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# What is the sum of the integers from 100 to 140 inclusive?

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Math Expert
Joined: 02 Sep 2009
Posts: 53006
What is the sum of the integers from 100 to 140 inclusive?  [#permalink]

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29 Jan 2019, 06:36
00:00

Difficulty:

25% (medium)

Question Stats:

67% (00:54) correct 33% (01:10) wrong based on 46 sessions

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What is the sum of the integers from 100 to 140 inclusive?

A. 5250
B. 4550
C. 4800
D. 4600
E. 4920

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Re: What is the sum of the integers from 100 to 140 inclusive?  [#permalink]

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29 Jan 2019, 07:14
Sum = average x quantity

Average: (140+100)/2=120
Quantity: 140-100=40... we add 1 to get 40+1=41 considering we have an inclusive set.

Sum: 120 x 41= 4,920.

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Re: What is the sum of the integers from 100 to 140 inclusive?  [#permalink]

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29 Jan 2019, 08:13
Let sum X=100+101+....+139+140
Also Sum X= 140+139...+101+100 (the same thing)
2x =(240+240..+240) —> adding 240,n times
Where n= count= (140-100)+1=41
Now 2x=240*n —> x=240/2*41 =
x=120*41 =4920
Ans.E

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Re: What is the sum of the integers from 100 to 140 inclusive?  [#permalink]

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29 Jan 2019, 08:51
Bunuel wrote:
What is the sum of the integers from 100 to 140 inclusive?

A. 5250
B. 4550
C. 4800
D. 4600
E. 4920

two ways to solve this question:

method 1:
total no of terms ; 140-100+1 = 41
d=1
a=100
s41=41/2 + (2*100+ (41-1)*1)
s41 = 4920
IMO E

method 2 :
since the terms are consective so mean = median = avg
so avg = last term+ first term /2 = 140+100/2 = 120

no of terms = 41
sum = 120*41 = 4920
IMO E
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Re: What is the sum of the integers from 100 to 140 inclusive?   [#permalink] 29 Jan 2019, 08:51
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