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18 Dec 2024, 09:36
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The number k is 123456...998999.
Now, numbers from 1 to 9 count to 9 digits.
Numbers from 10 to 99 count to 90*2=180 digits.
So, we need (341-189)=152 digits more to find the 34ist digit. Now, numbers from 100 onwards will have 3 digits. Now, closest multiple of 3 nearest to 152 is 153. 153=51*3.
So, the 51st digit starting with 100 will be 150.
It implies 1 will be the 151st digit, 5 will be 152nd digit and 0 will be the 153rd digit. We have to find out 152nd digit (341st overall) which is 5.
So, answer is 5 (D).
Now, numbers from 1 to 9 count to 9 digits.
Numbers from 10 to 99 count to 90*2=180 digits.
So, we need (341-189)=152 digits more to find the 34ist digit. Now, numbers from 100 onwards will have 3 digits. Now, closest multiple of 3 nearest to 152 is 153. 153=51*3.
So, the 51st digit starting with 100 will be 150.
It implies 1 will be the 151st digit, 5 will be 152nd digit and 0 will be the 153rd digit. We have to find out 152nd digit (341st overall) which is 5.
So, answer is 5 (D).
18 Dec 2024, 09:37
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Step 1: Count the total number of digits contributed by 1-digit, 2-digit, and 3-digit integers
1-digit integers (1 to 9):
There are 9 one-digit integers, and each contributes 1 digit.
Total digits = 9.
2-digit integers (10 to 99):
There are
99−10+1=90 two-digit integers, and each contributes 2 digits.
Total digits = 90×2=180.
3-digit integers (100 to 999):
There are 999−100+1=900 three-digit integers, and each contributes 3 digits.
Total digits = 900×3=2700.
Step 2: Determine which group the 341st digit belongs to
Digits contributed by 1-digit integers: 9
Digits contributed by 2-digit integers: 180
Thus, the first
9+180=189 digits come from the 1-digit and 2-digit integers.
The 341st digit is in the digits contributed by the 3-digit integers, as
341−189=152.
Step 3: Find the 152nd digit among the 3-digit integers
Each 3-digit integer contributes 3 digits.
To locate the exact digit:
Number of full 3-digit integers in the first 152 digits:
⌊152/3⌋=50 full integers.
Digits contributed by these 50 integers:
50×3=150.
The 151st and 152nd digits are in the next integer after these 50 full integers.
The next integer is
100+50=150.
150 contributes the digits 1,5,0.
The 151st digit is 1.
The 152nd digit is 5.
Final Answer:
The 341st digit is 5.
Answer: D.
1-digit integers (1 to 9):
There are 9 one-digit integers, and each contributes 1 digit.
Total digits = 9.
2-digit integers (10 to 99):
There are
99−10+1=90 two-digit integers, and each contributes 2 digits.
Total digits = 90×2=180.
3-digit integers (100 to 999):
There are 999−100+1=900 three-digit integers, and each contributes 3 digits.
Total digits = 900×3=2700.
Step 2: Determine which group the 341st digit belongs to
Digits contributed by 1-digit integers: 9
Digits contributed by 2-digit integers: 180
Thus, the first
9+180=189 digits come from the 1-digit and 2-digit integers.
The 341st digit is in the digits contributed by the 3-digit integers, as
341−189=152.
Step 3: Find the 152nd digit among the 3-digit integers
Each 3-digit integer contributes 3 digits.
To locate the exact digit:
Number of full 3-digit integers in the first 152 digits:
⌊152/3⌋=50 full integers.
Digits contributed by these 50 integers:
50×3=150.
The 151st and 152nd digits are in the next integer after these 50 full integers.
The next integer is
100+50=150.
150 contributes the digits 1,5,0.
The 151st digit is 1.
The 152nd digit is 5.
Final Answer:
The 341st digit is 5.
Answer: D.
18 Dec 2024, 09:43
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From 1 to 9, number of digits equals to 9
From 10 to 99, number of digits equal to 180
Remaining digits, total equals to 341-189, that is 152
After 99, there will be three digit numbers, so in order to get 152 digit
We need to 1st find the 50th number, then of the 51st three digit number, select the second digit
The 51st three digit number is 150 and its second digit that is the 3/41 digit from 1 to 999 is five
Answer is option D
From 10 to 99, number of digits equal to 180
Remaining digits, total equals to 341-189, that is 152
After 99, there will be three digit numbers, so in order to get 152 digit
We need to 1st find the 50th number, then of the 51st three digit number, select the second digit
The 51st three digit number is 150 and its second digit that is the 3/41 digit from 1 to 999 is five
Answer is option D
