanding Real Numbers

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

Possible Answers:

None of these can be prime.

Correct answer:

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.  

So the answer is

Example Question #8 : Real Numbers

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

Possible Answers:

125

-3

3

122

-122

Correct answer:

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 #6 : Understanding Real Numbers

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

Possible Answers:

Greater than

Not enough information given.

Correct answer:

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 #10 : Real Numbers

If \dpi{100} \small x\ and\ y are both negative, then \dpi{100} \small \frac{x+y}{-xy} could NOT be equal to.... 

 

Possible Answers:

\dpi{100} \small \frac{\sqrt{8}}{4}

\dpi{100} \small \frac{3}{4}

\dpi{100} \small 5

\dpi{100} \small -5

Correct answer:

\dpi{100} \small -5

Explanation:

\dpi{100} \small x+y is negative and \dpi{100} \small xy is positive

\dpi{100} \small \frac{Negative}{-Positive} = \frac{Negative}{Negative} = Positive

Therefore, the solution cannot be negative.

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