How many two digit numbers of distinct digits can be formed by

Question

Q-1: How many two digit numbers of distinct digits can be formed by using digits 1, 2, 3, 4, 5, 6 and 7 such that the numbers are divisible by 4?

A) 7
B) 8
C) 9
D) 10
E) 11

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ENGRTOMBA2018 · Answer

Counting the different combinations possible is the easiest method as the options tell you that the correct number is a relatively small number.

The total cases possible are:
12
16
24
32
36
 44  (not counted as we need distinct digits)
52
56
64
72
76

Edit: Total: 10

D is the correct answer.

KS15 · Answer

12,16,24,32,36,52,56,64,72,76
Answer D=10

mvictor · Answer

we don't have many possibilities: 6*7 = 42 possible numbers. making some assumptions, numbers in which 1, 3, 5, 7 are units digit can't be taken into consideration. we have 6 of each - total 24 numbers. we are left with 18. out of the 18, we can list those that can't be divisible by 4: 42, 62, 14, 34, 54, 74, 26, 46. 8 numbers. thus - answer is 18-8=10

another way, list all possible numbers:
12
16
24
32
36
52
56
64
72
76

we have 10 numbers.

chetan2u · Answer

hi,
  we don't require to do any calculations but understand the properties involved..

here for a number to be div by 4, the last 2-digits should be div by 4 and this gives us two cases-- 
  1) If the first digit is ODD, the units digit should be non multiple of 4 EVEN number..  
so hundreds digit can be any of 4 - 1,3,5,7- and units digit any of 2 - 2,6--
total 4*2=8..
  2) If the first digit is EVEN, the units digit should be multiple of 4..  
so hundreds digit can be ONLY 1 - 4 - and units digit any of 2 - 2,6-- since 4 will make both digits identical
total 1*2=2.

TOTAL = 8+2=10 
D

May help when there are lot of combinations possible..

Archit3110 · Answer

for a no to be divisible by 4 ; the digit should be twice divisible by 2 ; in this case possible unit digits value can be only 4,6 and the tens digit can be taken by other 5 digits so total combinations ; 5*2 ; 10 IMO D

hriday17 · Answer

The nos are- 12, 16, 24, 32, 36, 52, 56, 64, 72, 76. 
The answer to this question is 10

Fdambro294 · Answer

I might be missing something in the approach....

but the Units Digit does NOT have to be only 4 and 6

12 or 32 are 2 example that work fine also

it ended up as the right answer, but is this approach correct?

chetan2u · Answer

No, that is not the correct approach. 
By this method 14, 34 are also multiple of 4, but they are not. 
Also 12, 32, 72 are not, while they are.

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How many two digit numbers of distinct digits can be formed by

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