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26 May 2017, 04:50
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There is a sequence where each term is a positive integer and at least one of each digit of the term has 3 in an ascending order. What is the value of 150th term?
A. 326
B. 329
C. 342
D. 382
E. 392
A. 326
B. 329
C. 342
D. 382
E. 392
26 May 2017, 04:50
Kudos
Bookmarks
Official Solution:
There is a sequence where each term is a positive integer and at least one of each digit of the term has 3 in an ascending order. What is the value of 150th term?
A. 326
B. 329
C. 342
D. 382
E. 392
Since the question is about the 150th number when all positive integers with 3 are arranged in an ascending order,
For both vertical and horizontal numbers, there are 10 numbers that contain 3's, but since '33' overlaps, the number of integers from 1 to 99 that contain 3 becomes \(10+10-1 = 19\).
In the same logic, there are 19 of them between 100 and 199, and also 19 between 200~299. So, the number of integers that contain 3 until 299 is \(19+19+19 = 57\). Then, there are 57 integers that contain 3 between 1 and 299. However, the question is about 150th integer and since \(150 = 57+93\), the number of integers with 3 is 93rd integer from 300, so it is 392. The answer is E.
Answer: E
There is a sequence where each term is a positive integer and at least one of each digit of the term has 3 in an ascending order. What is the value of 150th term?
A. 326
B. 329
C. 342
D. 382
E. 392
Since the question is about the 150th number when all positive integers with 3 are arranged in an ascending order,
For both vertical and horizontal numbers, there are 10 numbers that contain 3's, but since '33' overlaps, the number of integers from 1 to 99 that contain 3 becomes \(10+10-1 = 19\).
In the same logic, there are 19 of them between 100 and 199, and also 19 between 200~299. So, the number of integers that contain 3 until 299 is \(19+19+19 = 57\). Then, there are 57 integers that contain 3 between 1 and 299. However, the question is about 150th integer and since \(150 = 57+93\), the number of integers with 3 is 93rd integer from 300, so it is 392. The answer is E.
Answer: E
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