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# There are a lot of houses such that the numbers of their doorplates ar

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Math Revolution GMAT Instructor
Joined: 16 Aug 2015
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There are a lot of houses such that the numbers of their doorplates ar  [#permalink]

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22 May 2016, 16:49
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Difficulty:

5% (low)

Question Stats:

97% (00:57) correct 3% (02:33) wrong based on 60 sessions

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There are a lot of houses such that the numbers of their doorplates are odd numbers and the first number of the doorplates is 545, the last number of the doorplates is 705. How many houses are there?

A. 61
B. 71
C. 81
D. 91
E. 101

* An answer will be posted in two days.

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Re: There are a lot of houses such that the numbers of their doorplates ar  [#permalink]

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23 May 2016, 07:52
Quote:
There are a lot of houses such that the numbers of their doorplates are odd numbers and the first number of the doorplates is 545, the last number of the doorplates is 705. How many houses are there?

A. 61
B. 71
C. 81
D. 91
E. 101

So it starts from 545 and goes like 547, 549,...... 705. and both first and last number are inclusive. Since every other number is odd, it's just 1/2 of the numbers and since it starts with an odd and ends with an odd inclusive add one to the result.
i.e., ([705-545][/2]+1 = 81
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Re: There are a lot of houses such that the numbers of their doorplates ar  [#permalink]

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23 May 2016, 10:19
MathRevolution wrote:
There are a lot of houses such that the numbers of their doorplates are odd numbers and the first number of the doorplates is 545, the last number of the doorplates is 705. How many houses are there?

A. 61
B. 71
C. 81
D. 91
E. 101

* An answer will be posted in two days.

No of odd numbers between 545 - 705 = 80

Total no of doors inclusive 545 & 705 = 80 +1 =>81

Hence answer will be (C)

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Math Revolution GMAT Instructor
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Re: There are a lot of houses such that the numbers of their doorplates ar  [#permalink]

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25 May 2016, 02:44
The number of consecutive odd numbers is (Last term-Frist term)/2+1. Then, (705-545)/2+1=81, and the correct answer is C.
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Re: There are a lot of houses such that the numbers of their doorplates ar   [#permalink] 25 May 2016, 02:44
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# There are a lot of houses such that the numbers of their doorplates ar

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