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# There is a sequence where each term is a positive integer and at least

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Senior SC Moderator
Joined: 14 Nov 2016
Posts: 1314
Location: Malaysia
There is a sequence where each term is a positive integer and at least  [#permalink]

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23 Feb 2017, 22:58
3
00:00

Difficulty:

65% (hard)

Question Stats:

53% (02:19) correct 47% (01:53) wrong based on 51 sessions

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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 $$150^{th}$$ term?

A. 326
B. 329
C. 342
D. 382
E. 392

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There is a sequence where each term is a positive integer and at least  [#permalink]

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23 Feb 2017, 23:56
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4
AustinKL wrote:
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 $$150^{th}$$ term?

A. 326
B. 329
C. 342
D. 382
E. 392

19 terms have digit 3 from 1 to 99
19 terms have digit 3 from 100 to 199
19 terms have digit 3 from 200 to 299
90 terms have digit 3 from 300 to 389
last 3 terms - 390, 391 and 392

so $$150^{th}$$ is 392

Hence option E is correct
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Re: There is a sequence where each term is a positive integer and at least  [#permalink]

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12 Jan 2018, 14:28
Hi All,

This is a really poorly-worded question, but I think the 'intent' of this question is to describe an increasing sequence of positive integers in which every integer that includes at least one 3 among its digits is in the sequence (so the numbers 3, 33, 153, 337, etc. would all be in the sequence). Assuming that the first term in the sequence is "3", we're asked to find the 150th term in the sequence.

From 1 to 99, there are 19 terms that contain at least one '3' (you can list them out - it's not hard to find them)
From 100 to 199, there are 19 terms that contain at least one '3' (you can list them out if needed)
From 200 to 299, there are 19 terms that contain at least one '3' (you can list them out if needed)

So far, there are 3(19) = 57 terms accounted for. Once we hit 300, EVERY term in the next 100 terms will contain at least one '3', so we need to go 93 terms 'in' to this set of 100 terms to find that 150th term... Starting at 300, 93 terms in would be 392.

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Re: There is a sequence where each term is a positive integer and at least  [#permalink]

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24 Jan 2018, 05:11
1
"at least one of each digit of the term has 3 in an ascending order" is perplexing phrase, isn't it?
I understood sequence 3,13,23, 113,....
Re: There is a sequence where each term is a positive integer and at least &nbs [#permalink] 24 Jan 2018, 05:11
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