A 4 digit number having all distinct digits is such that the product of all digits is 8 less than th

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11 Jun 2015 4 digit number

A 4 digit number having all distinct digits is such that the product of all digits is 8 less than the sum of all digits. How many such 4 digit number are possible.

OPtion

1) 21
2) 18
3) 9
4) 72
5) 45
6) 54
7) 63
8) 36
9) 51
10)27

Solution

Since sum of all distinct digits is more than their product so definitely one of the digits will be zero. Since sum is 8
only two cases arise
0,1,2,5 and 0,1,3,4
No of numbers having
0,1,2,5 are 3*3*2*1 = 18
Similarly for other
Total 36

Option 8)

Correct Option: 8 Best Solution (9)

Ayan Patra   9 years AGO

Since product of all digits is 8 less than the sum of all digits, it is only possible if one of the four digit is 0.
Now if one digit is 0 the possible combination of digits that satisfies the above mentioned condition are 0, 1, 2, 5 and 0, 1, 3, 4.
Now digits starting with 0 are not considered as 4 digit numbers so the number of valid 4 digit numbers that can be formed from each set of numbers are = 4! - 3! = 18.
For 2 sets = 18 x 2 = 36 numbers containing 4 digits can be formed.

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Supriya Mondal   9 years AGO

Two numbers are satisfy the above condition.
They are- 1250 and 1340
we can write 1250 in 3*3*2*1=18 ways
similarly we can write 1340 in 18 ways too
So, total 18+18=36 such 4 digits numbers are possible
So, option 8)36 is the right answer

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Ashwin Dinesh   9 years AGO

1,0,2,5 ---> 18
1,0,3,4 ---> 18
18+18=36
which is option 8

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Math Lovers   9 years AGO

Suppose number is abcd
then a*b*c*d + 8= a+b+c+d
where a!=b!=c!=d
its only possible when either of a, b, c or d is 0
hence,
8 = sum of 3 single digit number = a+b+c

=> (a,b,c) = (4,3,1) or (5,2,1)
now (4,3,1,0) can be arranged in 18 different ways to make 4 digit number.
in similar way,
now (5,2,1,0) can be arranged in 18 different ways to make 4 digit number.

so total 4 digit number = 36

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pratap kumar sahoo   9 years AGO

no possible=4301
4_ _ _ =6
3_ _ _ =6
1_ _ _ =6
5201
5 _ _ _=6
2 _ _ _=6
1_ _ _=6
so ans=36

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shivaprabhu   9 years AGO

the only two numbers we have that satisfies the the condition is ith numbers 0125 and 0143


therefore total combinations using 4 digits is 4! i.e 24
but the number cannot start with 0 therefore total number of combinations for one number is =4!-3! i.e 18

i.e number of combinations using both numbers is=36

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kishor Mali   9 years AGO

posssible comb are 0,1,3,4 and 0,1,2,5

1) 0,1,3,4 the 4 digit no for this is 18
2) 0,1,2,5 the 4 digit no for this is 18
so total 36

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vini   9 years AGO

The digit are 0, 1, 2 , 3 ,4 ,5 ,6 ,7,8, 9
Let the product of four number is 'A'
and sum of four number be 'B'
B - A = 8 (Given)
So the possible number are
Case 1
0 1 3 4
3*3*2*1 = 18 ways
Case 2
0 5 2 1
3*3*2*1 = 18 ways
So, total possible four digit numbers are ( 18+18)= 36

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Dinni   9 years AGO

4,3,1,0 in 18 ways &
5,2,1,0 in 18 ways.
Total 36 4-digit no.s will get.

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