Target Test Prep Sample Units Digit Pattern Questions
Which of the following is the units digit of 749?
Turning back to the units-digit matrix, we find that the units-digit pattern for powers of 7 is 7–9–3–1. Thus, all powers of 7 that are multiples of 4 have a units digit of 1. The closest multiple of 4 to 49 is 48. This means that 748 has a units digit of 1. Then, 749 has a units digit of 7.
If x is a positive integer, what is the units digit of 316x+18?
We can simplify this fraction to 316x+18 = 316x × 318. We know that the units digits of powers of 3 exhibit the four-number sequence 3–9–7–1. Let’s evaluate 316x and 318 separately:
A second way to solve this problem is to realize that because the product of 16 and any positive integer is a multiple of 16, it is also a multiple of 4. Thus, 316x must have a 1 as the units digit. Then we move forward 18 times in the pattern of 3, 9, 7, 1. Four moves in the pattern get us to 1, 8 moves get us to 1, 12 moves get us to 1, 16 moves get us to 1, and then 2 more moves bring us to the units digit 9.
Variables x and y are positive integers, and
The units digit of 7xy+y
We first need to determine the units pattern of the powers of 7:
71 = 7, 72 = 49, 73 = 343,74 = 2401. From here we see the units digits of powers of 7 follow the four-number pattern 7-9-3-1. We need to determine the units digit of 7xy+y. It may be helpful to express 7xy+y as (7xy) × 7y.
We know that
Thus, Quantity A is greater than Quantity B.