Question

What is the value of "a” if the last digit of $\left[\right(102{)}^2\times (107{)}^2\times (104{)}^2\times (106{)}^2\times (100+a{)}^2]$ is zero.

• A. 0
• B. 5
• C. 7
• D. Both A and B

Answer 1

The correct option is D

Both A and B

Last digit of ${102}^2$ = 4 Last digit of ${107}^2$ = 9 Last digit of ${104}^2$ = 6 Last digit of ${106}^2$ = 6

Last digit of $\left[\right(102{)}^2\times (107{)}^2\times (104{)}^2\times (106{)}^2\times (100+a{)}^2]$​ is 6, because $4\times 9\times 6\times 6=1296$
Given that, last digit of $\left[\right(102{)}^2\times (107{)}^2\times (104{)}^2\times (106{)}^2\times (100+a{)}^2]$is zero
To make it zero, last digit of $(100+a{)}^2$should be 5 or 0.
So, from the given options, a should be 0 or 5 (Since 6 0 = 0, 6 5 =30)