GMAT Math : Arithmetic
Study concepts, example questions & explanations for GMAT Math
All GMAT Math Resources
Example Questions
Example Question #3 : Decimals
True or false: The result 
Statement 1: Both denominators are even.
Statement 2: Both denominators are multiples of 3.
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 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 insufficient to answer the question.
Assume both statements to be true. A multiple of both 2 and 3 is also a multiple of 6, so both denominators are multiples of 6. Examine these two examples:
In both examples, the conditions of the problem, including both statements, are met, but in only one is the sum equivalent to a terminating decimal or integer.
Example Question #241 : Arithmetic
True or false: The result 
Statement 1: Neither denominator is a multiple of 5.
Statement 2: Both denominators are powers of 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.
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.
Statement 2 ALONE is sufficient to answer the question, but Statement 1 ALONE is NOT sufficient to answer the question.
Assume Statement 1 alone. Examine these two examples:
Both fit the main condition and that of Statement 1, but in only one case is the sum equal to a terminating decimal or integer.
Assume Statement 2 alone. A necessary and sufficient condition for a lowest-terms fraction to be equivalent to a terminating decimal is that its only prime factors are 2 and 5. By Statement 2, both denominators have 2 as their only prime factor, so both can be represented by terminating decimals; their product must be terminating as well.
Example Question #242 : Arithmetic
True or false: The result 
Statement 1: The denominator of 
Statement 2: The denominator of 
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.
Assume both statements. Examine these two examples; both fit the main condition and those given in both statements.
In only one case is the product equivalent to an integer or a terminating decimal.
Example Question #243 : Arithmetic
True or false: The result 
Statement 1: The denominator of 
Statement 2: The denominator of 
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.
EITHER statement ALONE is sufficient to answer the question.
Assume Statement 1 alone. Rewrite the fractions as follows:
By Statement 1, 
Since 
A similar argument can be used to demonstrate that Statement 2 proves the same of 
Example Question #244 : Arithmetic
True or false: The result 
Statement 1: The denominator of 
Statement 2: The denominator of 
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.
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.
BOTH statements TOGETHER are sufficient to answer the question, but NEITHER statement ALONE is sufficient to answer the question.
Assume Statement 1 alone. Examine these examples:
In both cases, the main conditon and that of Statement 1 are satisfied, but in only one case can the result be represented by a terminating decimal or integer.
A similar argument shows Statement 2 alone to be insufficient:
Assume both statements. Then rewrite the fractions as follows:
By Statement 1, 
and their product is
a terminating decimal.
Example Question #245 : Arithmetic
Solve for 
I) 
II) The slope of the line parallel to this equation is 
Statement II is sufficient to answer the question, but statement I is not sufficient to answer the question.
Neither statement is sufficient to answer the question. More information is needed.
Either statement is sufficient to answer the question.
Statement I is sufficient to answer the question, but statement II is not sufficient to answer the question.
Both statements are needed to answer the question.
Statement I is sufficient to answer the question, but statement II is not sufficient to answer the question.
We have one equation and two unknowns. To find x, we need to find y.
I) Tells us that y is .79 therefore we can plug this value into our equation and solve for x.
Plugging in the y value from Statement I and using algebraic operations to solve for x.
Multiply first term.
Subtract 4.74 from both sides.
Divide by -13.
II) Is irrelevant.
Therefore Statement I) alone is sufficient to answer the question but Statement II) alone is not.
Example Question #1 : Dsq: Understanding Real Numbers
Is z a negative number?
(1)
(2) 
Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.
Statements (1) and (2) TOGETHER are NOT sufficient.
EACH statement ALONE is sufficient.
BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.
Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.
Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.
(1) Subtracting 
(2) Subtracting 4 from both sides of 
Example Question #2 : Dsq: Understanding Real Numbers
If 
(1) The distance between 
(2) The distance between 
B. Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.
D. EACH statement ALONE is sufficient.
C. BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.
E. Statements (1) and (2) TOGETHER are NOT sufficient.
A. Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.
E. Statements (1) and (2) TOGETHER are NOT sufficient.
Looking at statements (1) and (2) separately, there is no information about the distance between 
Example Question #1 : Real Numbers
Data sufficiency question- do not actually solve the question
How many children are attending a party?
1. If 6 more children attend the party, there will be 24 children there.
2. If 10 children leave the party, there will be less than 12 children in attendance.
Both statements taken together are sufficient to ansewr the question, but neither statement alone is sufficient
Statement 1 alone is sufficient, but statement 2 alone is not sufficient to answer the question
Each statement alone is sufficient
Statements 1 and 2 together are not sufficient, and additional information is needed to answer the question
Statement 2 alone is sufficient, but statement 1 alone is not sufficient to answer the question
Statement 1 alone is sufficient, but statement 2 alone is not sufficient to answer the question
Statement 1 precisely tells how many children are attending the party while Statement 2 only provides a range.
Example Question #2 : Dsq: Understanding Real Numbers
A sandwich shop offers a discount in which customers pay $2.99 for each additional sandwich after purchasing their first sandwich. Emily bought her first sandwich for $4.95. If she purchased 5 additional sandwiches to take home, then the total amount she paid is equivalent to which of the following?
The price of 6 sandwiches can be expressed as 
All GMAT Math Resources
