GMAT Math : Problem-Solving Questions
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Example Questions
Example Question #13 : Understanding The Properties Of Integers
Express the quotient in scientific notation:
All of these expressions are equivalent to the correct quotient. But a number in scientific notation takes the form
Only 
Example Question #13 : Properties Of Integers
Rewrite 117 as a number in base eight.
One way to do this:
Divide 117 by 8. The remainder will be the last digit.
Now divide the quotient by 8. This remainder will be the second-to-last digit.
The quotient is less than 8, so it will be the first digit. The base-eight equivalent of 117 is
Example Question #14 : Properties Of Integers
A positive integer 
The easiest way to explain this is by example.
We can use 16, since
This makes 4 the correct choice.
Example Question #15 : Properties Of Integers
You are given that the product of eight nonzero numbers is negative. Which of the following is not possible?
Exactly one of the numbers is positive.
All of the numbers are negative.
All of the scenarios in the other choices are possible.
Exactly three of the numbers are negative.
Exactly one of the numbers is negative.
All of the numbers are negative.
The product of a group of nonzero numbers is negative if and only if an odd number of these factors is negative. This occurs in each of these scenarios except for one - all of the numbers (eight) being negative.
Example Question #16 : Properties Of Integers
A positive integer 
Any integer that is divisible by 5 must end in a 0 or a 5, so any integer which, when divided by 5, yields remainder 3 must end in 3 or 8. Since the cubes of 3 and 8 are 27 and 512, the cube of an integer that ends in one of these digits must end in 2 or 7, meaning that, when divided by 5, the remainder will be 2.
Example Question #17 : Properties Of Integers
For how many integers, 
Infinitely many
Since the numerator is always 1 greater than the denominator, we know that for large enough values of 
The other answer occurs as a special case as well. We can divide any number by 1 evenly, so when the denominator is 1 we get an integer:
In every other case, we will have a non-integer.
Example Question #19 : Understanding The Properties Of Integers
Which of the following numbers has a five in the last digit of its base-six representation?
If a number has a 5 in its base-six representation, then the number divided by 6 yields a remainder of 5. We test each of these five numbers by dividing each by 6 and noting the remainder:
Among the five choices, only 743 yields remainder 5 when divided by 6, so this is the correct choice.
Example Question #18 : Properties Of Integers
What is the sum of the odd numbers from 
We can divide this group number into two parts. The first part is 
The first group is symmetrical, so the sum of this group of numbers is 0. Now for the second part there are only two numbers left according to the question (sum of odd numbers), which is 157 and 159.
Therefore, the answer is 
Example Question #1731 : Problem Solving Questions
What is the product of all of the prime numbers between 20 and 30?
There are two prime numbers between 20 and 30; they are 23 and 29. Their product:
Example Question #1732 : Problem Solving Questions
What is the sum of all of the composite numbers from 31 to 40 inclusive?
The composite numbers that fall in the range 31-40 - those with more than two factors - are 32, 33, 34, 35, 36, 38, 39, and 40. Add them:
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