Latest TCS Aptitude Question SOLUTION: a person starts writting four digit numbers, how many times did he write 2

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(#M40157553) TCS Numerical Ability question probability Keep an EYE

a person starts writting four digit numbers, how many times did he write 2

Asked In TCS SACHIN SACHIN (8 years ago)

Unsolved Read Solution (12)

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Read Solution (12) :

Rajashekhar Guntuka   (8 years ago)

total 4 digit no. = 9*10*10*10 = 9000
not containing 2 = 8*9*9*9 = 5832
total 4 digit number contain 2 = 9000 - 5832 = 3168
So ans:3168

Is this solution Helpfull? Yes (23) | No (5)  

akhtar husain  (8 years ago)

lets see from 0-9 --> 1
from 10-19 --> 1
from 20-29 --> 11
from 30-39 --> 1
from 40-49 --> 1
from 50-59 --> 1
from 60-69 --> 1
from 70-79 --> 1
from 80-89 --> 1
from 90-99 --> 1

which makes 20 from 0 to 99

now please observer that similar pattern follows for
000 - 099 -->20
100 - 199 --> 20
300 - 399 --> 20
400 - 499 --> 20
500 - 599 --> 20
600 - 699 --> 20
700 - 799 --> 20
800 - 899 --> 20
900 - 999 --> 20

however for 200 to 299 we have that extra 2 as first digit for all these 100 numbers, so
200 - 299 --> 120

so
000 - 999 -->300

so for
1000 - 1999 -->300
3000 - 3999 -->300
4000 - 4999 -->300
5000 - 5999 -->300
6000 - 6999 -->300
7000 - 7999 -->300
8000 - 8999 -->300
9000 - 9999 -->300

again for
2000 - 2999 -->300 + 1000 as we have that extra 2 in the first digit for all these numbers, hence

2000 - 2999 -->1300

So total number of times digit 2 is used 1000 - 9999 is 3700

Join The Disc

Is this solution Helpfull? Yes (16) | No   

yash  (8 years ago)

Let the four digit number be abcd.

Case 1: 2 appears only once in the 4-digit number.
No. of ways of having a number of the form -
2bcd = 9*9*9 = 729
a2cd = 8*9*9 = 648
ab2d = 8*9*9 = 648
abc2 = 8*9*9 = 648

Total no. of ways = 2673
Total no. of times 2 appears = 2673

Case 2: 2 appears only twice in the 4-digit number.
No. of ways of having a number of the form -
22cd = 9*9 = 81
2b2d = 9*9 = 81
2bc2 = 9*9 = 81
a2c2 = 8*9 = 72
ab22 = 8*9 = 72
a22d = 8*9 = 72

Total no. of ways = 459
Total no. of times 2 appears = 459*2 = 918

Case 3: 2 appears only thrice in the 4-digit number.
No. of ways of having a number of the form -
222d = 9
22c2 = 9
2b22 = 9
a222 = 8

Total no. of ways = 35
Total no. of times 2 appears = 35*3 = 105

Case 4: 2 appears four times in the 4-digit number.
2222 i.e. only once
Total no. of times 2 appears = 4

So, total no. of times 2 appears = 2673+918+105+4 = 3700.

Is this solution Helpfull? Yes (9) | No   

Rajashekhar Guntuka   (8 years ago)

Ans:4000
X X X X
for thousand's position no of 2's 1×1000=1000
for hundredth position no of 2's
10×100=1000
for tenth's position no of 2's
10×10×10=1000
for one's position no of 2's
1000

So ans:4000

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

shivakumar ananthoju  (8 years ago)

use this formula :n*10^(n-1)
where n is equal to no of digits u want..

Is this solution Helpfull? Yes (3) | No   

ARPIT SHUKLA  (8 years ago)

25 common sence

Is this solution Helpfull? Yes (2) | No (7)  

sandesh  (6 years ago)

When 2 is at unit place=9*10*10*1
When 2 is at tenth place=9*10*1*10
When 2 is at hundred place=9*1*10*10
When 2 is at thousand place = 1*10*10*10
So Total no. = 900 + 900 + 900 + 1000 = 3700

Is this solution Helpfull? Yes (2) | No   

anishka jain  (8 years ago)

0 as one girl is already there

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

lav  (8 years ago)

1 digit---- 1 time
10---------- (1*10)+10=20
100---------(20*10)+100=300
1000--------(300*10)+1000=4000

Is this solution Helpfull? Yes | No (4)  

Subhrant Pandey  (8 years ago)

total no. ways a 4 digit no can be formed=9*10*10*10
total no ways in which a 4 digit no can be formed without using 2=8*9*9*9
total no ways in which a 4 digit no can be formed using 2=(9*10*10*10)-(8*9*9*9)=3168

Is this solution Helpfull? Yes | No   

Monisha T  (6 years ago)

i don't know

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Atishay Singhai  (4 years ago)

When 2 is at unit place=9*10*10*1
When 2 is at tenth place=9*10*1*10
When 2 is at hundred place=9*1*10*10
When 2 is at thousand place = 1*10*10*10
So Total no. = 900 + 900 + 900 + 1000 = 3700

Is this solution Helpfull? Yes | No   

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