Latest Elitmus Aptitude Question SOLUTION: when a certain number 'X' is multiplied by 18, the product 'y' has all digits as 4s. What is the minimum number of digits 'X' can have? (a)8 (b)9 (c)12 (d)18

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(#M40018183) ELITMUS question ELITMUS MATHS PUZZLE Keep an EYE

when a certain number 'X' is multiplied by 18, the product 'y' has all digits as 4s. What is the minimum number of digits 'X' can have?

(a)8
(b)9
(c)12
(d)18

Asked In Elitmus pavan (11 years ago)

Unsolved Read Solution (6)

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Read Solution (6) :

vinod  (11 years ago)

by verification: (12345679)*9= 111111111
(12345679)*18=222222222
and in the same way(12345679)*36=444444444
so the num multiplied with 18 to get all 4 digits is
=(12345679)*2*18=24691328*18
=444444444
so the minimum no of digits x can have are 8 digits

Is this solution Helpfull? Yes (29) | No (7)  

prayas goel  (10 years ago)

X*18=Y (having all 4s
Digit on R.H.S. must be divisible by 18 or must be divisible by p
So, considered a condition that satisfy RHS (divisible by 9 and having all 4s)
The only situation will be 9 times 4 i.e. 444444444
So when 444444444 divided by 18 it gives 24691358 (having 8 digits)

Is this solution Helpfull? Yes (6) | No (3)  

Safal kumar  (9 years ago)

x*18=444...
x=(444...)/18
x=(222...)/9
any no is divisible by 9 only when sum of all its digits is divisible by 9
so
2+2+2..9 times=18 which is divisible by 9
so, x=222222222/9=24691358, which has 8 digits.
Answer=8

Is this solution Helpfull? Yes (6) | No   

shubham jain  (10 years ago)

from where did u get the nos. 12345679 ???

Is this solution Helpfull? Yes (3) | No   

naga sarath chand  (10 years ago)

b-9 digits is exactly correct , the reason is x*18 = 44444...,so here the number
x = 4444444...../18.so 44444... should be divisible by 18,so it should be divisible by both 2 and 9.as last digit is 4 so divisible by 2 ok,but it should contain 9 fours to be divisible by 9. see 444444444(sum of digits = 36-divisible by 9).

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prayas goel  (10 years ago)

X*18=Y (having all 4s
Digit on R.H.S. must be divisible by 18 or must be divisible by 9
So, considered a condition that satisfy RHS (divisible by 9 and having all 4s)
The only situation will be 9 times 4 i.e. 444444444
So when 444444444 divided by 18 it gives 24691358 (having 8 digits)

Is this solution Helpfull? Yes (2) | No (1)  

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