GMAT Math : Arithmetic Mean
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Example Questions
Example Question #1181 :Data Sufficiency Questions
Given five distinct positive integers -
Statement 1:
Statement 2:
BOTH STATEMENTS TOGETHER provide sufficient information to answer the question, but NEITHER STATEMENT ALONE provides sufficient information to answer the question.
STATEMENT 2 ALONE provides sufficient information to answer the question, but STATEMENT 1 ALONE does NOT provide sufficient information to answer the question.
EITHER STATEMENT ALONE provides sufficient information to answer the question.
STATEMENT 1 ALONE provides sufficient information to answer the question, but STATEMENT 2 ALONE does NOT provide sufficient information to answer the question.
BOTH STATEMENTS TOGETHER do NOT provide sufficient information to answer the question.
BOTH STATEMENTS TOGETHER provide sufficient information to answer the question, but NEITHER STATEMENT ALONE provides sufficient information to answer the question.
The median of five numbers (an odd number) is the number in the middle when they are arranged in ascending order.
These two orderings are both consistent with the ordering given in Statement 1:
Therefore, Statement 1 alone provides insufficient information to answer the question. For a similar reason, so does Statement 2.
Assume both statements to be true. Then
Example Question #22 :Arithmetic Mean
Give the arithmetic mean of
Statement 1: A rectangle with length
Statement 2: A triangle with base of length
EITHER STATEMENT ALONE provides sufficient information to answer the question.
BOTH STATEMENTS TOGETHER do NOT provide sufficient information to answer the question.
BOTH STATEMENTS TOGETHER provide sufficient information to answer the question, but NEITHER STATEMENT ALONE provides sufficient information to answer the question.
STATEMENT 2 ALONE provides sufficient information to answer the question, but STATEMENT 1 ALONE does NOT provide sufficient information to answer the question.
STATEMENT 1 ALONE provides sufficient information to answer the question, but STATEMENT 2 ALONE does NOT provide sufficient information to answer the question.
BOTH STATEMENTS TOGETHER do NOT provide sufficient information to answer the question.
The area of a rectangle is the product of its length and width; the area of a triangle is half the product of its height and the length of its base. Therefore, from Statement 1, we get that
From Statement 2, we get that
In other words, the two statements are equivalent, so one of two things happens - either statement alone is sufficient, or both together are insufficient. We show that the latter is the case:
Case 1:
The mean of the two is
Case 2:
The mean of the two is
Therefore, knowing the area of the rectangle with these dimensions is not helpful to determining their arithmetic mean. This makes Statement 1, and, equivalently, both statements together, unhelpful.
Example Question #23 :Arithmetic Mean
Joseph's final grade is calculated from the mean of his test scores. His teacher also allows them to drop the lowest score before calculating the final grade. If Joseph received a
The average or mean is found by taking all of the scores and dividing by the total number of scores. Remember, we must first find the lowest score and not include that in the calculation. Therefore, we get:
Example Question #24 :Arithmetic Mean
You are given the data set
Statement 1: The mean of the data set is 44.3
Statement 2: The median of the data set is 48.5
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.
EITHER statement ALONE is sufficient to answer the question.
Knowing the mean of the set is enough to calculate
Knowing the median is enough to deduce
Therefore, either statement alone is sufficient to answer the question.
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