GMAT Math : Problem-Solving Questions

Study concepts, example questions & explanations for GMAT Math

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Example Questions

Example Question #1941 : Problem Solving Questions

 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 #1941 : Problem Solving Questions

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 #32 : Understanding Fractions

 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 #33 : Understanding Fractions

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

Possible Answers:

Correct answer:

Explanation:

Example Question #1942 : Problem Solving Questions

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:

Example Question #392 : Arithmetic

Simplify the following into a single fraction.

 

 

 

Possible Answers:

None of the other answers.

Correct answer:

Explanation:

To simply, we must first find the common denominator of the two fractions. That would be  or 

Hence we multiply the first fraction by  and the second fraction by , and we will have.

 

.

Now that the denominators match, we can add the fractions. The denominator stays the same after this, only the numerators add together.

 

 

Then factor out an  from the numerator to get the final answer.

 

Example Question #1 : Decimals

Rewrite as a fraction in lowest terms: 

Possible Answers:

Correct answer:

Explanation:

 

 

  

Example Question #1 : Decimals

Add one hundred seven ten-thousandths to seventeeen one-hundredths.

Possible Answers:

Two hundred seventy-seven one-thousandths

One thousand eight hundred seven ten-thousandths

One hundred eighty-seven one-thousandths

One thousand seven hundred seventeen ten-thousandths

One thousand one hundred seventy-seven ten-thousandths

Correct answer:

One thousand eight hundred seven ten-thousandths

Explanation:

One hundred seven ten-thousandths = 0.0107

Seventeeen one-hundredths = 0.17, or 0.1700

The sum:

This is one thousand eight hundred seven ten-thousandths.

Example Question #1 : Understanding Decimals

Multiply seventy-seven one-hundredths by sixty-six one-thousandths.

Possible Answers:

Forty-six thousand six hundred sixty-two hundred-thousandths

Five thousand eighty-two ten-thousandths

Five thousand eighty-two hundred-thousandths

Five hundred eighty-two ten-thousandths

Five hundred eighty-two hundred-thousandths

Correct answer:

Five thousand eighty-two hundred-thousandths

Explanation:

Seventy-seven one-hundredths = 0.77

Sixty-six one-thousandths = 0.066

The product:

 

 

 

 

0.77 and 0.066 have a total of five digits to the right of their decimal points, so position the decimal point in the answer so that there are five digits to its right. 

This is five thousand eighty-two hundred-thousandths.

Example Question #1 : Understanding Decimals

Divide eight hundred eighty-eight thousandths by sixty-four ten-thousandths.

Possible Answers:

Correct answer:

Explanation:

Eight hundred eighty-eight thousandths = 0.888

Sixty-four ten-thousandths = 0.0064 

Set up a long division:

Division

Move the decimal point four places right in both numbers so that the divisor will be a whole number. Note that this will require the use of placeholder zeroes in the dividend.

Division

(Note that leading zeroes have been removed.)

Carry out the long division, making sure you align the decimals:

Division

The quotient of this division is that of the original problem, so the correct choice is 138.75.

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