Latest Elitmus Aptitude Question SOLUTION: Q. A number \'Z\' contains all the digits from 1 to 9 exactly once. Z is divisible by 99. what will b the number on its hundredth place. Option a) 1 b) 2 c) 3 d) 4

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(#M40032524) ELITMUS Numerical Ability question Algebra Keep an EYE

Q. A number 'Z' contains all the digits from 1 to 9 exactly once. Z is divisible by 99. what will b the number on its hundredth place.
Option
a) 1
b) 2
c) 3
d) 4

Asked In Elitmus somesh modi (10 years ago)

Unsolved Read Solution (13)

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Read Solution (13) :

Saraswathy  (10 years ago)

Let d digits be abcdefghi
if it is divisible by 99 , it shud be divisible by both '9' nd '11'
divisible by 11 means ----> (a+c+e+g+i)-(b+d+f+h) / 11
--------------------------> (7+5+6+2+8)-(1+3+4+9) = 28-17 which is divisible by 11

so the number is 715364298

nd the 100th digit is "2"

Is this solution Helpfull? Yes (16) | No (22)  

Anoop  (9 years ago)

more than one answers are possible like
142738596
542738196
541738296
541728396

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

Saraswathy  (10 years ago)

can i know the right answer if its wrong...

Is this solution Helpfull? Yes (5) | No (3)  

deep chandra bhatt  (10 years ago)

with all due respect wt abt 917365482 i got this ans

Is this solution Helpfull? Yes (2) | No (4)  

Ayush Rastogi  (10 years ago)

suppose digits be abcdefghi
if it is divisible by 99 ,
it shud be divisible by both '9' (7+5+6+2+8)+(1+3+4+9) = 45 which is divisible by 9

and
divisible by 11 means is (a+c+e+g+i)-(b+d+f+h)/11
(7+5+6+2+8)-(1+3+4+9) = 28-17 which is divisible by 11

so the number is 715364298

so the 100th digit is 2

Is this solution Helpfull? Yes (2) | No (4)  

Adil khan  (6 years ago)

approach is right but in the question not mentioned that number is greatest or smallest .so question is incomplete because if u find any no which divisible by 99 if u exchange the no from odd place sum of the digits of odds place always be 28 and the even place 17 see ur self in above examples
like 7+5+6+2+8 or if exchang the no 5+7+6+2+8 or 2+8+7+5+6 and similar for even place.

Is this solution Helpfull? Yes (2) | No   

deep chandra bhatt  (10 years ago)

this can be answer 214365789 then 100 digit is 7

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

Saraswathy  (10 years ago)

but there is no such option...

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

kumar madhav  (10 years ago)

At 100th place we can put 9,8,6,4,1 .Among the options 4 can be the answer.

Is this solution Helpfull? Yes (1) | No   

monika  (7 years ago)

99 = 9×11 where 9 and 11 are coprime. Therefore, if a number is divisible by 9 and 11, it is divisible by 99 also

Here all the digits from 1 to 9 are used exactly once. 1+2+...+9 = 45. 45 is divisible by 9.
=> any number formed by using the digits 1 to 9 exactly one is divisive by 9

Hence, any number formed by using 1 to 9 exactly once is divisible by 99 if the same is divisible by 11

For number to be divisible by 11, [Sum of odd numbered digits] - [sum of even numbered digits] = 0 or divisible by 11

for example, (5+6+7+2+8) - (1+3+4+9) = 11

Hence, 516374298 is a number which is divisible by 99
In this case, the digit at hundredth place is 2

But this is not the only answer. We can get other numbers also in a similar way such as 245837196 and accordingly different answers for the hundredth place digit(like 1 in this case)

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

Rupesh Kumar Rohit  (7 years ago)

99 = 9×11 where 9 and 11 are coprime. Therefore, if a number is divisible by 9 and 11, it is divisible by 99 also

Here all the digits from 1 to 9 are used exactly once. 1+2+...+9 = 45. 45 is divisible by 9.
=> any number formed by using the digits 1 to 9 exactly one is divisive by 9

Hence, any number formed by using 1 to 9 exactly once is divisible by 99 if the same is divisible by 11

For number to be divisible by 11, [Sum of odd numbered digits] - [sum of even numbered digits] = 0 or divisible by 11

for example, (5+6+7+2+8) - (1+3+4+9) = 11

Hence, 516374298 is a number which is divisible by 99
In this case, the digit at hundredth place is 2

AND

But this is not the only answer. We can get other numbers also in a similar way such as 245837196 and accordingly different answers for the hundredth place digit like 1

Is this solution Helpfull? Yes (1) | No   

Rajeev kumar  (7 years ago)

number is divisible by 99 means divisible by 9 and 11 both
number formed by digit 1 to 9 i.e (1+2+3+4+5+6+7+8+9)=45 is always divisible by 9
but not divisible by 11
condition for divisibility by 11 is-(sum of odd places number-sum of even places number)
so here, hit and trial method
digit taken from 1 to 9
for e.g (5+6+7+8+2)-(3+4+1+9)=11
is divisible by 11
so number is 536471298
hundredth place digit is 2

Is this solution Helpfull? Yes (1) | No   

abhishekkumar  (10 years ago)

wt abt 928675341

Is this solution Helpfull? Yes | No (1)  

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