GMAT Math : GMAT Quantitative Reasoning
Study concepts, example questions & explanations for GMAT Math
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Example Questions
Example Question #4 : Arithmetic
The greatest common factor of 32 and a number 
1) 3 is also a factor of 
2) 5 is also a factor of 
EITHER Statement 1 or Statement 2 ALONE is sufficient to answer the question.
BOTH statements TOGETHER are NOT sufficient to answer the question.
Statement 1 ALONE is sufficient to answer the question, but Statement 2 ALONE is not sufficient.
Statement 2 ALONE is sufficient to answer the question, but Statement 1 ALONE is not sufficient.
BOTH statements TOGETHER are sufficient to answer the question, but NEITHER statement ALONE is sufficient to answer the question.
BOTH statements TOGETHER are NOT sufficient to answer the question.
That 
Example:
To find 
Example:
To find 
In each case, 3 and 5 are factors of 
The answer is that both statements together are insufficient.
Example Question #4 : Arithmetic
What is the area of a rhombus in square inches?
1) One of its angles measures
2) One of its sides measures 10 inches
BOTH statements TOGETHER are sufficient to answer the question, but NEITHER statement ALONE is sufficient to answer the question.
EITHER Statement 1 or Statement 2 ALONE is sufficient to answer the question.
BOTH statements TOGETHER are NOT sufficient to answer the question.
Statement 1 ALONE is sufficient to answer the question, but Statement 2 ALONE is not sufficient.
Statement 2 ALONE is sufficient to answer the question, but Statement 1 ALONE is not sufficient.
BOTH statements TOGETHER are sufficient to answer the question, but NEITHER statement ALONE is sufficient to answer the question.
As is true of any other parallelogram, the area of the rhombus is the base multiplied by the height. The common sidelength alone can be used to determine the base, but without the angles, the height cannot be determined. Using trigonometry, the angle can be used to determine the height relative to the base, but without the base, the height is unknown.
If we know both of the given statements, then part of one base, an altitude from an endpoint of the opposite base, and one adjacent side form a 30-60-90 triangle. The hypotenuse of that triangle is 10 inches, and the altitude is half that, or 5 inches. This makes the area 50 square inches.
The answer is that both statements together are sufficient to answer the question, but neither statement alone.
Example Question #3101 : Gmat Quantitative Reasoning
Data Sufficiency Question
Out of 100 students, 60 took French and 25 took German. How many students took neither?
1. 15 students took Spanish
2. 7 students took both French and German
both statements taken together are sufficient to answer the question, but neither statement alone is sufficient
statements 1 and 2 together are not sufficient, and additional data is needed to answer the question
statement 1 alone is sufficient, but statement 2 alone is not sufficient to answer the question
statement 2 alone is sufficient, but statement 1 alone is not sufficient to answer the question
each statement alone is sufficient
statement 2 alone is sufficient, but statement 1 alone is not sufficient to answer the question
Statement 1 does not tell us anything about the number of students taking French or German. The information from statement 2 is sufficient, if 60 took French, 25 took German, and 7 took both, we can calculate the number that took neither.
Example Question #3102 : Gmat Quantitative Reasoning
If 
Statement 1: 
Statement 2: 
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 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.
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.
There are infinitely many primes, and several integers between 13 and 23, so knowing just one of these statements is not enough. But only two integers in the stated range - 17 and 19 - are prime, so knowing both statements tells you that 
Example Question #3103 : Gmat Quantitative Reasoning
If a positive integer 
Statement 1: If 
Statement 2: If 
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.
EITHER statement ALONE is sufficient to answer the question.
EITHER statement ALONE is sufficient to answer the question.
The question is the same as asking whether 
Statement 1 says that the square of 
Statement 2 says that 
Therefore, either statement alone tells us that 
Example Question #6 : Properties Of Integers
What is the last digit of a positive integer 
Statement 1: The last digit of 
Statement 2: The last digit of 
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.
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.
Statement 2 ALONE is sufficient to answer the question, but Statement 1 ALONE is NOT sufficient to answer the question.
If the last digit of 
If the last digit of 
Example Question #11 : Properties Of Integers
How many negative numbers are in the set 
Statement 1:
Statement 2:
BOTH statements TOGETHER are insufficient 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.
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.
Statement 1 ALONE is sufficient to answer the question, but Statement 2 ALONE is NOT sufficient to answer the question.
Statement 1 tells you that 
Statement 2 tells you that of 
Example Question #12 : Properties Of Integers
This six-digit number has two digits missing:
If the blanks are to be filled with the same digit, what is that digit?
Statement 1: The number is divisible by 4.
Statement 2: The number is divisible by 3.
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.
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.
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 number is divisible by 4, then the last two digits make a number that is divisible by 4; this allows that digit to be 0, 4, or 8.
If the number is divisible by 3, then its digit sum is divisible by 3. This allows the comon digit to be 1, 4, or 7:
Neither statement alone narrows the common digit to one possibility, but if both statements are true, the only possibility becomes 4.
Example Question #13 : Properties Of Integers
This five-digit number has two digits missing:
If both blanks are two be filled with the same digit, what is that digit?
Statement 1: The number is divisible by 5.
Statement 2: The number is not divisible by 3.
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 insufficient to answer the question.
There are two different choices we can make for the common digit that would make both statements true, 0 and 5. This makes the last digit 0 or 5, making Statement 1 true, Also, this makes the digit sum either
or
Either way, the digit sum is not a multiple of 3, and the number itself is not a multiple of 3.
Therefore, the two statements together do not provide enought information to answer the question definitively.
Example Question #3104 : Gmat Quantitative Reasoning
You are given four numbers, 
Statement 1:
Statement 2:
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 sufficient to answer the question, but NEITHER statement ALONE is sufficient to answer the question.
EITHER statement ALONE is sufficient to answer the question.
BOTH statements TOGETHER are insufficient to answer the question.
BOTH statements TOGETHER are insufficient to answer the question.
Neither of these statements help you, individually or together. If three of the four numbers are equal to zero, then both products will equal zero. There is no way of knowing which of the numbers is non-zero.
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