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07 May 2019, 01:03
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C
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[GMAT math practice question]
A book has 1000 pages numbered 1, 2, 3, …, and so on. How many times does the digit 2 appear on the page numbers?
A. 200
B. 250
C. 300
D. 400
E. 500
A book has 1000 pages numbered 1, 2, 3, …, and so on. How many times does the digit 2 appear on the page numbers?
A. 200
B. 250
C. 300
D. 400
E. 500
07 May 2019, 03:35
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MathRevolution
Ignore page 1000, since it does not include the digit 2.
To make the calculation easier, consider the remaining pages numbered as 3-digit integers, beginning with 000 and ending with 999:
000, 001, 002...997, 998, 999
There are 1000 options between 000 to 999, inclusive.
Since each option is composed of 3 digits, the total number of digits = 3*1000 = 3000.
The probability that 2 will appear in any given position is the same as the probability that 3 will appear in any given position.
Implication:
Each of the 10 digits 0 through 9 will appear the SAME NUMBER OF TIMES.
Thus, the number of times that 2 will appear \(= \frac{3000}{10} = 300\).
joaopschultz
Joined: 09 Apr 2019
Last visit: 09 Apr 2021
Posts: 5
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Location: Brazil
Schools: Kellogg '23 Booth '23 Wharton '23
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07 May 2019, 15:38
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MathRevolution
In my humble opinion, the best approach is to analyze the probability for each digit class.
First of all, let's eliminate the thousands class since there are no 2's in this class. We are left with:
Ones: 1 out of 10 (numbers in the xx2 form), so \(\frac{1}{10} * 1000 = 100\)
Tens: 10 out of 100 (numbers in the x2x form), so \(\frac{10}{100} * 1000 = 100\)
Hundreds: 100 out of 1000 (numbers from 200 to 299), so \(\frac{100}{1000} * 1000 = 100\)
Which will give us: \(100 + 100 + 100 = 300\)
Answer: C
