If a and b are distinct positive integers. The units digit of a^2 is equal to the units digit of a, and the units digit of b^2 is equal to the units digit of b. If the units digit of a·b is equal to neither the units digit of a nor the units digit of b, then what is the units digit of a·b? Choose the correct answer: A) 0 B) 1 C) 4 D) 5 E) 6
There are four digits which when squared give the same units digits: 0, 1, 5, 6   0^2 = 0   1^2 = 1   5^2 = 25   6^2 = 36   So a and b must take 2 of these values. They are positive integers so 0 is not possible.   If one of the digits is 1, when the other is multiplied by 1, you will get the same digit. 1*5 = 5   So 1 is out of the picture.   Then you have only two digits left 5 and 6. So out of a and b, one must be 5 and the other 6.   5*6= 
<gadget id="calculator">5*6</gadget>
<output>30</output>
30 so units digit of their product= 0   0nswer (0)
<result>A</result>
If a and b are distinct positive integers. The units digit of a^2 is equal to the units digit of a, and the units digit of b^2 is equal to the units digit of b. If the units digit of a·b is equal to neither the units digit of a nor the units digit of b, then what is the units digit of a·b?