Number System
Aptitude

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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

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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.....


Radhika
 ()

Because the question says, 'no digit being repeated in the numbers' thats why :)