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# What is the sum of all integers from 45 to 155 inclusive?

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Math Expert
Joined: 02 Sep 2009
Posts: 50627
What is the sum of all integers from 45 to 155 inclusive?  [#permalink]

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17 Oct 2018, 01:48
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Difficulty:

35% (medium)

Question Stats:

70% (01:05) correct 30% (01:04) wrong based on 76 sessions

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What is the sum of all integers from 45 to 155 inclusive?

A. 10,000
B. 10,100
C. 11,000
D. 11,100
E. 13,200

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Joined: 15 Feb 2018
Posts: 82
What is the sum of all integers from 45 to 155 inclusive?  [#permalink]

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17 Oct 2018, 02:09
1
Inclusive so it is 155-45+1=111 numbers
45+155=200, 46+154=200...99+101
There are 55 pairs like this ($$\frac{111}{2}$$ = 55 r 1). The remainder of 1 will be the number 100.
55·200+100=11,100
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What is the sum of all integers from 45 to 155 inclusive?  [#permalink]

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17 Oct 2018, 09:08
1
Im not sure but wouldnt this be how to solve this question;

Find number of terms: (last term-first term)+1, so (155-45)+1= 110
Then find average of terms: (FT+LT)/2 = (155+45)/3=100

Sum of all terms = mean x number of terms = 110 x 100 = 11000
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Re: What is the sum of all integers from 45 to 155 inclusive?  [#permalink]

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18 Oct 2018, 03:26
zwander
You recognised the extra 1 "+1" but then didn't include it in the rest of the solution.
See the post above yours that explains it.
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Re: What is the sum of all integers from 45 to 155 inclusive?  [#permalink]

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18 Oct 2018, 07:47
philipssonicare oh wow what a silly mistake! Thanks for catching it
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Re: What is the sum of all integers from 45 to 155 inclusive?  [#permalink]

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19 Oct 2018, 14:23
Bunuel wrote:
What is the sum of all integers from 45 to 155 inclusive?

A. 10,000
B. 10,100
C. 11,000
D. 11,100
E. 13,200

A quick way to perform this arithmetic is to recall that if we know the average of a set of numbers, we can multiply by the number of numbers (i.e., the quantity) to get the sum. We can use the equation: sum = average x quantity

average of evenly-spaced set = (smallest number + largest number)/2 = (45 + 155)/2 = 200/2 = 100

quantity = 155 - 45 + 1 = 111

Thus, the sum is 100 x 111 = 11,100

Answer: D
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Re: What is the sum of all integers from 45 to 155 inclusive?  [#permalink]

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19 Oct 2018, 20:10
Significance of the "+1" when finding number of terms?
Re: What is the sum of all integers from 45 to 155 inclusive? &nbs [#permalink] 19 Oct 2018, 20:10
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# What is the sum of all integers from 45 to 155 inclusive?

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