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What is the units digit of (a +b)^{2} – (ab)^{2}, where a and b are nonnegative integers?
(1) The difference between any two consecutive multiples of a is 5
(2) b when multiplied by any even integer results in the same units digit, not necessarily equal to units digit of b.
What is the units digit of z^{x}, where x and z are positive integers?
(1) z when divided by 100 has its hundredths digit as 5
(2) The product of z^{2} and z^{3} has the same units digit as z^{2}.
For any positive number n, the function #n represents the value of the number n rounded to the nearest integer. If k is a positive number, what is the units digit of #k?
(1) #(10k) = 10k
(2) #(100k) is 10300.
Arrange the following terms in the increasing order of their units digits:
I. 7^{5}
II. 8^{6}
III. 12^{3}
For any positive number x, the function [x] denotes the greatest integer less than or equal to x. For example, [1] = 1, [1.367] = 1 and [1.999] = 1.
If k is a positive integer such that k^{2} is divisible by 45 and 80, what is the units digit of
n is a positive integer that lies between 100 and 200, exclusive, and has no digits repeated. Is the units digit of n equal to 5?
(1) n is divisible by 9 and the 2digit number formed by inverting the units and tens digit of n is a prime number.
(2) The difference between the units digit and the tens digit of n is the same as the difference between the tens digit and the hundreds digit of n and is equal to 2.
If p and q are positive integers, what is the remainder when (27)^{12p} + (3)^{6q} is divided by 5?
(1) p is an odd prime number
(2) q is divisible by 10
If x and y are distinct positive integers and x+y is even, what is the remainder when (x+y)^{a} is divided by 10, where a is a positive integer?
(1) Units digit of y is 6
(2) (xy)^{a} is divisible by 10.
If a and b are positive integers, is the sum a + b divisible by 4?
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