Latest Elitmus Aptitude Question SOLUTION: sum of all 4 digit num. exactly divisible by 3 if no digit is repeated ( i.e. 1454 is not allowed becoz 4 is 2 times here, 1436 is allowed, etc)

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(#M40157065) ELITMUS Numerical Ability question permutation & combination Keep an EYE

sum of all 4 digit num. exactly divisible by 3 if no digit is repeated ( i.e. 1454 is not allowed becoz 4 is 2 times here, 1436 is allowed, etc)

Asked In Elitmus Dwarkesh (7 years ago)

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NIDHISH  (7 years ago)

To check divisibility by 3: Sum up all digits and that sum obtained should be divisible by 3.

By applying this rule:

The first 4 digit number divisible by 3: 1002 (Sum of the digits: 3)

The last 4 digit number divisible by 3: 9999 (Sum of the digits: 36)
9999=1002+(n−1)3
8,997=(n−1)3
2999=(n−1)
n=3000

Now use this value of n in formula of sum:

Sum: (n/2)∗(a+l)
(n/2)∗(a+l)
=>(3000/2)∗(1002+9999)
=>(3000/2)∗(1002+9999)

=>1500∗11001
=>1500∗11001

=>16501500

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Subhabrata Sarkar  (7 years ago)

Done in the exact way someone solved a previous similar question.

We know that zero can't be in thousands place. But let's assume that our number could start with zero.

The formula to find sum of all numbers in a permutation is

111 * no of ways numbers can be formed for a number at given position * sum of all given digits

No of 1 s depends on number of digits

So,the answer us

1111 * 504 *(0+1+2+3+4+5+6+7+8+9) = 25197480

We got 504 as follows..if we have 0 in units place we can form a number in 9*8*7 ways...this is for all numbers. So we have substituted 504 in formula..

Now, this is not the final answer because we have included 0 in thousand's place...so we have to remove the sum of all numbers that starts with 0.

This is nothing but the sum of all 3 digits numbers formed by 1 2 3 4 5 6 7 8 9.. because 0 at first place makes it a 3 digit number.

So the sum for this is 111 * 72 * (1+2+3+4+5+6+7+8+9).
= 359640

Hope u understood why we use 72.. each number can be formed in 9*8 ways

So, the final answer is 25197480-359640= 24837840

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somanita  (7 years ago)

I think ans will be 32173848
as per question 4 digit number exactly divisible by 3 and also digits are not repeated
so 1st num will be 1023 then 1026.....
i.e 1023,1026,1029..........9876
now using the formula n/2{a+l}
it ll be 32173848

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Sangeetha Chinnasamy  (7 years ago)

1425 is the ans.becoz it is the 4 digit no exactly divisble by 3

Is this solution Helpfull? Yes (1) | No (14)  

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