What is the sum of integers from -190 to 195, inclusive? : Problem Solving (PS)

monirjewel

Manager

Joined: 06 Feb 2010

Posts: 125

Concentration: Marketing, Leadership

Schools: University of Dhaka - Class of 2010

GPA: 3.63

WE:Business Development (Consumer Products)

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

20 Oct 2010, 05:36

13

Bookmarks

00:00

A

B

C

D

E

Difficulty:

5% (low)

Question Stats:

83% (01:06) correct

17% (01:11) wrong

based on 382 sessions

Hide Show timer Statistics

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

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

Show Answer

Official Answer

Official Answer and Stats are available only to registered users. Register/Login.

siyer

Manager

Joined: 15 Apr 2010

Posts: 114

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

20 Oct 2010, 06:15

2

Kudos

1

Bookmarks

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

Intern

Joined: 15 Aug 2010

Posts: 26

Location: Nigeria

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

20 Oct 2010, 09:49

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

Wofford

Intern

Joined: 10 Oct 2010

Posts: 14

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

20 Oct 2010, 13:56

195 - 191/2 * 5 = 965

E

ulm

Manager

Joined: 03 Jun 2010

Posts: 98

Location: United States (MI)

Concentration: Marketing, General Management

Schools: Ross '15 (A) Darden '14 (D) Duke '15 (D)

WE:Business Development (Consumer Products)

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

21 Oct 2010, 02:44

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

Jasontuyj2012

Intern

Joined: 04 Aug 2011

Posts: 17

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

20 Aug 2011, 06:20

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

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

blink005

Manager

Joined: 20 Aug 2011

Posts: 66

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

20 Aug 2011, 08:51

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

Spidy001

Senior Manager

Joined: 01 Feb 2011

Posts: 309

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

20 Aug 2011, 11:37

1

Kudos

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

Intern

Joined: 19 Aug 2011

Posts: 3

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

20 Aug 2011, 15:56

1

Kudos

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

sairajesh063

Intern

Joined: 31 Oct 2011

Posts: 30

Location: India

Re: sum of the integers [#permalink]

15 Dec 2011, 22:25

-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.

msvel2304

Manager

Joined: 21 Sep 2011

Posts: 90

Concentration: Entrepreneurship, General Management

Schools: Babson '15 (WL) Kelley '15 (D) Carlson '15 (A) Rotman '15 (A) ISB '14 (D) Wake Forest '15 (WL)

GMAT 1: 530 Q42 V20

GMAT 2: 540 Q43 V28

GMAT 3: 680 Q48 V35

WE:Business Development (Hospitality and Tourism)

Re: sum of the integers [#permalink]

15 Dec 2011, 23:33

IMO E.

-190 to +190 everything will cancel out.

Sum of 191 to 195 = 965

TomB

Manager

Joined: 18 Sep 2009

Posts: 197

Re: sum of the integers [#permalink]

16 Dec 2011, 11:39

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.

answer is E

blink005

Manager

Joined: 20 Aug 2011

Posts: 66

Re: sum of the integers [#permalink]

16 Dec 2011, 21:19

-190 to +190 will cancel out each other

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

yuerchang

Intern

Joined: 07 Feb 2017

Posts: 1

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

07 Feb 2017, 22:58

1

Kudos

1

Bookmarks

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

L

rohit8865

Director

Joined: 05 Mar 2015

Posts: 852

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

07 Feb 2017, 23:56

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

L

saswata4s

Current Student

Joined: 28 May 2014

Posts: 425

GMAT 1: 730 Q49 V41 Verified score

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

08 Feb 2017, 00:54

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.
_________________

440 to 730: If I Can, You Can Too

Signature Read More

L

BillyZ

Current Student

Joined: 14 Nov 2016

Posts: 1175

Location: Malaysia

Concentration: General Management, Strategy

Schools: Sloan '23 (D) Tuck '23 (D) Darden '23 (D) Ross '23 (D) Kellogg '23 (D) Wharton '23 (D) Booth '23 (D) Fuqua '24 (A) Harvard '24 (D) Stanford '24 (D)

GMAT 1: 750 Q51 V40 (Online) Verified score

GPA: 3.53

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

08 Feb 2017, 04:00

2

Kudos

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 \(= 195 - (-190) + 1 = 386\)

\(Sum = 2.5 * 386 = 965\)

The answer is E.
_________________

"Be challenged at EVERY MOMENT."

“Strength doesn’t come from what you can do. It comes from overcoming the things you once thought you couldn’t.”

"Each stage of the journey is crucial to attaining new heights of knowledge."

Rules for posting in verbal forum | Please DO NOT post short answer in your post!

Advanced Search : https://gmatclub.com/forum/advanced-search/

Signature Read More

L

chetan2u

RC & DI Moderator

Joined: 02 Aug 2009

Status:Math and DI Expert

Posts: 11123

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

08 Feb 2017, 05:02

Expert Reply

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...
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
_________________

1. Absolute modulus:. 2. Fractions: 3. Percentage increase: 4. Combinations:

Signature Read More

L

Abhishek009

Board of Directors

Joined: 11 Jun 2011

Status:QA & VA Forum Moderator

Posts: 6073

Location: India

GPA: 3.5

WE:Business Development (Commercial Banking)

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

08 Feb 2017, 07:39

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
_________________

Thanks and Regards

Abhishek....

PLEASE FOLLOW THE RULES FOR POSTING IN QA AND VA FORUM AND USE SEARCH FUNCTION BEFORE POSTING NEW QUESTIONS

How to use Search Function in GMAT Club | Rules for Posting in QA forum | Writing Mathematical Formulas |Rules for Posting in VA forum | Request Expert's Reply ( VA Forum Only )

Signature Read More

L

ScottTargetTestPrep

Target Test Prep Representative

Joined: 14 Oct 2015

Status:Founder & CEO

Affiliations: Target Test Prep

Posts: 18738

Location: United States (CA)

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

13 Feb 2017, 08:37

1

Kudos

1

Bookmarks

Expert Reply

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.

Answer: E
_________________

Scott Woodbury-Stewart | Founder and CEO | Scott@TargetTestPrep.com

Try 5-Day Full Access Trial For FREE
Perfect 5-Star Rating on GMAT Club
Conner Scored GMAT Focus 755 (100%)

See why Target Test Prep is the top rated GMAT course on GMAT Club. Read Our Reviews

Signature Read More

gmatclubot

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

13 Feb 2017, 08:37

GMAT Problem Solving (PS) Questions

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

GMAT Question Banks