In each of the problems, a question is followed by two statements containing certain data. You are to determine whether the data provided by the statements are sufficient to answer the question. Choose the correct answer based upon the statement's data, your knowledge of mathematics, and your familiarity with everyday facts.

If the units digit of integer n is greater than 2, what is the units digit of n ?

(1) The units digit of n is the same as the units digit of n^{2}.

(2) The units digit of n is the same as the units digit of n^{3}.

Show/Hide Answer and Explanation

Correct Answer: E

Explanation:

Arithmetic operations: If the units digit of nis greater than 2, then it can
only be the digits 3, 4, 5, 6, 7, 8, or 9.

(1) To solve this problem, it is necessary to find a digit that is the same as the units digit of
its square. For example, both 43 squared (1,849) and 303 squared (91,809) have a units digit of 9,
which is different from the units digit of 43 and 303. However, 25 squared (625) and 385 squared
(148,225) both have a units digit of 5, and 16 and 226 both have a units digit of 6 and their squares
(256 and 51,076, respectively) do, too. However,there is no further information to choose between 5 or 6; NOT sufficient.

(2) Once again, 5 and 6 are the only numbers
which, when cubed, will both have a 5 or 6
respectively in their units digits. However, the
information given does not distinguish between
them; NOT sufficient.

Since (1) and (2) together yield the same
information but with no direction as to which to
choose, there is not enough information to
determine the answer.

The correct answer is E;
both statements together are still not sufficient.

Practice Questions in Sets

All questions (MCQ) are arranged in sets of questions on pages. You will see 12 questions pre page.