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A group of buildings is numbered using all the even numbers between 41

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Bunuel
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A group of buildings is numbered using all the even numbers between 41 [#permalink] New post   20 Feb 2020, 06:27
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A group of buildings is numbered using all the even numbers between 412 and 680 inclusive, How many buildings are in the group ?

A. 134
B.135
C. 137
D. 139
E. 143
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B
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Re: A group of buildings is numbered using all the even numbers between 41 [#permalink] New post   20 Feb 2020, 06:34
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IMO: B

The numbers between a range can be counted by finding the range. Since the number required is even numbers, then it is a multiple of 2.
Multiple of “x” number between a range = (range / x) +1

Therefore, (680-412)/2 +1= 135

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Re: A group of buildings is numbered using all the even numbers between 41 [#permalink] New post   20 Feb 2020, 22:29
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Bunuel wrote:
A group of buildings is numbered using all the even numbers between 412 and 680 inclusive, How many buildings are in the group ?

A. 134
B.135
C. 137
D. 139
E. 143


Solution


    • We can observe that the building numbers are in an A.P. with a constant difference of 2.
      o Also, 412 is the first term while 680 is the last term of this A.P.
    • So, \(680 = 412 + (n-1)*2\) , where n is the number or buildings in the group(or the number of terms in A.P.).
    • \(n = \frac{(680 -412)}{2 }+ 1 = 135\)
Thus, the correct answer is Option B
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Re: A group of buildings is numbered using all the even numbers between 41 [#permalink] New post   20 Feb 2020, 23:20
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Bunuel wrote:
A group of buildings is numbered using all the even numbers between 412 and 680 inclusive, How many buildings are in the group ?

A. 134
B.135
C. 137
D. 139
E. 143


I prefer to solve such a problem without learning any formula so he is my 1 cent

Total Even Numbers from 1 to 680 = 680/2 = 340

We have to exclude all even numbers which are from 1 to 410 (because we need 412 to be included) from these 340 numbers

Total Even Numbers from 1 to 410 = 410/2 = 205

So All even numbers from 412 to 680 inclusive = 340 - 205 = 135

Answer: Option B
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Re: A group of buildings is numbered using all the even numbers between 41 [#permalink] New post   20 Sep 2022, 05:09
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Re: A group of buildings is numbered using all the even numbers between 41 [#permalink]
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