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08 Jan 2025, 01:12
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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
A. 0
B. 1
C. 4
D. 5
E. 9
08 Jan 2025, 01:12
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Official Solution:
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
We begin by determining the number of digits contributed by each group of numbers:
1-digit numbers (1 through 9) contribute 9 digits.
2-digit numbers (10 through 99) contribute 90 * 2 = 180 digits.
3-digit numbers contribute \(3 * x\) digits, where x is the number of 3-digit numbers included.
Setting up the equation to locate the 341st digit:
\(9 + 180 + 3 * x = 341\)
\(x = 50 + \frac{2}{3}\)
This means the 341st digit is in the 51st 3-digit number (since \(50 + \frac{2}{3}\) indicates we need the next number after the first 50).
Starting from 100, the 51st 3-digit number is 100 + 51 - 1 = 150. Since we have \(\frac{2}{3}\) remaining, the required digit is the second digit of 150, which is 5.
Therefore, the 341st digit is 5.
Answer: D
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
We begin by determining the number of digits contributed by each group of numbers:
1-digit numbers (1 through 9) contribute 9 digits.
2-digit numbers (10 through 99) contribute 90 * 2 = 180 digits.
3-digit numbers contribute \(3 * x\) digits, where x is the number of 3-digit numbers included.
Setting up the equation to locate the 341st digit:
\(9 + 180 + 3 * x = 341\)
\(x = 50 + \frac{2}{3}\)
This means the 341st digit is in the 51st 3-digit number (since \(50 + \frac{2}{3}\) indicates we need the next number after the first 50).
Starting from 100, the 51st 3-digit number is 100 + 51 - 1 = 150. Since we have \(\frac{2}{3}\) remaining, the required digit is the second digit of 150, which is 5.
Therefore, the 341st digit is 5.
Answer: D
Mrinalsingh13
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Last visit: 15 Mar 2026
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GMAT 1: 750 Q50 V41
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12 Sep 2025, 08:25
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I don’t quite agree with the solution. How did we get x = 50 + 2/3 from 9 + 180 + 3x = 341?
3x comes equal to 71 from the above question.
3x comes equal to 71 from the above question.
