Latest CAT Aptitude Question SOLUTION: when a certain number x is multiplied by18,the product y has all digits as 4s.what is the minimum number of digits x can have?

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(#M40010362) CAT Logical Reasoning question Keep an EYE

when a certain number x is multiplied by18,the product y has all digits as 4s.what is the minimum number of digits x can have?

Asked In CAT deepika (11 years ago)

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Read Solution (10) :

Huzefa Chikhly  (11 years ago)

x*18=444....
x=(444....)/18
x=(222....)/9

we know that any no. is divisible by 9 only when sum of all its digit is divisible by 9
so
2+2+2...9times=18 which is divisible by 9
so
x=222222222
so there r 9 digits in x

Is this solution Helpfull? Yes (34) | No (14)  

Mayuresh Srivastava  (10 years ago)

222222222*18=3999999996
it is not equal to 4444....
as the qstn is 'minimum' no of digits.
ans is 8 digits and the no is 24691358

Is this solution Helpfull? Yes (23) | No (9)  

Nilesh  (11 years ago)

9 digits
so that sum of digits is divisible by 9.

Is this solution Helpfull? Yes (3) | No (12)  

Siddartha Mulumudi  (9 years ago)

Its simple....
4444444444...... / 18. Go on divide until U get reminder 0. When U get reminder 0. Stop and note down the total number of digits in the answer

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

deepika  (11 years ago)

9 digits is the answer,but how??plz elaborate..

Is this solution Helpfull? Yes (1) | No (7)  

deepika  (11 years ago)

here its asked how many digits can x have??so,18*8digits=all 4's. number of 4's are 9.

Is this solution Helpfull? Yes (1) | No (6)  

Dasaradha Ramaiah  (9 years ago)

24691358 is the number and it has 8 digits.

Is this solution Helpfull? Yes | No (1)  

siddharth prakash singh  (9 years ago)

Good explanation SIDDARTHA. Thanx

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Sanjay Mogra  (7 years ago)

Digit 444444444...n is written as 4 (10^n-1)/9 so 18 x = 4( 10 ^n-1)/9 So n will be 9 . So digit of x will be 1 less than of 4444 number that is 8

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ss  (5 years ago)

FIRST METHOD to solve :

x= 444444..... / 18
x= 22222..... / 9
sum of the digits should be divisible by 9.
so 2+2+2....(9times) =18 which is divisible by 9.
(Since 2 is less than 9 therefore, 22 will be the first no. to be divided by 9. Thus deducting one 2 from 9
2s. i.e 9-1=8 )
so there are 8 minimum digits.
and the number will come out to be 24691358.
24691358 * 18 = 444444444.


SECOND METHOD
to solve this is keep on dividing 444.... by 18 unless the remainder comes out to be 0. The quotient will be our x . x=24691358
Count the number of digits that is our answer i.e 8.
24691358 * 18 = 444444444

Is this solution Helpfull? Yes | No (1)  

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