GMAT Question of the Day - Daily to your Mailbox; hard ones only

It is currently 21 Oct 2018, 18:28

Close

GMAT Club Daily Prep

Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track
Your Progress

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History

Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.

Close

Request Expert Reply

Confirm Cancel

What is the sum of the integers 45 through 175 inclusive?

  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics  
Author Message
TAGS:

Hide Tags

Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 50009
What is the sum of the integers 45 through 175 inclusive?  [#permalink]

Show Tags

New post 22 Dec 2015, 04:26
1
3
00:00
A
B
C
D
E

Difficulty:

  35% (medium)

Question Stats:

68% (01:25) correct 32% (01:45) wrong based on 172 sessions

HideShow timer Statistics

Most Helpful Expert Reply
Math Expert
User avatar
V
Joined: 02 Aug 2009
Posts: 6974
What is the sum of the integers 45 through 175 inclusive?  [#permalink]

Show Tags

New post 22 Dec 2015, 04:50
2
3
Bunuel wrote:
What is the sum of the integers 45 through 175 inclusive?

A. 12,295
B. 13,000
C. 14,300
D. 14,410
E. 28,820



Two ways to do it..

algebric way..

sum of n consecutive positive integers=\(\frac{n(n+1)}{2}\)..
in one case n=44 and other 175... subtract the sum to get the answer
sum of first 175 +ive numbers=\(175*\frac{176}{2}=15400\)..
sum of first 44 +ive numbers=\(44*\frac{45}{2}=990\)..
answer=\(15400-990=14410\)..

average mean method..
since they are consecutive number we can use average method too...
average of all numbers from 45 to 175 = average of 45 and 175=\(\frac{45+175}{2}=110\)
total integers = \(175-45+1=131...\)
sum =\(131*110=14410..\) ans
D
_________________

1) Absolute modulus : http://gmatclub.com/forum/absolute-modulus-a-better-understanding-210849.html#p1622372
2)Combination of similar and dissimilar things : http://gmatclub.com/forum/topic215915.html
3) effects of arithmetic operations : https://gmatclub.com/forum/effects-of-arithmetic-operations-on-fractions-269413.html


GMAT online Tutor

General Discussion
Board of Directors
User avatar
P
Joined: 01 Sep 2010
Posts: 3304
Re: What is the sum of the integers 45 through 175 inclusive?  [#permalink]

Show Tags

New post 22 Dec 2015, 04:37
Board of Directors
User avatar
P
Status: QA & VA Forum Moderator
Joined: 11 Jun 2011
Posts: 4095
Location: India
GPA: 3.5
WE: Business Development (Commercial Banking)
GMAT ToolKit User Premium Member
Re: What is the sum of the integers 45 through 175 inclusive?  [#permalink]

Show Tags

New post 03 Jan 2017, 11:30
Bunuel wrote:
What is the sum of the integers 45 through 175 inclusive?

A. 12,295
B. 13,000
C. 14,300
D. 14,410
E. 28,820


45, 46 , 47....173,174,175

a = 45
n = 175 - 45 + 1 => 131
d = 1

\(s = \frac{n}{2}[2a + (n - 1)d]\)

\(s = \frac{131}{2}[2*45 + (131 - 1)1]\)

\(s = \frac{131}{2}[90 + 130]\)

\(s = \frac{131}{2}[220]\)

\(s = 131*110\)

\(s = 14410\)

Hence, answer will be (D) 14,410
_________________

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 )

Intern
Intern
avatar
B
Joined: 08 Jul 2017
Posts: 18
Re: What is the sum of the integers 45 through 175 inclusive?  [#permalink]

Show Tags

New post 03 Nov 2017, 20:18
For those who like formulas more, there's a way you can apply geometry to this. Since we're looking for the sum of everything between two numbers, you can imagine it like a trapezoid, with the bounds (45 and 175) acting as b1 and b2, and the range (175-45, plus 1) as the height.

The formula for a trapezoid is
= (1/2) * (b1 + b2) * (h)
= (1/2) * (45 + 175) * (175 - 45 + 1)
= (1/2) * (220) * (131)
= (110) * (131)

and to make it easier to write it all out

= (10) * (11) * (131)
= 14410
Senior SC Moderator
avatar
V
Joined: 22 May 2016
Posts: 2038
Premium Member CAT Tests
What is the sum of the integers 45 through 175 inclusive?  [#permalink]

Show Tags

New post 04 Nov 2017, 11:33
Bunuel wrote:
What is the sum of the integers 45 through 175 inclusive?

A. 12,295
B. 13,000
C. 14,300
D. 14,410
E. 28,820

(# of terms)(average) = Sum

1) Number of terms:\((\frac{LastTerm-FirstTerm}{Increment} + 1)\)

\((\frac{175-45}{1}+1)=130+1 = 131\) terms*

2) Average (arith. mean): \(\frac{First+ Last}{2}\)

=\(\frac{45+175}{2}= 110\)

3) (# of terms)(average) = Sum
(131)(110) =
(130 + 1)(100 + 10), FOIL
13,000 + 1,300 + 100 + 10 = 14,410

Answer D

*This formula is the general one -- can be used for multiples, odds, evens, consecutive integer sequences that do not begin with 1, etc. The "increment" part in questions about consecutive integers, which differ by 1, often is omitted
_________________

___________________________________________________________________
For what are we born if not to aid one another?
-- Ernest Hemingway

Intern
Intern
avatar
B
Joined: 25 May 2017
Posts: 10
GMAT 1: 750 Q49 V44
What is the sum of the integers 45 through 175 inclusive?  [#permalink]

Show Tags

New post 04 Nov 2017, 18:08
This question is testing two things:

1. Find number of integers in a set
2. Find sum of integers in a set

Now,
To find the number of integers in a set (consecutive):


Formula is (Last term - First term) + 1
= 175 - 45 + 1
= 131

Formula for sum of an arithmetic series (when there is a common difference)

Sum = \(\frac{n}{2}\) (first term + last term)
where n = number of integers

= \(\frac{131}{2}\) (45 + 175)
= \(\frac{131}{2}\) (220)
= 131 * 110
= 14,410

PS there is a trick to doing long multiplications like these. Forget about the zero for a second, and think about just 131 * 11. You can see that the digit right before the last 0 will have to be 1. The only option that fits is D.
= 131 * 110
_________________

GmatIvyPrep
Yale MBA Graduate and GMAT-Focused Tutor for 4+ years
Contact: gmativyprep@gmail.com for a consultation and private tutoring rates

Image

Material offered free of charge along with full end-to-end GMAT Quantitative Course:
- High-level (700+) practice question sets for Quantitative section by topic
- AWA writing template that helped students get a full score on the Essay
- Complete pack of Verbal Material for SC, RC and CR

GMAT Club Bot
What is the sum of the integers 45 through 175 inclusive? &nbs [#permalink] 04 Nov 2017, 18:08
Display posts from previous: Sort by

What is the sum of the integers 45 through 175 inclusive?

  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics  


Copyright

GMAT Club MBA Forum Home| About| Terms and Conditions and Privacy Policy| GMAT Club Rules| Contact| Sitemap

Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne

Kindly note that the GMAT® test is a registered trademark of the Graduate Management Admission Council®, and this site has neither been reviewed nor endorsed by GMAC®.