A four digit number is such that the product of all of its digits is 126. The sum of all the digits

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29 Jul 2015 Four digit number

A four digit number is such that the product of all of its digits is 126. The sum of all the digits is equal to the 2 digit number formed by using thousands digit and tens digit (Thousand digit in tens place & ten digit in units place) which in turn is equal to 19. Then difference of units and thousand place of the number is, given that this difference is positive.

OPtion

1) 0
2) 1
3) 2
4) 3
5) 4
6) 5
7) 6
8) 7
9) 8
10)9

Solution

Let the number is 1000a+100b+10c+d
According to given conditions
a*b*c*d = 126
a+b+c+d = 10a+c = 19
so a = 1 and c = 9
b*d = 126/9 = 14
b+d = 9
on solving b = 2, d = 7 and b = 7, d = 2
so difference = 7-1 = 6 and 2-1 = 1

Option 6)

Correct Option: 6 Best Solution (1)