GMAT Quantitative Reasoning Practice Test 7

Question : 11 of 100

Marks: +1, -0

Is the average of

X

consecutive numbers odd?
(1) The first number in the series is odd.
(2) The sum of the numbers is odd.

Statement (1) BY ITSELF is sufficient to answer the question, but statement (2) by itself is not.
Statement (2) BY ITSELF is sufficient to answer the question, but statement (1) by itself is not.
Statements (1) and (2) TAKEN TOGETHER are sufficient to answer the question, even though NEITHER statement BY ITSELF is sufficient.
Either statement BY ITSELF is sufficient to answer the question.
Statements (1) and (2) TAKEN TOGETHER are NOT sufficient to answer the question, requiring more data pertaining to the problem.

Validate

Solution:

Statement (1) is insufficient by itself, take

X

as 2 : if the first number is odd, the sum of the two numbers is odd. Take

X

as 3 : if the first number is odd, the sum of the three numbers is even.
Statement (2) tells us that the sum of the numbers is odd and therefore the median must be odd.
If the median is odd the average of these numbers is also odd because that means that there is an even amount of even numbers and an odd amount of odd numbers. This statement is sufficient by itself.

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