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QUESTION #14:If N = ( 1436)^A*(1054)^B. Where A and B are positive integers. What is the units digit of N?

(1) A + B = 6

(2) B = 2

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JAMBOBREE OFFICIAL SOLUTION:The unit’s digit of N can be calculated by multiplying the unit’s place of (1436)^A with the unit’s digit of (1054)^B.

Units digit of (1436)^A will be 6 as we know that 6 raised to any positive integer will always result in an integer whose units digit is 6

To calculate the units digit of (1054)^B can be calculated by using the cyclicity concept. Now according to cyclicity concept 4 raised to any positive odd integer will always result in an integer with unit’s digit as 4 and 4 raised to any positive even integer will always result in an integer with unit’s digit as 6.

Statement 1 In the equation A + B = 6 if we take different values of A we will have different values of B. so B can be odd or even.

Hence If B is even then the unit’s digit of (1436)^A*(1054)^B will be 6

And If B is odd then the units digit of (1436)^A*(1054)^B will be 4

Hence as we do not have a definite answer for the questions asked so the statement is insufficient

Statement 2 As B= 2 so the units digit of (1436)^A^(1054)^B will be 6. We have a definite answer for the question asked. So this statement is sufficient to answer.

Answer is B
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