GMAT Question of the Day - Problem Solving - Number Properties (digits)
What is the units digit of 88^47 - 98^37?
GMAT Question of the Day Solution
Did you pick C? That's the twist. Skip down for why C is wrong. The units digit of any integer has a repeating pattern. Here are some example but try this out yourself. Oh - and here's a little time saver: when multiplying you only need to worry about the units digits. So 8*8 = 64. To do the next in the sequence do 8*4 NOT 8*64.
2: 2, 4, 8, 6
3: 3, 9, 7, 1
5: 5, 5, 5, 5
8: 8, 4, 2, 6
In this case we have 88^47 which has a units digit of 2 and 98^37 which has a units digit of 8. How can you figure out where you are in the sequence? Good question. Take the exponent and divide it by the number of numbers in the pattern. In this case there are 4 numbers in the pattern so 47/4 is 11 remainder 3. The remainder is key. That tells us that we are in the third number of the pattern, 2.
2-8 = -6 If you get a negative number you should pause and think. Many people will choose 6 as the answer. In this case 6 is wrong. Why? 88^47 > 98^37 so you have to imagine the rest of the number. You have to borrow a 1. The easiest thing to is to add a 1 in front of the 2. So 12 - 8 = 4.
Additional GMAT Units Digit Practice Questions
Here is another units digit question from the GMAT Official Guide: If n = (33)^43 + (43)^33 what is the units digit of n?
This GMAT question of the day puzzle goes beyond digits into powers of 10 but is a great one to be familiar with as I've seen this style on a multiple official GMATs.
Here's a digits Data Sufficiency Question from GMAT Question of the Day It's a bit more involved but good practice.