gmatophobia wrote:
DS Question 1 - Dec 21 If p and q are integers, then what is the units digit of 155^(9q) + 138^p + 146^q (1) The remainder is 2, when the positive integer p is divided by 8 (2) q is a prime number less than 10 Source:
GMAT Whiz | Difficulty : Hard
12 days of xmas vibes!
For these types of questions, it is helpful to rewrite the target question:
Note that 5 and 6 always have the same units digit, provided that the exponent is an integer>=1. Therefore, we want to know if q>=1.
138^p. any number with units digit 8 raised to pos exponent, will have units cycle in 8,4,2,6. In that order. So we want to figure out where 8^p will end, if possible.
1) This statement tells us that p=8k+2.
therefore, p must be an even number. p is also never a multiple of 4 - it can only be a multiple of 2. That tells us that the units digits of 138^p will always be 4.
Don’t fall for the trap here of picking A - we still don’t know anything about q. If q is 0 or fraction, the units digit will be very different if q is integer>=1
2) This tells us that q=2,3,5,7. Essentially, Q is a integer>=1, therefore 155^9p always has units digit ending in 5, and 146^q has units digit ending in 6. We do not know anything about p though. Insuff.
3) Combining the two, we know that units digit of 155^9q is 5, 138^p is 4, and 146^q is 6. Therefore, we can figure out the units digit of the whole equation.
C.