All GMAT Math Resources
Example Questions
Example Question #442 : Arithmetic
Define an operation on the integers as follows:
If both and
are odd, then
.
If both and
are even, then
.
If is odd and
is even, or vice versa, then
.
Add to
. What is the sum?
Both and
can be calculated using the definition of
for the case of exactly one of
and
being odd and one being even:
.
Add:
Example Question #46 : Understanding Real Numbers
Define an operation on the integers as follows:
If both and
are prime, then
.
If neither nor
is prime, then
.
If exactly one of and
is prime, then
.
Multiply by
. What is the product?
A prime number has exactly two factors, 1 and the number itself.
Neither 6 nor 1 is a prime number; 1 has only one factor and is not considered to be prime, and 6 has more than two factors - 1, 2, 3, and 6. Therefore, can be evaluated using the defintion of
for two numbers whose absolute values are not prime:
2 and 3 are prime numbers, since each has exactly two factors, 1 and the number itself. Therefore, can be evaluated using the defintion of
for two numbers whose absolute values are prime:
The product is
Example Question #41 : Understanding Real Numbers
Define an operation on the integers as follows:
If both and
are prime, then
.
If neither nor
is prime, then
.
If exactly one of and
is prime, then
.
Subtract from
. What is the result?
2 is a prime number, since 2 has only two factors, 1 and 2 itself. 50 is not a prime number, since 50 has other factors, such as 2. can be evaluated using the definition of
for exactly one of
and
prime:
Neither 4 nor 25 are prime, since each has factors other than 1 and itself; for example, and
.
can be evaluated using the definition of
for neither
nor
prime:
The difference:
Example Question #2001 : Problem Solving Questions
is the additive inverse of
. Which of the following expressions is equivalent to
for all values of the variables?
If is the additive inverse of
, then
, or, equivalently,
By way of substitution and the identity property of addition,
Example Question #49 : Understanding Real Numbers
Define an operation on the integers as follows:
If both and
are prime, then
.
If neither nor
is prime, then
.
If exactly one of and
is prime, then
.
Evaluate .
17 and 13 are both prime numbers, since each has exactly two factors - 1 and the number itself. Therefore, we first evaluate using the definition of
for
and
both prime:
Therefore, . 7 is also prime, since its only two factors are 1 and 7 itself. 30, however, is not prime, since 30 has factors other than 1 and itself - for example,
. Therefore,
is evaluated using the definition of
for exactly one of
and
prime:
, the correct response.
Example Question #50 : Understanding Real Numbers
Define an operation on the integers as follows:
If both and
are prime, then
.
If neither nor
is prime, then
.
If exactly one of and
is prime, then
.
Which of the following expressions is the greatest of the five?
Of the integers shown in the five choices, the following are primes, since they have exactly two factors, 1 and the number itself: 2, 5.
1 is not consdered to be a prime, having exactly one factor (1). Also, 4, 10, 20, 25, 50, and 100 are not primes, since each has at least one factor other than 1 and itself.
and
can both be evaluated using the definition of
for exactly one of
and
prime - that is, by multiplying the numbers:
Each of ,
, and
can be evaluated using the definition of
for neither of
and
prime - that is, by adding the numbers:
The greatest of the five expressions is .
Example Question #1 : Descriptive Statistics
Consider the following set of numbers:
85, 87, 87, 82, 89
What is the range?
The range is the difference between the maximum and minimum value.
Example Question #1 : Range
What is the range for the following data set:
The range is the highest value number minus the lowest value number in a sorted data set:
We need to sort the data set:
Example Question #1 : Calculating Range
What is the range for the following set:
The range is the difference between the highest and lowest number.
First sort the set:
Example Question #1 : Descriptive Statistics
Below is the stem-and-leaf display of a set of test scores.
What is the range of this set of scores?
The range of a data set is the difference of the highest and lowest scores,
The numbers in the "stem" of this display represent tens digits of the test scores, and the numbers in the "leaves" represent the units digits. The highest and lowest scores represented are 87 and 42, so the range is their difference: .
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