GMAT Math : Fractions

Study concepts, example questions & explanations for GMAT Math

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Example Questions

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Example Question #31 : Fractions

Simplify the following expression: 

Possible Answers:

Correct answer:

Explanation:

In order to simplify , we must remember that dividing by a fraction is the same as multiplying by its reciprocal. Therefore:

 

Example Question #32 : Fractions

When positive integer  is divided by 16, the remainder is 15. What is the remainder when  is divided by 8 ?

Possible Answers:

Correct answer:

Explanation:

We can set up the following equation from what we are told in the question:  where  is the quotient, then we divide  by 8:  or . From there we can  see that  will yield a remainder of , which is our final answer.

Example Question #33 : Fractions

Simplify the following expression: 

Possible Answers:

Correct answer:

Explanation:

In order to simplify the expression , let's first change the terms to reflect a common denominator:

Example Question #1941 : Problem Solving Questions

When positive integer  is divided by 12, the remainder is 7. What is the remainder when  is divided by 3?

Possible Answers:

Correct answer:

Explanation:

The remainder cannot be greater or equal to the divisor, so we can already eliminate 3, 4 and 5. Then, we can set up an equation with the given information. We know that when  is divided by 12, the remainder is 7 : , where  is the quotient. So, let's try to divide  by 3 and we get :  or . Therefore, the remainder must be one, since when 7 is divided by 3, the remainder is .

Example Question #34 : Fractions

 and  are positive integers and . What is the remainder?

Possible Answers:

Correct answer:

Explanation:

We are told that . In other words, the remainder  can be expressed as follows: 

 or 

If we simplify, we get .

Therefore, we can see that  is a multiple of . The only possible multiple of  in the answer choice is .

Example Question #32 : Fractions

What is  ?

Possible Answers:

Does not exist 

Correct answer:

Explanation:

Here we can be tempted to answer that the answer does not exist since there can be no division by 0; however, , or in other words, the factorial of 0 is 1. Therefore, the final answer is given by  or .

Example Question #1942 : Problem Solving Questions

 of a number, , is . What is ?

Possible Answers:

Correct answer:

Explanation:

We can solve this problem by setting up our equation and solving for the number, :

Example Question #1943 : Problem Solving Questions

 of a number, , is . What is the value of ?

Possible Answers:

Correct answer:

Explanation:

Example Question #33 : Fractions

Solve: 

Possible Answers:

Correct answer:

Explanation:

In order to add the two fractions, we must find the lowest common denominator. To do this, we simply multiply  each fraction by the denominator of the opposite over itself:

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