Bunuel
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.
We are given that the units digit of integer n is greater than 2 and we need to determine that units digit.
Statement One Alone:
The units digit of n is the same as the units digit of n^2.
If the units digit of n is the same as the units digit of n^2, then the units digit can be 0, 1, 5, or 6 (since 0^2 = 0, 1^2 = 1, 5^2 = 25 and 6^2 = 36). However, we are given that the units digits is greater than 2, so n can be either 5 or 6. Since we can’t determine exactly which digit it is, statement one alone is not sufficient to answer the question.
Statement Two Alone:
The units digit of n is the same as the units digit of n^3.
If the units digit of n is the same as the units digit of n^2, then the units digit can be 0, 1, 4, 5, 6, or 9. (since 0^3 = 0, 1^3 = 1, 4^3 = 64, 5^3 = 125, 6^3 = 216 and 9^3 = 729). However, we are given that the units digits is greater than 2, so n can be 4, 5, 6 or 9. Since we can’t determine exactly which digit it is, statement two alone is not sufficient to answer the question.
Statements One and Two Together:
With two statements together, the units digit of n can still be either 5 or 6. Since we can’t determine which one it is, the two statements together are still not sufficient to answer the question.
Answer: E