[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
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- Max@Math Revolution
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E
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Ignore page 1000, since it does not include the digit 2.Max@Math Revolution wrote:[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
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 = 3000/10 = 300.
The correct answer is C.
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=>
The page numbers 2, 12, 20, 21, 22, ... , 29, 32, 42, ... , 92 contain 19+1 = 20 copies of the digit, 2.
The page numbers 102, 112, 120, 121, ... , 129, 132, 142, ... , 192 similarly contain 20 copies of the digit 2.
The page numbers 200, 201, ... , 299 contain 120 copies of the digit, 2.
Page numbers 302, 312, 320, 321, ... , 329, 332, 342, ... , 392 contain 20 copies of the digit, 2.
...
Page numbers 902, 912, 920, 921, 922, ... , 929, 932, 942, ... , 992 contain 20 copies of the digit, 2.
The total number of copies of the digit, 2 printed on the pages is
9*20 + 120 = 300.
Therefore, the answer is C.
Answer: C
The page numbers 2, 12, 20, 21, 22, ... , 29, 32, 42, ... , 92 contain 19+1 = 20 copies of the digit, 2.
The page numbers 102, 112, 120, 121, ... , 129, 132, 142, ... , 192 similarly contain 20 copies of the digit 2.
The page numbers 200, 201, ... , 299 contain 120 copies of the digit, 2.
Page numbers 302, 312, 320, 321, ... , 329, 332, 342, ... , 392 contain 20 copies of the digit, 2.
...
Page numbers 902, 912, 920, 921, 922, ... , 929, 932, 942, ... , 992 contain 20 copies of the digit, 2.
The total number of copies of the digit, 2 printed on the pages is
9*20 + 120 = 300.
Therefore, the answer is C.
Answer: C
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