# Difficult Number System Solved QuestionAptitude Discussion

 Q. Let $n$ be the number of different 5 digit numbers, divisible by 4 with the digits 1, 2, 3, 4, 5 and 6, no digit being repeated in the numbers. What is the value of $n$?
 ✖ A. 144 ✖ B. 168 ✔ C. 192 ✖ D. None of these

Solution:
Option(C) is correct

Test of divisibility by 4 is that the last two digits should be divisible by 4.

Case 1 : When the last 2 digits are 12, i.e., _ _ _$12 = 4 × 3 × 2 = 24$ numbers

Case 2 : When the last 2 digits are 16, there are 24 numbers

Case 3 : When the last 2 digits are 24 there are 24 numbers

Case 4 : When the last 2 digits are 32 there are 24numbers

Case 5 : When last 2 digits are 36 there are 24 numbers

Case 6 : When last 2 digits are 52 there are 24 numbers

Case 7 : When last 2 digits are 56 there are 24 numbers

Case 8 : When last 2 digits are 64 there are 24 numbers

Total $= 8 × 24 =$ 192

## (5) Comment(s)

Arun
()

Why option B is incorrect?

Divyansh
()

why 32,52,56,64 is considered as they r not divisible by3, then how 24 came

Balu
()

It is clearly mentioned the number should be divisible by number 4

Deepak Kumar Dubey
()

why last two digit 44 not consider here plz explain.....