Latest TCS Aptitude Question SOLUTION: A number when divided by 100 leaves a quotient (Q) and a remainder (R). How many three-digit natural numbers are there such that Q + R is divisible by 11?

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A number when divided by 100 leaves a quotient (Q) and a remainder (R). How many three-digit natural numbers are there such that Q + R is divisible by 11?

Asked In TCS Prashant (12 years ago)

Unsolved Read Solution (11)

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Nikhil  (12 years ago)

it will be like

110 / 100 => Q=1 , R=10

Q+R= 11
11/11 =0

similarly for 121,132,143,154,165,176,187,198

i.e total 100-200 = 9 numbers
so in 100-1000 there will be 9*9 = 81 numbers

Is this solution Helpfull? Yes (39) | No (6)  

shubham  (12 years ago)

From 100 to 200. Q would be 1 and reminder(R)need to be 10,
21,32,43,54,65,76,87,98 again 9 numbers.
From 200 to 100. Q would be 2 and R need to be
9,20,31,42,53,64,75,86,97 again 9 numbers.....
LIKEWISE
100 to 200----9 numbers
200 to 300----9 numbers
300 to 400----9
400 to 500----9
500 to 600----9
600 to 700----9
700 to 800-----9
800 to 900-----9
900 to 1000 ---9
so total 9x9=81 numbers

Is this solution Helpfull? Yes (10) | No (6)  

raj  (12 years ago)

There will be only 9 such numbers...

These numbers are:-

990 =>
990/100 => Q=9 & R=90
And, Q+R = 9+90 = 99 is divisible by 11

880 =>
880/100 => Q=8 & R=80
And, Q+R = 8+80 = 88 is divisible by 11

770 =>Similarly check for rest of the values
660 =>
550 =>
440 =>
330 =>
220 =>

110 =>
110/100 => Q=1 & R=10
And, Q+R = 1+10 = 11 is divisible by 11

So, total 9 numbers exists b/w 101 to 999 (i.e in all three-digit natural numbers)

Is this solution Helpfull? Yes (7) | No (21)  

raj  (12 years ago)

Sorry guys, mine above shown answer is wrong...plz dont 'like' it
Correct answer is 81 only.

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

sachin kumar  (12 years ago)

because no. is 3 digit we will have to take q=single digit no.(1,2,3,4,5,6,7,8,9)
when q=1,then we take
r;
10
10*2+1=21
10*3+2=32
10*4+3=43
.
.
.
10*9+8=98

total combinations=9;
now we take q=2,3,4,5.......9
every q give 9 combination
so,3-digit natural numbers=9*9=81ans

Is this solution Helpfull? Yes (3) | No   

Arka Laha  (12 years ago)

there will be 81 such nos... becoz btween 100 and 200 the nos are 110,121,132,143,154,165,176,187,198 there the q+r is divisible by 11 so similerly between 200,300.........till 900,1000..

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

Nikhil  (12 years ago)

answer is 81

100-200 = 9 numbers
200-300 =9 numbers

so total 9*9 = 81

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

PRADYUMNA KUMAR JHA  (12 years ago)

answer would be 9
it will multiples of 110 up to 9times
like 110,220,330,440.............,990 if .we divide these no by 100 so Q+R will be definetly divisible by 11

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

rahul  (12 years ago)

hii guys correct answer is 81

Is this solution Helpfull? Yes | No   

DEWANSHU AWASTHI  (12 years ago)

answer is 81

N100 =Q+R
100

Is this solution Helpfull? Yes | No (2)  

Rahul Sharma  (11 years ago)

n1=110 and n2=990
even both extreme three digits numbers divisble by 11.
so (n2-n1)/11 +1 =81

Is this solution Helpfull? Yes | No   

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