GMAT Quantitative Reasoning Practice Test 5

Question : 67 of 100

Marks: +1, -0

Is the square
root of

A

an integer?
(1) The last digit of

A

is 8 .
(2)

A

is divisible by 6 .

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:

If you square each digit

\{0,1,2, . . ., 8,9\}

, you will see that the possible last digits for a square are

0,1,4,5,6

and 9 . Thus, if the last digit of

A

8, A

cannot be a square and the square root of

A

is not an integer. Statement (1) by itself is sufficient.
Statement (2) by itself is insufficient since there are numbers that are divisible by 6 and have an integer square root and numbers divisible by 6 that do not have an integer square root.

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