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Natural Numbers

by Aman verma » Sun Feb 21, 2010 2:12 am
Q: All the natural numbers less than 1000 but not containing the digit 5 are arranged horizontally in descending order .What is the 555th number on the list ?

a) 111

b)182

c)213

d)284

e)315
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by harsh.champ » Sun Feb 21, 2010 2:16 am
Aman verma wrote:Q: All the natural numbers less than 1000 but not containing the digit 5 are arranged horizontally in descending order .What is the 555th number on the list ?

a) 111

b)182

c)213

d)284

e)315
Now,
If 5 is there,we get 445.
NOw,555/5=111
Hence,subtracting we get 334.
111/5=22.2
Hence we get 310
22.2/5 =4.44
Hence,315 E. is the answer
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by shashank.ism » Sun Feb 21, 2010 2:39 am
Aman verma wrote:Q: All the natural numbers less than 1000 but not containing the digit 5 are arranged horizontally in descending order .What is the 555th number on the list ?

a) 111

b)182

c)213

d)284

e)315
the no. would be arranged (without excluding digit 5 ) 1000, 999,998,,,,,,,,,,,,,,,,1
so 555 no. will be 1000-555 +1 = 446
now we exclude alll digit having 5
now 555/5 =111 these are all unit digits..
again 55/5 = 11 --> 11x9 = 99
again 5/5= 1 --> 45 -10 -5 = 30
so subtract 111+99+30= 122
446-240 = 206

I think I m doing some mistake her ..but it will be around 213 Ans C
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by Aman verma » Sun Feb 21, 2010 3:09 am
Ans: [spoiler]c) 213[/spoiler].But I don't have the solution.If anybody could provide the correct solution...
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by ajith » Sun Feb 21, 2010 3:27 am
Aman verma wrote:Q: All the natural numbers less than 1000 but not containing the digit 5 are arranged horizontally in descending order .What is the 555th number on the list ?
Let us see how many natural numbers are there between 1 to 1000; containing 5

1-100 (10+9) - 19


1-499 => 19*5
500-599 = 100
600-999 = 19*4

Total = 19*9+100

There are 271 numbers

No of other numbers(not containing 9) = 729

Out of these we need to find out 555th in descending order

or (729-555) = 174th in ascending order

There are 81 between 1-100
there are 81 between 101-200
162
9 more between 200-210 ; total 171
213 is the 174th
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by harsh.champ » Sun Feb 21, 2010 3:29 am
Aman verma wrote:Ans: [spoiler]c) 213[/spoiler].But I don't have the solution.If anybody could provide the correct solution...
Hey Aman,
You have written that the OA is C.I found the answer to be E.
I am posting my method below:-
If 5 is there,we get 445.
NOw,555/5=111
Hence,subtracting we get 334.
111/5=22.2
Hence we get 310
22.2/5 =4.44
Hence,315 E. is the answer
Can someone guide me where I went wrong??
Thanks in advance.
It takes time and effort to explain, so if my comment helped you please press Thanks button :)



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by ajith » Sun Feb 21, 2010 3:32 am
harsh.champ wrote: Hey Aman,
You have written that the OA is C.I found the answer to be E.
I am posting my method below:-
If 5 is there,we get 445.
NOw,555/5=111
Hence,subtracting we get 334.
111/5=22.2
Hence we get 310
22.2/5 =4.44
Hence,315 E. is the answer
Can someone guide me where I went wrong??
Thanks in advance.
If 5 is there we get 445?

I do not get that statement
I do not get why you did the rest of the stuff either
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by harsh.champ » Sun Feb 21, 2010 3:39 am
ajith wrote:
harsh.champ wrote: Hey Aman,
You have written that the OA is C.I found the answer to be E.
I am posting my method below:-
If 5 is there,we get 445.
NOw,555/5=111
Hence,subtracting we get 334.
111/5=22.2
Hence we get 310
22.2/5 =4.44
Hence,315 E. is the answer
Can someone guide me where I went wrong??
Thanks in advance.
If 5 is there we get 445?

I do not get that statement
I do not get why you did the rest of the stuff either
Ok,I will explain it to you-step by step.
In the question,it is written-
but not containing the digit 5 are arranged horizontally
Lets assume those no.s are included.
Then 1000,999,998,997,.........................,445-This will be the 555th no.-Agreed.
Now, I am subtracting those no.s which are divisible by 5(1000,995,....)
SO you get 555/5=111 numbers-Agreed
Now,I have also counted 111/5 nos. i.e 22.2
Like this I had adopted my approach.
I know that the answer does not match with the OA but I can't seem to figure out where I went wrong .
It takes time and effort to explain, so if my comment helped you please press Thanks button :)



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by ajith » Sun Feb 21, 2010 4:12 am
harsh.champ wrote:
Ok,I will explain it to you-step by step.
In the question,it is written-
but not containing the digit 5 are arranged horizontally
Lets assume those no.s are included.
Then 1000,999,998,997,.........................,445-This will be the 555th no.-Agreed.
Now, I am subtracting those no.s which are divisible by 5(1000,995,....)
SO you get 555/5=111 numbers-Agreed
Now,I have also counted 111/5 nos. i.e 22.2
Like this I had adopted my approach.
I know that the answer does not match with the OA but I can't seem to figure out where I went wrong .
your approach doesnt take into account numbers from 500-599 all of them has 5
moreover it doesnt take care of 50-59

and it is not logical to deduct powers of 5
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by firdaus117 » Sun Feb 21, 2010 4:20 am
Lets consider three digit number without 5 as 'HTO' where H,T,O are respectively digits at hundreds,tens and ones place.
Now,we start counting the numbers from 999,998,997 i.e. in descending order.
Now, H can be 9,8,7,6,4,3,2 and 1.Total 8 values.
T and O each can take 9 values from 0 to 9 except 5.
Total numbers=8*9*9=648
Now exclude numbers in range 100-199=9*9=81 numbers from 648 values.
Remaining numbers=648-81=567 values.(Still we need to lessen 567-555=12 numbers)
Now there are 9 values b/w 200-209.210,211 and 212 are the remaining three.
The countdown stops at 213 for 555th number. :D
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by shashank.ism » Sun Feb 21, 2010 5:47 am
harsh.champ wrote:
Aman verma wrote:Ans: [spoiler]c) 213[/spoiler].But I don't have the solution.If anybody could provide the correct solution...
Hey Aman,
You have written that the OA is C.I found the answer to be E.
I am posting my method below:-
If 5 is there,we get 445.
NOw,555/5=111
Hence,subtracting we get 334.
111/5=22.2
Hence we get 310
22.2/5 =4.44
Hence,315 E. is the answer
Can someone guide me where I went wrong??
Thanks in advance.
Harsh you have left many numbers in between

like number with 5xx = 45-10 -5
number with x5x =11x9 ==99
number at end = 5 = 111
though i was not able to get exact ans but I was near solution ...U left the numbers 5xx and x5x....please consider those numbers..u will get to the solution..
meanwhile I m checking ajith ans...he has solved the problem .well...
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