GMAT Math : GMAT Quantitative Reasoning
Study concepts, example questions & explanations for GMAT Math
All GMAT Math Resources
Example Questions
Example Question #1013 : Data Sufficiency Questions
You are given two positive integers, 
Statement 1: 
Statement 2: 
BOTH statements TOGETHER are insufficient to answer the question.
Statement 1 ALONE is sufficient to answer the question, but Statement 2 ALONE is NOT sufficient to answer the question.
EITHER statement ALONE is sufficient to answer the question.
Statement 2 ALONE is sufficient to answer the question, but Statement 1 ALONE is NOT sufficient to answer the question.
BOTH statements TOGETHER are sufficient to answer the question, but NEITHER statement ALONE is sufficient to answer the question.
BOTH statements TOGETHER are sufficient to answer the question, but NEITHER statement ALONE is sufficient to answer the question.
If we only know that 
Example 1: If 
Example 2: If 
A similar argument shows that if we only know that 
Suppose we know both.
If we know that 
If we know that 
Then
So, when 
Example Question #3131 : Gmat Quantitative Reasoning
You are given four numbers, 
Statement 1:
Statement 2:
BOTH statements TOGETHER are sufficient to answer the question, but NEITHER statement ALONE is sufficient to answer the question.
Statement 1 ALONE is sufficient to answer the question, but Statement 2 ALONE is NOT sufficient to answer the question.
Statement 2 ALONE is sufficient to answer the question, but Statement 1 ALONE is NOT sufficient to answer the question.
BOTH statements TOGETHER are insufficient to answer the question.
EITHER statement ALONE is sufficient to answer the question.
BOTH statements TOGETHER are sufficient to answer the question, but NEITHER statement ALONE is sufficient to answer the question.
The product of two or more numbers is 0 if and only if at least one of the numbers is 0.
Each of the individual statements eliminates only two possible answers to the question; Statement 1 eliminates 
Example Question #3132 : Gmat Quantitative Reasoning
I am thinking of two distinct prime numbers: what are they?
Statement 1: Both numbers are between 40 and 50.
Statement 2: Their difference is 2.
BOTH statements TOGETHER are sufficient to answer the question, but NEITHER statement ALONE is sufficient to answer the question.
EITHER statement ALONE is sufficient to answer the question.
Statement 1 ALONE is sufficient to answer the question, but Statement 2 ALONE is NOT sufficient to answer the question.
Statement 2 ALONE is sufficient to answer the question, but Statement 1 ALONE is NOT sufficient to answer the question.
BOTH statements TOGETHER are insufficient to answer the question.
BOTH statements TOGETHER are sufficient to answer the question, but NEITHER statement ALONE is sufficient to answer the question.
Statement 1 is not sufficient, since there are three primes - 41, 43 and 47 - between 40 and 50.
Statement 2 is not sufficient, since there are numerous pairs of primes that differ by 2 - 3 and 5 are one pair, as are 5 and 7.
Both statements together are sufficient, however; from Statement 1, we know that the primes are chosen from 41, 43, and 47, and from Statement 2, we know that we can only choose 41 and 43.
Example Question #3133 : Gmat Quantitative Reasoning
What is the last digit of whole number 
Statement 1: The last digit of its base 5 representation is 2.
Statement 1: The last digit of its base 2 representation is 1.
BOTH statements TOGETHER are sufficient to answer the question, but NEITHER statement ALONE is sufficient to answer the question.
Statement 1 ALONE is sufficient to answer the question, but Statement 2 ALONE is NOT sufficient to answer the question.
EITHER statement ALONE is sufficient to answer the question.
BOTH statements TOGETHER are insufficient to answer the question.
Statement 2 ALONE is sufficient to answer the question, but Statement 1 ALONE is NOT sufficient to answer the question.
BOTH statements TOGETHER are sufficient to answer the question, but NEITHER statement ALONE is sufficient to answer the question.
If the base 5 representation of 
If the base 2 representation of 
Neither statement alone provides a definitive answer to the question, but both facts taken together do - only a number ending in 7 satisfies both conditions.
Example Question #3134 : Gmat Quantitative Reasoning
I am thinking of two distinct prime numbers. What are they?
Statement 1: Both are between 30 and 40.
Statement 2: Their product is 1,147.
BOTH statements TOGETHER are sufficient to answer the question, but NEITHER statement ALONE is sufficient to answer the question.
Statement 2 ALONE is sufficient to answer the question, but Statement 1 ALONE is NOT sufficient to answer the question.
EITHER statement ALONE is sufficient to answer the question.
BOTH statements TOGETHER are insufficient to answer the question.
Statement 1 ALONE is sufficient to answer the question, but Statement 2 ALONE is NOT sufficient to answer the question.
EITHER statement ALONE is sufficient to answer the question.
There are only two prime numbers between 30 and 40 - they are 31 and 37. Statement 1 provides enough information.
There is only one way to factor 1,147 as the product of two primes: 
Example Question #3135 : Gmat Quantitative Reasoning
A whole number has four digits. True or false: The integer is divisible by 9.
Statement 1: The sum of the digits is 26.
Statement 2: The last two digits are 98.
Statement 1 ALONE is sufficient to answer the question, but Statement 2 ALONE is NOT sufficient to answer the question.
BOTH statements TOGETHER are insufficient to answer the question.
Statement 2 ALONE is sufficient to answer the question, but Statement 1 ALONE is NOT sufficient to answer the question.
BOTH statements TOGETHER are sufficient to answer the question, but NEITHER statement ALONE is sufficient to answer the question.
EITHER statement ALONE is sufficient to answer the question.
Statement 1 ALONE is sufficient to answer the question, but Statement 2 ALONE is NOT sufficient to answer the question.
A necessary and sufficient condition for a whole number to be divisible by 9 is that the sum of its digits must be divisible by 9. Statement 1 provides proof that this condition is not met, since 26 is not a multiple of 9. Statement 2 provides irrelevant information.
Example Question #41 : Arithmetic
A whole number has four digits. True or false: The integer is divisible by 12.
Statement 1: The sum of the digits in the number is 36.
Statement 2: The last digit of the number is 9.
Statement 2 ALONE is sufficient to answer the question, but Statement 1 ALONE is NOT sufficient to answer the question.
EITHER statement ALONE is sufficient to answer the question.
BOTH statements TOGETHER are insufficient to answer the question.
Statement 1 ALONE is sufficient to answer the question, but Statement 2 ALONE is NOT sufficient to answer the question.
BOTH statements TOGETHER are sufficient to answer the question, but NEITHER statement ALONE is sufficient to answer the question.
EITHER statement ALONE is sufficient to answer the question.
Assume Statement 1 alone. If the sum of the digits of a four-digit number is 36, then the average value of each digit is 
Now assume Statement 2 alone. For a number to be divisible by 12, it must also be divisible by any factors of 12, including 2. This is only possible if the last digit is even, which it is not. Therefore, the number is not divisible by 12.
Example Question #41 : Arithmetic
A whole number has four digits. True or false: The integer is divisible by 11.
Statement 1: The sum of the digits is 22.
Statement 2: The last two digits are 55.
Statement 2 ALONE is sufficient to answer the question, but Statement 1 ALONE is NOT sufficient to answer the question.
BOTH statements TOGETHER are insufficient to answer the question.
BOTH statements TOGETHER are sufficient to answer the question, but NEITHER statement ALONE is sufficient to answer the question.
Statement 1 ALONE is sufficient to answer the question, but Statement 2 ALONE is NOT sufficient to answer the question.
EITHER statement ALONE is sufficient to answer the question.
BOTH statements TOGETHER are insufficient to answer the question.
Assume both statements to be true. The numbers 6,655 and 7,555 both end in 55 and have digit sum 22. However,
and
Only the former is divisible by 11, so the two statements together do not answer the question.
Example Question #43 : Arithmetic
True or false: Positive integer 
Statement 1:
Statement 2:
BOTH statements TOGETHER are insufficient to answer the question.
Statement 2 ALONE is sufficient to answer the question, but Statement 1 ALONE is NOT sufficient to answer the question.
EITHER statement ALONE is sufficient to answer the question.
Statement 1 ALONE is sufficient to answer the question, but Statement 2 ALONE is NOT sufficient to answer the question.
BOTH statements TOGETHER are sufficient to answer the question, but NEITHER statement ALONE is sufficient to answer the question.
EITHER statement ALONE is sufficient to answer the question.
Assume Statement 1 alone. Then:
Either
Each of 5 and 7 has exactly two factors, 1 and itself, so either way 
Assume Statement 2 alone. Then:
Either
or
Each of 7 and 11 has exactly two factors, 1 and itself, so either way 
Example Question #44 : Arithmetic
True or false: Positive integer 
Statement 1: The last digit of 
Statement 2: 
BOTH statements TOGETHER are sufficient to answer the question, but NEITHER statement ALONE is sufficient to answer the question.
BOTH statements TOGETHER are insufficient to answer the question.
Statement 2 ALONE is sufficient to answer the question, but Statement 1 ALONE is NOT sufficient to answer the question.
Statement 1 ALONE is sufficient to answer the question, but Statement 2 ALONE is NOT sufficient to answer the question.
EITHER statement ALONE is sufficient to answer the question.
Statement 1 ALONE is sufficient to answer the question, but Statement 2 ALONE is NOT sufficient to answer the question.
Assume Statement 1 alone. An integer is divisible by 2 if and only if its last digit is 0, 2, 4, 6, or 8. Therefore, it therefore follows that 
Assume Statement 2 alone. Then:
Either
Therefore, it is not clear whether or not 
All GMAT Math Resources
