Question

Find a 4-digit odd number using each of the digits 3,2,6,5 only once such that when the first and the last digits are intercharged,it is divisible by 4.

Answer 1

divisibility rule for 4
is first of all last digit should be even
and the last two digits should be divisible by 4
thus
we see that even numbers are 2 and 6
after interchanging digits
last two digits
let say 62 but 62 not divisible by 4
26 it is also not divisible by 4
32 it is divisible
36 it is divisible
52 it is divisible
56 it is divisible
now we know that third digit of number can be 3 and 5
and first digit can be 2 and 6
now we have two choices to fill first digit either 2 or 6
and 2 choices for 3 rd digit
either 3 or 5
now for remaining two digits it can be filled only by 2 ways
thus such total numbers are 2*2*2 = 8
these numbers are
•2635
•2536
•6532
•6235
•2653
•2356
•6352
•6253