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# What is the sum of integers from -190 to 195, inclusive?

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What is the sum of the integers from -190 to 195 inclusive? [#permalink]

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20 Oct 2010, 04:36
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What is the sum of the integers from -190 to 195 inclusive?

A) 0
B) 5
C) 375
D) 875
E) 965
[Reveal] Spoiler: OA

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Re: What is the sum of the integers from -190 to 195 inclusive? [#permalink]

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20 Oct 2010, 05:15
From -190 to +195 we know that all numbers from 1 to 190 will have both positive and negative terms. So they will just cancel each other out.

The numbers that remain will be 191, 192,193, 194 and 195 whose sum can be easily calculated. The answer is E.
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Re: What is the sum of the integers from -190 to 195 inclusive? [#permalink]

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20 Oct 2010, 08:49
^^ Great explanation. My own approach was to use the formula (avg of 1st and last number) * total number . But I got stuck.
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Re: What is the sum of the integers from -190 to 195 inclusive? [#permalink]

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20 Oct 2010, 12:56
195 - 191/2 * 5 = 965

E

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Re: What is the sum of the integers from -190 to 195 inclusive? [#permalink]

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21 Oct 2010, 01:44
-190+190=0
-189+189=0
...
we still have 191+192+193+194+195=965
(E)

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What is the sum of the integers from -190 to 195, inclusive? [#permalink]

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20 Aug 2011, 05:20
What is the sum of the integers from -190 to 195, inclusive?

a) 0
b) 5
c) 375
d) 875
e) 965

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Re: What is the sum of the integers from -190 to 195, inclusive? [#permalink]

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20 Aug 2011, 07:51
This can be viewed as a sum of consecutive terms problem

the sequence consists of integers between -191 and 196
the sequence starts at -190 and ends at +195

in an arithmetic progression,
the nth term is given by tn=a+(n-1)d
here tn=195, a=-190, d=1
hence, 195=-190+(n-1)
or n=386

Sum of n terms can be calculated by sn=n/2(a+l)
a=first term, l=last term, n=no. of terms

sn=386*(-190+195)/2
sn=193*5
sn=965
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Re: What is the sum of the integers from -190 to 195, inclusive? [#permalink]

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20 Aug 2011, 10:37
the series is in ap.

AP - sum of the series = (n/2)(2a+ (n-1)d)

n = 190+1+195 (190 negative terms, 1 zero and 195 positive terms)
= 386

a = -190
d = 1

=> sum of this series = (386/2)(-380+385) = 965

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Re: What is the sum of the integers from -190 to 195, inclusive? [#permalink]

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20 Aug 2011, 14:56
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Sum of -190 to +190 will be zero. You just have to sum up 191 t0 195 which is 965.

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Re: sum of the integers [#permalink]

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15 Dec 2011, 21:25
-190+(-189)+(-188+).....+(-4)+(-3)+(-2)+(-1) + 0+1+2+3+4+........+188+189+190+191+192+193+194+195

Everything will cancel out except the last 5 numbers(191+192+193+194+195)

So, the ans will be 965.
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Re: sum of the integers [#permalink]

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15 Dec 2011, 22:33
IMO E.

-190 to +190 everything will cancel out.

Sum of 191 to 195 = 965
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Re: sum of the integers [#permalink]

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16 Dec 2011, 10:39
as the list is consecutive integers, we can use following formulas:

sum/n= average.
sum=(average)(n)
average=a+b/2=190+195/2=2.5
number of items(n)=B-A+1=195-(-190)+1=195+191=386.
sum=average*n=2.5*386=965.

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Re: sum of the integers [#permalink]

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16 Dec 2011, 20:19
-190 to +190 will cancel out each other

Sum= 190*5 +(1+2+3+4+5)= 950+15= 965
E
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What is the sum of integers from -190 to 195, inclusive? [#permalink]

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07 Feb 2017, 21:58
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What is the sum of integers from -190 to 195, inclusive?
A 0
B 5
C 375
D 875
E 965

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Re: What is the sum of integers from -190 to 195, inclusive? [#permalink]

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07 Feb 2017, 22:56
yuerchang wrote:
What is the sum of integers from -190 to 195, inclusive?
A 0
B 5
C 375
D 875
E 965

integers from 1 to 190 gets cancelled from similar negative values
left only 191+192+193+194+195 = 965

Ans E

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Re: What is the sum of integers from -190 to 195, inclusive? [#permalink]

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07 Feb 2017, 23:54
The series is: -190, -189, -188,........ -2, -1, 0, 1, 2, ........ 188, 189, 190, 191, 192, 193, 194, 195;

Hence, the -ve and +ve values from -190 to +190 cancel each other leaving only 191, 192, 193, 194, 195;
So, the sum of the series:
191 + 192 + 193 + 194 + 195 = 190*5 + (1+2+3+4+5) = 950 + 15 = 965; Answer E.

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What is the sum of integers from -190 to 195, inclusive? [#permalink]

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08 Feb 2017, 03:00
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yuerchang wrote:
What is the sum of integers from $$-190$$ to $$195$$, inclusive?
A 0
B 5
C 375
D 875
E 965

SUM = AVERAGE x NUMBER OF DATA POINTS

$$Average = \frac{(-190 + 195)}{2} = \frac{5}{2} = 2.5$$

Number of data point $$= 195 - (-190) + 1 = 386$$

$$Sum = 2.5 * 386 = 965$$

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Re: What is the sum of integers from -190 to 195, inclusive? [#permalink]

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08 Feb 2017, 04:02
yuerchang wrote:
What is the sum of integers from -190 to 195, inclusive?
A 0
B 5
C 375
D 875
E 965

Hi,

We know -190 to 190 will cancel out..
now what is important is how fast you can calculate 191+192+193+194+195

There are five terms which are close to 200, so ans will be close to 5*200=1000...

If you want exact answer, it may be beneficial to calculate how far answer will be from 1000..
So they are 5+6+7+8+9 away, this is 35...
And 1000-35=965...

E
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Re: What is the sum of integers from -190 to 195, inclusive? [#permalink]

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08 Feb 2017, 06:39
yuerchang wrote:
What is the sum of integers from -190 to 195, inclusive?
A 0
B 5
C 375
D 875
E 965

Integers from -190 to 190 is -

( -190 , -189 , -188...........-2 , -1 ,0 ) + ( 0 , 1 , 2 ............188 , 189 , 190) = 0

Sum of integers from -190 to 195 = Sum of Integers from -190 to 190 ( ie, 0 ) + 191 + 192 + 193 + 194 + 195 => 965

Hence, answer must be (E) 965
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Re: What is the sum of integers from -190 to 195, inclusive? [#permalink]

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13 Feb 2017, 07:37
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Expert's post
yuerchang wrote:
What is the sum of integers from -190 to 195, inclusive?
A 0
B 5
C 375
D 875
E 965

In determining the sum of the integers from -190 to 195 inclusive, we should recognize that all of the negative integers will cancel out with their positive counterparts.

For instance, we have -190 and 190, -150 and 150, -10 and 10, etc.

Thus, the only positive numbers that won’t cancel out with their negative counterparts are 191, 192, 193, 194, and 195.

To determine the sum of these numbers, we can use this formula: sum = average x quantity.

Since we have an evenly spaced set, the average is equal to the median, which is 193, and the quantity is 5.

Thus, the sum = 193 x 5 = 965.

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Re: What is the sum of integers from -190 to 195, inclusive?   [#permalink] 13 Feb 2017, 07:37

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