GMAT Question of the Day – Data Sufficiency – Number Properties
If m and z are positive integers such that m > z, what is the remainder when 2^(4m+6) – z is divided by 10?
(1) z = 4
(2) m = 6
Whenever an integer ends in 0 it is divisible by 10. The amount that the units digit strays from zero is the remainder when that number is divided by 10. So the remainder in this case is decided by the units digit. This should give you a clue that you need to focus on where we are in the units digit pattern of 2. 2, 4, 8, 6 is the pattern. If we know where we are in this pattern then we can figure out the remainder.
(1) This is sufficient. We do not need to know m because m is multiplied by 4. So regardless of what number m is that part of the exponent will always represent the 6 in the pattern above. Then we add the 6 in the exponent so that would take us to the 4 in the pattern. Once we know z we can see that we’ll get bumped down to a units digit of zero. Therefore the remainder is zero.
(2) Knowing m is irrelevant. You need to know the value of z. Insufficient.