GMAT Quantitative Reasoning Practice Test 5

Question : 91 of 100

Marks: +1, -0

M is a positive
integer, is

M

odd?
(1)

2 M^3+2 M

is divisible by 8 .
(2)

M+10

is divisible by 10 .

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

Solution:

Statement (1) tells us that

2 M^3+2 M

is divisible by 8 and so

M^4+M

is divisible by 4 and is even. We have two choices:

M^\beta

and

M

are either odd or even. This statement is insufficient. Statement (2) is sufficient, if

M+10

is divisible by 10 then

M+10

is an even number. This statement is sufficient.

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