GMAT Math : Data-Sufficiency Questions
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Example Questions
Example Question #1 : Dsq: Calculating Mode
Find the mode of the following set of numbers:
The mode is the number that occurs most frequently. Therefore, our answer is 
Example Question #1201 : Data Sufficiency Questions
What is the value of 
(1) The mode of the numbers in the list is 
(2) 
Statements (1) and (2) TOGETHER are not sufficient.
Statement (1) ALONE is sufficient, but Statement (2) ALONE is not sufficient.
Each Statement ALONE is sufficient.
Statement (2) ALONE is sufficient, but Statement (1) ALONE is not sufficient.
Both statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.
Statement (1) ALONE is sufficient, but Statement (2) ALONE is not sufficient.
The mode is the value that appears most often in a set of data. In our list the value that appears most often is m+1. Therefore m+1 is the mode of the numbers in the list.
Only statement (1) is useful in finding the value of m as it states that the mode of the numbers in the list is 14.
Statement (1) ALONE is sufficient, but Statement (2) ALONE is not sufficient.
Example Question #1 : Median
What is the median number of students assigned per workshop at School R?
(1) 30% of the workshops at School R have 6 or more students assigned to each workshop.
(2) 40% of the workshops at School R have 4 or fewer students assigned to each workshop.
C. BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.
B. Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.
D. EACH statement ALONE is sufficient.
A. Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.
E. Statements (1) and (2) TOGETHER are NOT sufficient.
C. BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.
Looking at statements (1) and (2) separately, we cannot get the median number since we don’t know the 50th percentile. However, putting the two statements together, we know that the 50th percentile is 5. So the median is 5.
Example Question #2 : Median
The median of the numbers 
None of the other answers are correct.
The four numbers 
Example Question #2 : Median
What is the mean of this set?
1)
2)
If 
If 
The two statements are equivalent. This is enough to allow the mean to be found:
The answer is that either statement alone is sufficient to answer the question.
Example Question #1 : Dsq: Calculating Median
Data Sufficiency Question
The mean of 8 numbers is 17. Is the median also 17?
1. The range of the numbers is 11.
2. The mode is 17.
each statement alone is sufficient
both statements taken together are sufficient to answer the question, but neither statement alone is sufficient
statement 1 alone is sufficient, but statement 2 alone is not sufficient to answer the question
statements 1 and 2 together are not sufficient, and additional data is needed to answer the question
statement 2 alone is sufficient, but statement 1 alone is not sufficient to answer the question
statements 1 and 2 together are not sufficient, and additional data is needed to answer the question
The range tells us the difference between the maximum and the minimum values, but provides no information about the median. The mode indicates the number that appears most frequently in the data set. While it is possible that the median is 17, it is impossible to determine the median from the data provided.
Example Question #223 : Arithmetic
On Monday, 40 people are asked to rate the quality of product A on a seven point scale (1=very poor, 2=poor.....6=very good, 7=excellent).
On Tuesday, a different group of 40 is asked to rate the quality of product B using the same seven point scale.
The results for product A:
7 votes for category 1 (very poor);
8 votes for category 2;
10 votes for 3;
6 vote for 4;
4 votes for 5;
3 votes for 6;
2 votes for 7;
The results for product B:
2 votes for category 1 (very poor);
3 votes for category 2;
4 votes for 3;
6 vote for 4;
10 votes for 5;
8 votes for 6;
7 votes for 7;
It appears that B is the superior product.
Which one of the following statements is true?
The median score for product A is less than the mean score for product A.
The mean score of product A is greater than the mean score of product B.
The median score of product A is greater than the mean score of product A.
The median score of product B is less than the mean score of product B.
The median score of product A is greater than the median score of product B.
The median score for product A is less than the mean score for product A.
Median of A = 3
Mean of A = 3.2
Median of B = 5
Mean of B = 4.8
Example Question #1 : Dsq: Calculating Median
What is the median of the following numbers?
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.
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 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 would not be helpful.
Example 1: If 
Example 2: If 
In contrast, if Statement 2 is true, since 
Example Question #2 : Median
Consider the data set
What is the value of 
Statement 1: The data set is bimodal.
Statement 2: The median of the data set is 7.
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.
Statement 1 ALONE is sufficient to answer the question, but Statement 2 ALONE is NOT sufficient to answer the question.
Statement 1 is sufficient to prove that 
Statement 2 is insufficient. The median of this data set, which has fifteen elements, is its eighth-greatest element. This happens if 
For example, if 
If 
The median of both sets is 7.
Example Question #3321 : Gmat Quantitative Reasoning
A data set comprises thirteen elements, the median of which is 75. Two new elements are added to the data set. Does the median change?
Statement 1: One of the elements added to the data set is 30.
Statement 2: One of the elements added to the data set is 40.
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.
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.
BOTH statements TOGETHER are insufficient to answer the question.
The median of a data set with thirteen elements is the seventh-highest element; the median of a data set with fifteen elements is the eighth-highest.
The two statements together provide insufficient information, as we show with two examples.
The data set
has thirteen elements and median 75; after 30 and 40 are added, the set is
which has median 75.
By contrast, the data set
has thirteen elements and median 75; after 30 and 40 are added, the set is
which has median 74.
Both sets started out with median 75, but the addition of 30 and 40 changed one median and not the other.
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