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

Question

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

A) 0
B) 5
C) 375
D) 875
E) 965

siyer · Answer

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.

smuvern · Answer

^^ Great explanation. My own approach was to use the formula (avg of 1st and last number) * total number . But I got stuck.

Wofford · Answer

195 - 191/2 * 5 = 965

E

ulm · Answer

-190+190=0
-189+189=0
...
we still have 191+192+193+194+195=965
(E)

Jasontuyj2012 · Answer

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

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

blink005 · Answer

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

Spidy001 · Answer

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

Answer is E.

nish21in · Answer

Sum of -190 to +190 will be zero. You just have to sum up 191 t0 195 which is 965.

sairajesh063 · Answer

-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.

msvel2304 · Answer

IMO E.

-190 to +190 everything will cancel out.

Sum of 191 to 195 = 965

TomB · Answer

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.

answer is E

blink005 · Answer

-190 to +190 will cancel out each other

Sum= 190*5 +(1+2+3+4+5)= 950+15= 965
E

yuerchang · Answer

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

rohit8865 · Answer

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

Ans E

saswata4s · Answer

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.

BillyZ · Answer

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

The answer is E.

chetan2u · Answer

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...
965 should be the answer..

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

Abhishek009 · Answer

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

ScottTargetTestPrep · Answer

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.

Answer: E

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

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

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