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How many positive integers less than 500 begin

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How many positive integers less than 500 begin [#permalink] New post 20 Jun 2018, 04:49
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Question Stats:

27% (01:34) correct 72% (01:41) wrong based on 11 sessions
How many positive integers less than 500 begin with a 3, end with a 3, or both?

A) 149
B) 150
C) 159
D) 199
E) 200


*I'll post a full solution in 2 days
[Reveal] Spoiler: OA

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Brent Hanneson – Creator of greenlighttestprep.com
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1 KUDOS received
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Kudos [?]: 1105 [1] , given: 7

Re: How many positive integers less than 500 begin [#permalink] New post 22 Jun 2018, 05:07
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GreenlightTestPrep wrote:
How many positive integers less than 500 begin with a 3, end with a 3, or both?

A) 149
B) 150
C) 159
D) 199
E) 200


*I'll post a full solution in 2 days


There are 499 integers from 1 to 499 inclusive.

Let's determine how many of those 499 integers DO NOT meet the condition of beginning with a 3, ending with a 3, or both

1-digit integers that DO NOT begin with a 3, end with a 3, or both
1, 2, 4, 5, 6, 7, 8, and 9
TOTAL = 8

2-digit integers that DO NOT begin with a 3, end with a 3, or both
In the tens position, we can have 1, 2, 4, 5, 6, 7, 8, or 9 (8 possibilities)
In the units position, we can have 0, 1, 2, 4, 5, 6, 7, 8, or 9 (9 possibilities)
TOTAL number of 2-digit integers that DO NOT begin with a 3, end with a 3, or both = (8)(9) = 72

3-digit integers that DO NOT begin with a 3, end with a 3, or both
In the hundreds position, we can have 1, 2, or 4 (3 possibilities)
In the tens position, we can have 0, 1, 2, 3, 4, 5, 6, 7, 8, or 9 (10 possibilities)
In the units position, we can have 0, 1, 2, 4, 5, 6, 7, 8, or 9 (9 possibilities)
TOTAL number of 3-digit integers that DO NOT begin with a 3, end with a 3, or both = (3)(10)(9) = 270

So, the TOTAL number of integers that DO NOT meet the given condition = 8 + 72 + 270 = 350

TOTAL number of integers that MEET the given condition
So, the = 499 - 350 = 149

Answer: A

Cheers,
Brent
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Re: How many positive integers less than 500 begin [#permalink] New post 11 Jul 2018, 00:03
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Less than 500, we have 1 digit, 2 digits, 3 digits number.
+1 digit numbers: only 3 ( 1 outcome)
+2 digits, we can have: a3 (9 outcomes since a cannot be 0) or 3b (b cannot be 3 since overlap, hence only 9 outcomes)
+3 digits, we can have: 3bc (100 outcomes)or 1b3,2b3,4b3(each has 10 outcomes, then total 30)
Total 149 outcomes
Re: How many positive integers less than 500 begin   [#permalink] 11 Jul 2018, 00:03
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