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12 Days of Christmas GMAT Competition - Day 3: If k is the number form

1 2 3 4 5

Arsh001

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19 Dec 2024, 03:58

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Bunuel

12 Days of Christmas 2024 - 2025 Competition with $40,000 of Prizes

If k is the number formed by writing the integers from 1 to 999 sequentially (123456789101112...998999), what is the 341st digit in k?

A. 0
B. 1
C. 4
D. 5
E. 9

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We've used 189 digits for single-digit and two-digit numbers.

- We have 189 digits for single-digit and two-digit numbers.
- aHave 50 * 3 = 150 digits from three-digit numbers, up to 149.
- 341st digit will be the second digit of the 51 three-digit number, 5.

So, the 341st digit in k is 5.

varunkeeja

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19 Dec 2024, 04:22

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I did it mechanically.
12345678910- here 0 is the 11th digit.
11121314151617181920- here 0 is 31st digit.
so now there is a pattern till we are dealing with the 2 digit numbers we will add 20 in the previous digit we have find 0. ex- now to find the next 0 we will add 20 to 31st digit- 51st digit and so on.
so we will get series here- 31,51,71,91,.....181. here 181 st digit represents the tens 0 in number 100.
so now since we will deal with 3 digit numbers we will start adding 30.
ex- add 31 since we have to take hundread digit 0 into consideration as well.- 212 digit will be zero in 110.
now, keeping on adding 30- 252,282,312,342.
here 342nd digit is the zero in 150 so 341st digit is 5

missionmba2025

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Bunuel

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Numbers from 1 to 9 contribute only 1 digit to the chain. Hence, the 9th digit will be 9.

Numbers from 10 to 99 contribute 2 digits each to the chain. Total digits contributed = 2*90 = 180

Hence, the 190th digit will be 9.

Remaining digits = 341 - 189 = 152.

Each number post 99 contributes 3 digits to the chain. Hence, 50 digits contribute 150 digits. We have two digits more to go -

The 151th number is 1
The 152th number is 5

Option D

Tishaagarwal13

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19 Dec 2024, 05:03

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Total number of digits:
1 to 9 = 9 digits
10-99 = 2*(99-10+1) = 180
100-999 = 3*k

The equation would be:
9+180+3k = 341
k = 152/3 or 50*2/3

So, starting from 100, the 50th 3-digit number would be 100+50-1 = 149.
For the remaining 2/3rd, we will take the 2nd digit of the next number 150 i.e. 5.

Hence the correct answer is D) 5

Bunuel

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TheLegacy

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19 Dec 2024, 06:08

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We must recognize that we deal with two patterns: +20 (tenths) and +30 (hundreds).

10th digit is 1 (of 10)
30th digit is 2 (of 20),
50th digit is 3 (of 30),
...

190th digit is 1 (of 100).

We are now dealing with hundreds... so:

190th digit is 1 (of 100)
220th digit is 1 (of 110)
250th digit is 1 (of 120)
280th digit is 1 (of 130)
310th digit is 1 (of 140)
340th digit is 1 (of 150)

Hence the 341th digit will be 5 (of 150).

(I honestly spent some time, not the standard 2:00 min...if you know a faster approach, please let me know, thx =)

aarati17

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Ans: D. 5

The natural numbers are written sequentially

So, 1-9 makes the count as 9
10-99 => 90 numbers with each number consisting of 2 digits. So, total digits = 90*2 = 180

Digits remaining = 341-180-9 = 152

Starting from 100, each number has 3 digits

So, from 100 to 149, there are 50 numbers and total digits = 50*3=150

Total digits till now = 9+180+150 = 339
Remaining digits = 2
So the last number will be 150 and the 341st number should be 5 (2nd digit of 150)

Bunuel

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rns2812

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19 Dec 2024, 07:12

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Number of single digit numbers(1-9) = 9
Number of double digit numbers(10-99) = 90
Number of three digit numbers(100-999) = 990

Number of digits taken in k by single digit numbers = 9 * 1 = 9
Number of digits taken in k by double digit numbers = 90 * 2 = 180

Number of digits left = 341- 180 - 9 = 152

Number of 3 digit numbers possible with 152 digits = 152/3 = 50 numbers

100 - 149 -> 150 digits
Next number = 150

Remaining digits = 2

Required answer = 5 (OPTION D)

Bunuel

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jkkamau

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19 Dec 2024, 07:13

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Writing the numbers upto 40 reveals that the numbers increase after every 20 digits so divide 340 by 20 with the following digit being a 5. For instance 20th digit is 15, 40th digit is 25m 60th digit is 35 meaning the 341st digit will be a 5 hence D.

Bunuel

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kalpak8

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19 Dec 2024, 08:23

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Every 1 digit number will occupy a single space so the first 9 numbers will occupy 9 spaces.
Similarly, 2 digit nos. (10, 11 ...99) which are 90 nos = 90x2= 180 spaces.
and 3 digits will occupy 3 spaces (100,101..) and u can calculate up to 341st number.
9+180+x = 341, x=152 and divided by 3 we can conclude it will be after 50th 3 digit number. which is 149.

Bunuel

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Mardee

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19 Dec 2024, 08:32

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No of digits from 1 to 9 = 9 digits
No of digits from 10 to 99 = 90 x 2 = 180 (Total number = 99 - 10 + 1 = 90)
No of digits from 100 to 999 = 900 x 3 = 2700 (Total number = 999 - 100 + 1 = 900)

So number is between 100 to 999
We check from 189th digit position for the 341st digit
=> 341 - 189 = 152

To find which number we divide 152 by 3, which gives us a value of 50 with remainder 2

So, 50th 3 digit number = 149
Since remainder 2, the 341st digit = 4

C. 4

Nikkz99

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19 Dec 2024, 08:47

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we have 9 digits of 1 digit number (as it starts from the number 1); there will be 180 digits in 2 digit number : inclusive of 10 and 99; so as of now we have total of 189 digits. We need to find the 341st digit. so 341-189 -> 152nd digit from the 3 digit number.

so 152/3 -> 50.67 which means 2nd digit of a number after 150 which is nothing but 15[/b]1

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There are 9 one digit which will be first 9 digits of k
There are 90 two digit numbers starting form 10 - 99 which forms next 180 digits of k
Hence from 341 the remaining are 152 digits
From this first 50 three digit numbers starting from 100 -149 give the next 150 digits
150 is the next number and 5 will be the 341st digit

Hence option D. 5 is the answer

Bunuel

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totamofficiis

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28 Mar 2026, 10:14

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Can anyone please explain why i am not supposed to come from the left side. why 341st digit does not mean 10^341 th digit. I might be missing something. Because there is no obvious reason to start from the right. and we read number from the left. (right?) I am so confused do we say 1st digit of 1276 is 1 or 6?