Latest Elitmus Aptitude Question SOLUTION: When a certain no 'x' is multiplied by 18,the product 'y' has all digits as 4s. What is the minimum no of digits'x' can have? a)8 b)9 c)12 d)18

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(#M40038700) ELITMUS Numerical Ability question no system Keep an EYE

When a certain no 'x' is multiplied by 18,the product 'y' has all digits as 4s. What is the minimum no of digits'x' can have?
a)8 b)9 c)12 d)18

Asked In Elitmus Amit Kumar Pal (9 years ago)

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shreya  (9 years ago)

Ans (a)8
18x=y
x=y/18
18=9*2
according to the divisibility rule of 2 and 9
y is divisible by 2
for being divisible by 9 sum of all digits should be divisible by 9
so 9 times 4 = 36 is divisible by 9 (minimum sum)
18x=444444444
x=444444444/18
x= 8 digit no.

Is this solution Helpfull? Yes (47) | No (11)  

Pratik Keshri  (9 years ago)

a/q -18*x=y ,which contain all 4
then y should be divisible by 18 completely ,to get integer value of x
or ,it should be divisible by 9 and 2 completely
now a no will only be divisible by 9 if sum of the no is divisible by 9
so, clearly it wl be 9(9times4=36)

Is this solution Helpfull? Yes (18) | No (6)  

Abhinav Mishra  (9 years ago)

question is
18x=y where in y all digits are 4
so we can say
9x=y where in y all digits are 2
so,
x=y/9
here x is an integer so y should be divisible by 9
and divisibility rule for 9 is sum of all digit will be divisible by 9
and y containing only 2 so 9 digit make the sum 18 which is divisible by 9
so number of digit will be 9

Is this solution Helpfull? Yes (5) | No (1)  

Abhinav Mishra  (9 years ago)

question is
18x=y where in y all digits are 4
so we can say
9x=y where in y all digits are 2
so,
x=y/9
here x is an integer so y should be divisible by 9
and divisibility rule for 9 is sum of all digit will be divisible by 9
and y containing only 2 so 9 digit make the sum 18 which is divisible by 9
so number of digit will be 9

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

Mithun Kumar Kesari  (9 years ago)

18x=y
so x=y/18, for minimum value of x, so y must have minimum value which is divisible by 18
now y/18 gives 246958
so x has 6 digits.

note- in the question we have to find the no digits of x not y.

Is this solution Helpfull? Yes (2) | No   

saurabh agarwal  (9 years ago)

9 ans...

Is this solution Helpfull? Yes (1) | No (5)  

Akeel Mansuri  (7 years ago)

18x=y where in y all digits are 4
so we can say
9x=y where in y all digits are 2
so,
x=y/9
here x is an integer so y should be divisible by 9
and divisibility rule for 9 is sum of all digit will be divisible by 9
and y containing only 2 so 9 digit make the sum 18 which is divisible by 9
i.e. X*9=2222…18 times
therefore , X= (2222….18 time)/9= 24691358
so , no of digits in X is 8

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