The product of the units digit, the tens digit, and the hundreds digit of the positive integer m is 96. What is the units digit of m?
(1) m is odd.
(2) The hundreds digit of m is 8
Question inference-
Let m= abc ( where a,b,c are the units in hundreds, tens and units place respectively)
Now, from question we know that axbxc = 96
also, a,b,c, are digits and hence belongs to the set { 0,1,2,3,4,5,6,7,8,9 }
Factorizing 96 we get 96= 2^5 x 3^1
Only possible solution sets of abc from above equations are { 2, 8, 6} , { 4, 4, 6}, { 8, 4, 3 }
Since, 2 x 8 x 6, 4 x 4 x 6, 8 x 4 x3 = 96
Now statement 1 :
(1) M is odd, hence units digit is odd and only solution set where one number is odd is { 8, 4, 3 }hence unit digit = 3 ( Sufficient)
Now statement 2 :
(2) Hundred digit of m is 8,
we have 2 solution sets where 8 appears => { 2,8,6} & { 8,4,3}
hence it is clearly insufficient
Correct Answer is A