# 1336 - Data Sufficiency

Data Sufficiency MCQ No. : 49512

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 n2.

(2) The units digit of n is the same as the units digit of n3.

#### 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.

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