GMAT Math : Data-Sufficiency Questions
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Example Question #1161 : Data Sufficiency Questions
Ben is given a simple stats problem. Of the 1,000 students at Our Town Community College, 600 are female, 400 are male. The problem asks: if we select 20 students at random, what is the probability that our sample of 20 will contain 10 or 11 or 12 or 13 females.
The simple solution is to go to the binomial table and add up the 4 probabilities of 10, 11, 12 and 13 with a population percentage of 0.6:
However, Ben likes to do things the hard way. He decides to use the normal distribution as an approximation to the binomial. Why? No one knows why. Ben is just Ben.
He gets the Z value and percentile for 9.5 and then obtains the Z value and percentil value for 13.5. He then subtracts the 9.5 percentile from the 13.5 percentile and hopefully ends up with something close to .6224
What is:
the Z value for 9.5
the percentile for 9.5
the Z value for 13.5
the percentile for 13.5
-1.64
.28
.89
.90
-1.34
.23
.71
.85
-1.14
.13
.68
.75
-1.5
.30
.77
.92
-1.02
.33
.77
.95
-1.14
.13
.68
.75
Example Question #1162 : Data Sufficiency Questions
We randomly sampled 175 people in Our Town USA and found that 62.9% of them favored Coke over Pepsi. We decided on a 90% 2 tailed test (z=1.64) and proclaimed that we were 90% confident of the 62.9% plus or minus 6%.
We arrived at the 6% by first calculating the standard deviation:
and then multiplying .0365 by z (1.64)
What sample size do we need to be plus or minus 4%?
sample size =
Example Question #3272 : Gmat Quantitative Reasoning
A data set comprises a large number of entries. What is the interquartile range of the set?
Statement 1: The 75th percentile is 745
Statement 2: The median is 556
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.
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 insufficient to answer the question.
Two things are needed to calculate the interquartile range - the first quartile and the third quartile (the median is irrelevant). Statement 1 gives you the latter (the third quartile, by definition, is the 75th percentile) but neither gives you the former.
Example Question #13 : Descriptive Statistics
A data set comprises 1,000 entries. What is its interquartile range?
Statement 1: The 75th percentile is 64.
Statement 2: The 25th percentile is 30.
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.
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.
BOTH statements TOGETHER are sufficient to answer the question, but NEITHER statement ALONE is sufficient to answer the question.
The interquartile range is the difference between the third and first quartiles - that is, the 75th percentile and the 25th percentile. Knowing both is necessary and sufficient.
Example Question #14 : Descriptive Statistics
Seven kids in a kindergarten class have the following ages:
Amy and Lilly join this kindergarten class. What is the range of the nine kids' ages?
(1) Amy is 
(2) The sum of the ages of both kids is 
BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient
Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient
Statements (1) and (2) TOGETHER are not sufficient
EACH statement ALONE is sufficient
Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient
BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient
Statement (1) alone does not give us any information to find out the age of Lilly, therefore it is not sufficient.
Statement (2) alone does not give us enough information to determine the ages of each kid. Therefore it is not sufficient.
Statement (1) and (2) give us the following information:
A = 6 and A + L = 13, therefore L = 13 - 6 = 7
With the ages of both kids we can find the new age range = 8 - 2 = 6
Example Question #182 : Arithmetic
What is the value of 
(1) The range of the numbers in the list is 
(2)
Both statements TOGETHER are not 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.
Statement (2) ALONE is sufficient, but Statement (1) ALONE is not sufficient.
Statement (1) ALONE is sufficient, but Statement (2) ALONE is not sufficient.
Statement (1) indicates that the range of the numbers is 20. The range is the difference between the highest number and the lowest number. The difference between each pair of numbers in the list is less than 20. Therefore, n is the lowest number in the list. We can then calculate n as follows:
Therefore Statement (1) is SUFFICIENT.
Statement (2) states that n<5 which means n is the lowest number in the list. However this information alone is not sufficient to find the value of n.
Therefore Statement (2) is not SUFFICIENT.
Statement (1) ALONE is sufficient, but Statement (2) ALONE is not sufficient.
Example Question #14 : Descriptive Statistics
What is the range of the numbers in the list above?
(1) 
(2) 
Statements (1) and (2) TOGETHER are not sufficient.
Both statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.
Statement (2) ALONE is sufficient, but Statement (1) ALONE is not sufficient.
Each Statement ALONE is sufficient.
Statement (1) ALONE is sufficient, but Statement (2) ALONE is not sufficient.
Statement (2) ALONE is sufficient, but Statement (1) ALONE is not sufficient.
The range of a set of numbers is the difference between the maximum and the minimum values of these numbers. In order to determine the range of these numbers, we need to know the values of n and 2n-1 or at least we should know that n and 2n-1 are not the minimum or the maximum values, meaning n and 2n-1 do not affect the range of these numbers.
(1)
Therefore n is not the minimum value in this list. However, we do not if 2n-1 is the maximum value. Statement (1) ALONE is not sufficient.
(2)
n and 2n-1 do not affect the range then. The range of these numbers is:
Statement (2) ALONE is sufficient.
Example Question #1 : Arithmetic Mean
Is 3 the average of a sequence？
(1)There are 3 numbers in the sequence
(2)The mode of the sequence is 3
Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.
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.
BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.
Statements (1) and (2) TOGETHER are NOT sufficient.
For statement (1), since we don’t know the value of each number, we cannot calculate the average of the sequence. For statement (2), the mode of the sequence is 3 means that “3” occurs most times in the sequence, but we cannot get to the average because we don’t know the value of other numbers. If we look at the two conditions together, we will know that there are 2 or 3 “3”'s in the sequence, but we don’t know exactly how many times “3” occurs. If the 3 numbers are all “3”s, then we can answer the question; If not, then we cannot answer the question. Thus both statements together are not sufficient.
Example Question #2 : Arithmetic Mean
Calculate the average of the 5 integers.
Statement 1: They are consecutive even integers.
Statement 2: The smallest of the integers is 8 less than the largest of the five integers.
EACH statement ALONE is sufficient.
Statements 1 and 2 TOGETHER are NOT sufficient.
Statement 2 ALONE is sufficient, but statement 1 is not sufficient.
Statement 1 ALONE is sufficient, but statement 2 is not sufficient.
BOTH statements TOGETHER are sufficient, but NIETHER statement ALONE is sufficient.
Statements 1 and 2 TOGETHER are NOT sufficient.
We are looking for an average here. Statement 1 tells us we are looking for even consecutive integers such as 2, 4, 6, 8, and 10. Statement 2 tells us the difference between the smallest and largest integer; however, the difference between the largest and smallest of five consecutive even (or odd) integers will ALWAYS be 8, regardless of what 5 consecutive integers we choose; therefore the two statements don't give us enough information to solve for the average.
Example Question #3 : Arithmetic Mean
Data sufficiency question- do not actually solve the question
Find the mean of a set of 5 numbers.
1. The sum of the numbers is 72.
2. The median of the set is 15.
Statement 1 alone is sufficient, but statement 2 is not sufficient to answer the question
Both statements taken together are sufficient to answer the question, but neither question alone is sufficient
Each statement alone is sufficient
Statements 1 and 2 are not sufficient, and additional information is required to answer the question
Statement 2 alone is sufficient, but statement 1 is not sufficient to answer the question
Statement 1 alone is sufficient, but statement 2 is not sufficient to answer the question
Statement 2 does not provide enough information about the mean as it can vary greatly from the median. Statement 1 is sufficient to calculate the mean, because even though it is impossible to calculate the set of numbers, the mean is calculated by dividing the sum by the total number of incidences in the set.
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