GMAT Math : Problem-Solving Questions

Study concepts, example questions & explanations for GMAT Math

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Example Questions

Example Question #1751 : Problem Solving Questions

Add the factors of 29.

Possible Answers:

Correct answer:

Explanation:

29 is a prime number and therefore has two factors, 1 and itself. The sum of the two is 30.

Example Question #34 : Understanding The Properties Of Integers

How many integers from 71 to 100 inclusive do not have 2, 3, or 5 as a factor?

Possible Answers:

Correct answer:

Explanation:

The factors of 2 are exactly the integers that end in 2, 4, 6, 8, or 0, and the factors of 5 are exactly the integers that end in 5 or 0. Therefore, we will start with the integers that end in 1, 3, 7, and 9, and eliminate the multiples of 3:

Of these, 81, 87, 93, and 99 are the only multiples of 3. Remove them and we have the set

a set of eight elements.

Example Question #34 : Properties Of Integers

Which of these numbers is relatively prime with 45?

Possible Answers:

Correct answer:

Explanation:

For a number to be relatively prime with 45, it cannot share any of its prime factors. 

,

so a number is relatively prime with 45 if and only if neither 3 nor 5 is a factor.

57 and 63 are multiples of 3, so both of these can be eliminated. 65 and 115 are multiples of 5, so both of these can be eliminated. 

But the prime factorization of 88 is , so 88 and 45 are relatively prime.

Example Question #1752 : Problem Solving Questions

What is the median of the prime numbers between 40 and 90?

Possible Answers:

Correct answer:

Explanation:

The prime numbers between 40 and 90 are: 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89. Since there are twelve, the median is the mean of the sixth- and seventh-highest numbers:

Example Question #1753 : Problem Solving Questions

To the nearest whole number, what is the mean of the prime numbers between 50 and 100?

Possible Answers:

Correct answer:

Explanation:

The prime numbers between 50 and 100 are: 53, 59, 61, 67, 71, 73, 79, 83, 89, 97. There are ten primes total, so add them and divide by 10:

This rounds to 73.

Example Question #36 : Understanding The Properties Of Integers

Which of the following values of  makes this statement true?

Possible Answers:

Correct answer:

Explanation:

For  to be true,  must be a multiple of 18. An integer is divisible by 18 if and only if it is divisible by 2 and 9.

Since all of the choices are even, we test to see which one is divisible by 9. The easiest way to do this is to apply the divisibility test by finding each the sum of the digits in each number. If the sum of the digits is divisible by 9, then the number is divisible by 9 as well.

 

 

Of the five choices, only 19,836 has a digit sum divisible by 9.

 

Example Question #34 : Understanding The Properties Of Integers

A group of  children,  girls and  boys go to visit the city council. They walk in a single file, girls at the front and the boys follow.

How many different arrangements can the single file line take?

Possible Answers:

Correct answer:

Explanation:

To solve this problem we use factorials. This is a quicker way to find out the number of combination for this specific set of data.

The number of ways to arrange the 2 girls is 2! and the number of ways to arrange the 3 boys is 3!.

Therefore the number of possible file arrangements is:

Example Question #1754 : Problem Solving Questions

What is the least common multiple of  and ?

Possible Answers:

Correct answer:

Explanation:

The multiples of 10 are: 10 , 20 , 30 , 40 , 50 , 60 , 70 and so on

The multiples of 12 are: 12 , 24 , 36 , 48 , 60 , 72 , 84 and so on

So the LCM (10 ; 12) = 60

Example Question #204 : Arithmetic

A group of people can be divided into  samples of an equal number of people or  samples of an equal number of people. What can be the lowest number of people in the group?

Possible Answers:

Correct answer:

Explanation:

The lowest number of people in the group is the least common multiple of 10 and 16.

The least common multiple is:

The lowest possible number of people in the group is 80.

 

Example Question #1751 : Problem Solving Questions

If  is an integer, which of the following is guaranteed to be false?

Possible Answers:

 is a negative number.

 can be written as a ratio of two other integers

Correct answer:

Explanation:

Integers are the counting numbers, their negatives, and zero.

 

 and 

 

 is false, because there is no counting number between  and .

 

It is possible (although not always) for  to be written as a ratio of two other integers. For example, , an integer, can be written as ; a ratio of two other integers (though in our minds, we would quickly simplify this fraction to )

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