Data Sufficiency

If x, y are positive integers, what is the unit digit of 2^(4x+2)+y?
1) x=1
2) y=2

*An answer will be posted in 2 days

Max@Math Revolution wrote:If x, y are positive integers, what is the unit digit of 2^(4x+2)+y?
1) x=1
2) y=2

*An answer will be posted in 2 days

(1) NOT SUFFICIENT. If x = 1, then the expression simplifies to 2^6 + y = 64 + y. The units digit of the expression depends on the value of y, which we do not know. If y = 0, then the units digit is 4. If y = 5, then the units digit is 9.

(2) SUFFICIENT. The key to this is to recognize that the units digit of 2 raised to an integer power follows a predictable pattern. 2^1 = 2, 2^2 = 4, 2^3 = 8, 2^4 = 16, 2^5 = 32 (pattern repeats)... Note every time we raise 2 to the power of a POSITIVE multiple of 4, the units digit will be 6. So the expression we have is 2^(4x+2). Since x is restricted to being a positive integer value, this expression will yield a power which is 2 greater than a multiple of 4. Looking back at the pattern I identified, this corresponds to a units digit of 4. Adding 2 to a number with a units digit of 4 yields a number with a units digit of 6.

Answer choice: B

In the original condition, there are 2 variables (x and y). Hence, there is a high chance that C is the correct answer. Using 1) & 2), C is the correct answer. However, since this is an integer question, we can apply the common mistake type 4(A). From con 2), the unit digit of 2^4x+2 is always 5. Hence, we only have to know y, and the condition is sufficient. The correct answer, thus, is B.

- Forget conventional ways of solving math questions. In DS, Variable approach is the easiest and quickest way to find the answer without actually solving the problem. Remember equal number of variables and independent equations ensures a solution.