GMAT Question of the Day: Daily via email | Daily via Instagram New to GMAT Club? Watch this Video

It is currently 11 Jul 2020, 13:02

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

A page is torn from a novel. The sum of the remaining page numbers is

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

Hide Tags

Find Similar Topics 
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 65187
A page is torn from a novel. The sum of the remaining page numbers is  [#permalink]

Show Tags

New post 14 Apr 2020, 08:08
00:00
A
B
C
D
E

Difficulty:

  75% (hard)

Question Stats:

29% (02:02) correct 71% (02:31) wrong based on 51 sessions

HideShow timer Statistics

A page is torn from a novel. The sum of the remaining page numbers is 10,000. What could be the page-numbers on the torn page ?

I. 76 and 77
II. 33 and 34
III. 5 and 6.

A. I only
B. II only
C. III only
D. I and II only
E. I and III only


Are You Up For the Challenge: 700 Level Questions

_________________
GMAT Club Legend
GMAT Club Legend
User avatar
V
Status: GMATINSIGHT Tutor
Joined: 08 Jul 2010
Posts: 4345
Location: India
GMAT: QUANT EXPERT
Schools: IIM (A)
GMAT 1: 750 Q51 V41
WE: Education (Education)
Reviews Badge
Re: A page is torn from a novel. The sum of the remaining page numbers is  [#permalink]

Show Tags

New post 14 Apr 2020, 08:23
Bunuel wrote:
A page is torn from a novel. The sum of the remaining page numbers is 10,000. What could be the page-numbers on the torn page ?

I. 76 and 77
II. 33 and 34
III. 5 and 6.

A. I only
B. II only
C. III only
D. I and II only
E. I and III only


Are You Up For the Challenge: 700 Level Questions



CONCEPT: Sum of first n consecutive integers, \(1+2+3....+n = (\frac{1}{2})*n(n+1)\)


Here the sum should be close to 10,000 and greater than 10,000

Lets calculate (1/2)*n(n+1) = 10000
n*(n+1) = 20000
i.e.n ≈ 141

141*142 = 20022

i.e. (1/2)*141*142 = 10011

So ew are short of 11

OR

We are short of 142(next page)+11 = 153

I. 76 and 77 Sum of 76 and 77 = 153 POSSIBLE
II. 33 and 34
III. 5 and 6. Sum of 5 and 6 = 11 POSSIBLE

Answer: Option E
_________________
Prepare with PERFECTION to claim Q≥50 and V≥40 !!!
GMATinsight .............(Bhoopendra Singh and Dr.Sushma Jha)
e-mail: info@GMATinsight.com l Call : +91-9999687183 / 9891333772
One-on-One Skype classes l Classroom Coaching l On-demand Quant course l Admissions Consulting

Most affordable l Comprehensive l 2000+ Qn ALL with Video explanations l LINK: Courses and Pricing
Click for FREE Demo on VERBAL & QUANT
Our SUCCESS STORIES: From 620 to 760 l Q-42 to Q-49 in 40 days l 590 to 710 + Wharton l
FREE GMAT Resource: 22 FREE (FULL LENGTH) GMAT CATs LINKS l NEW OG QUANT 50 Qn+VIDEO Sol.
Intern
Intern
avatar
B
Joined: 18 Feb 2020
Posts: 38
Location: India
Concentration: General Management, Entrepreneurship
Re: A page is torn from a novel. The sum of the remaining page numbers is  [#permalink]

Show Tags

New post 14 Apr 2020, 12:13
GMATinsight wrote:
Bunuel wrote:
A page is torn from a novel. The sum of the remaining page numbers is 10,000. What could be the page-numbers on the torn page ?

I. 76 and 77
II. 33 and 34
III. 5 and 6.

A. I only
B. II only
C. III only
D. I and II only
E. I and III only


Are You Up For the Challenge: 700 Level Questions



CONCEPT: Sum of first n consecutive integers, \(1+2+3....+n = (\frac{1}{2})*n(n+1)\)


Here the sum should be close to 10,000 and greater than 10,000

Lets calculate (1/2)*n(n+1) = 10000
n*(n+1) = 20000
i.e.n ≈ 141

141*142 = 20022

i.e. (1/2)*141*142 = 10011

So ew are short of 11

OR

We are short of 142(next page)+11 = 153

I. 76 and 77 Sum of 76 and 77 = 153 POSSIBLE
II. 33 and 34
III. 5 and 6. Sum of 5 and 6 = 11 POSSIBLE

Answer: Option E


Hi Can you Pls explain how did you get 142 + 11= 153. Thanks in advance.
Senior Manager
Senior Manager
avatar
S
Joined: 18 Dec 2017
Posts: 300
Re: A page is torn from a novel. The sum of the remaining page numbers is  [#permalink]

Show Tags

New post 14 Apr 2020, 19:32
AdiBatman wrote:
GMATinsight wrote:
Bunuel wrote:
A page is torn from a novel. The sum of the remaining page numbers is 10,000. What could be the page-numbers on the torn page ?

I. 76 and 77
II. 33 and 34
III. 5 and 6.

A. I only
B. II only
C. III only
D. I and II only
E. I and III only


Are You Up For the Challenge: 700 Level Questions



CONCEPT: Sum of first n consecutive integers, \(1+2+3....+n = (\frac{1}{2})*n(n+1)\)


Here the sum should be close to 10,000 and greater than 10,000

Lets calculate (1/2)*n(n+1) = 10000
n*(n+1) = 20000
i.e.n ≈ 141

141*142 = 20022

i.e. (1/2)*141*142 = 10011

So ew are short of 11

OR

We are short of 142(next page)+11 = 153

I. 76 and 77 Sum of 76 and 77 = 153 POSSIBLE
II. 33 and 34
III. 5 and 6. Sum of 5 and 6 = 11 POSSIBLE

Answer: Option E


Hi Can you Pls explain how did you get 142 + 11= 153. Thanks in advance.

Suppose instead of 141 pages in the book, if there were 142 pages then sum of the pages would have been 10153 then extra sum would have been 153
Which is 77 +76 =153
So this is also the possibility

Posted from my mobile device
GMAT Club Legend
GMAT Club Legend
User avatar
V
Status: GMATINSIGHT Tutor
Joined: 08 Jul 2010
Posts: 4345
Location: India
GMAT: QUANT EXPERT
Schools: IIM (A)
GMAT 1: 750 Q51 V41
WE: Education (Education)
Reviews Badge
Re: A page is torn from a novel. The sum of the remaining page numbers is  [#permalink]

Show Tags

New post 14 Apr 2020, 23:29
1
AdiBatman wrote:
GMATinsight wrote:
Bunuel wrote:
A page is torn from a novel. The sum of the remaining page numbers is 10,000. What could be the page-numbers on the torn page ?

I. 76 and 77
II. 33 and 34
III. 5 and 6.

A. I only
B. II only
C. III only
D. I and II only
E. I and III only


Are You Up For the Challenge: 700 Level Questions



CONCEPT: Sum of first n consecutive integers, \(1+2+3....+n = (\frac{1}{2})*n(n+1)\)


Here the sum should be close to 10,000 and greater than 10,000

Lets calculate (1/2)*n(n+1) = 10000
n*(n+1) = 20000
i.e.n ≈ 141

141*142 = 20022

i.e. (1/2)*141*142 = 10011

So we are short of 11

OR

We are short of 142(next page)+11 = 153

I. 76 and 77 Sum of 76 and 77 = 153 POSSIBLE
II. 33 and 34
III. 5 and 6. Sum of 5 and 6 = 11 POSSIBLE

Answer: Option E


Hi Can you Pls explain how did you get 142 + 11= 153. Thanks in advance.


Hi AdiBatman

Sum of 1 to 141 is (1/2)*141*142 = 10011 so the sum of page number should be 11 more i.e. pages torn must have sum of page numbers 11

But

other possibilities is that there were 142 pages and in that case the missing sum would be 11+142(next page number) = 153

I hope this help!!! :)
_________________
Prepare with PERFECTION to claim Q≥50 and V≥40 !!!
GMATinsight .............(Bhoopendra Singh and Dr.Sushma Jha)
e-mail: info@GMATinsight.com l Call : +91-9999687183 / 9891333772
One-on-One Skype classes l Classroom Coaching l On-demand Quant course l Admissions Consulting

Most affordable l Comprehensive l 2000+ Qn ALL with Video explanations l LINK: Courses and Pricing
Click for FREE Demo on VERBAL & QUANT
Our SUCCESS STORIES: From 620 to 760 l Q-42 to Q-49 in 40 days l 590 to 710 + Wharton l
FREE GMAT Resource: 22 FREE (FULL LENGTH) GMAT CATs LINKS l NEW OG QUANT 50 Qn+VIDEO Sol.
Intern
Intern
avatar
B
Joined: 18 Feb 2020
Posts: 38
Location: India
Concentration: General Management, Entrepreneurship
Re: A page is torn from a novel. The sum of the remaining page numbers is  [#permalink]

Show Tags

New post 15 Apr 2020, 06:29
thanks! Got it! Basically x=141 or 142. I missed it.
Thanks for the explanation.
Intern
Intern
avatar
Joined: 09 Oct 2019
Posts: 6
Re: A page is torn from a novel. The sum of the remaining page numbers is  [#permalink]

Show Tags

New post 16 Apr 2020, 02:46
I think it's A because a book/novel can only have even pages
So for 141 pages is no chance
GMAT Club Legend
GMAT Club Legend
User avatar
V
Status: GMATINSIGHT Tutor
Joined: 08 Jul 2010
Posts: 4345
Location: India
GMAT: QUANT EXPERT
Schools: IIM (A)
GMAT 1: 750 Q51 V41
WE: Education (Education)
Reviews Badge
Re: A page is torn from a novel. The sum of the remaining page numbers is  [#permalink]

Show Tags

New post 16 Apr 2020, 06:10
rudi0setyawan wrote:
I think it's A because a book/novel can only have even pages
So for 141 pages is no chance


rudi0setyawan

What makes you think that a book/novel can't have odd pages.

It's only the page number which can very well be even or odd

The numbering is done in many ways in books. A few pages in beginning in Roman count where the introduction is mentioned, the dedication letter is mentiones.

Towards the end there may be some advertise and all and the numbers mentioned on pages can well be Odd number too
_________________
Prepare with PERFECTION to claim Q≥50 and V≥40 !!!
GMATinsight .............(Bhoopendra Singh and Dr.Sushma Jha)
e-mail: info@GMATinsight.com l Call : +91-9999687183 / 9891333772
One-on-One Skype classes l Classroom Coaching l On-demand Quant course l Admissions Consulting

Most affordable l Comprehensive l 2000+ Qn ALL with Video explanations l LINK: Courses and Pricing
Click for FREE Demo on VERBAL & QUANT
Our SUCCESS STORIES: From 620 to 760 l Q-42 to Q-49 in 40 days l 590 to 710 + Wharton l
FREE GMAT Resource: 22 FREE (FULL LENGTH) GMAT CATs LINKS l NEW OG QUANT 50 Qn+VIDEO Sol.
Target Test Prep Representative
User avatar
V
Status: Founder & CEO
Affiliations: Target Test Prep
Joined: 14 Oct 2015
Posts: 11083
Location: United States (CA)
Re: A page is torn from a novel. The sum of the remaining page numbers is  [#permalink]

Show Tags

New post 17 Apr 2020, 10:21
2
1
Bunuel wrote:
A page is torn from a novel. The sum of the remaining page numbers is 10,000. What could be the page-numbers on the torn page ?

I. 76 and 77
II. 33 and 34
III. 5 and 6.

A. I only
B. II only
C. III only
D. I and II only
E. I and III only


Are You Up For the Challenge: 700 Level Questions


Recall that the sum of the consecutive integers from 1 to n is given by n(n + 1)/2. Let’s analyze each Roman numeral:

I: 76 and 77

If the page numbers on the torn page was 76 and 77, then the sum of the pages of the novel was 10,000 + 76 + 77 = 10,153. To determine whether 10,153 is the sum of consecutive integers, let’s solve n(n + 1)/2 = 10,153:

n(n + 1)/2 = 10153

n^2 + n = 20306

n^2 + n - 20306 = 0

(n + 143)(n - 142) = 0

n = -143 or n = 142

We see that 10,153 is the sum of the integers from 1 to 142; therefore it is possible that the page numbers on the torn page were 76 and 77.

II: 33 and 34

If the page numbers on the torn page was 33 and 34, then the sum of the pages of the novel was 10,000 + 33 + 34 = 10,067. To determine whether 10,067 is the sum of consecutive integers, let’s solve n(n + 1)/2 = 10,067:

n(n+1)/2 = 10067

n^2 + n = 20134

n^2 + n - 20134 = 0

This equation has no integer roots. Thus, the page numbers on the torn page cannot be 33 and 34.

III: 5 and 6

If the page numbers on the torn page was 5 and 6, then the sum of the pages of the novel was 10,000 + 5 + 6 = 10,011. To determine whether 10,011 is the sum of consecutive integers, let’s solve n(n + 1)/2 = 10,011:

n(n+1)/2 = 10011

n^2 + n = 20022

n^2 + n - 20022 = 0

(n + 142)(n - 141) = 0

We see that 10,011 is the sum of the integers from 1 to 141; therefore it is possible that the page numbers on the torn page were 5 and 6.

Answer: E


_________________

Scott Woodbury-Stewart

Founder and CEO

Scott@TargetTestPrep.com

  214 REVIEWS

5-STARS RATED ONLINE GMAT QUANT SELF STUDY COURSE

NOW WITH GMAT VERBAL (BETA)

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

Intern
Intern
avatar
B
Joined: 25 May 2020
Posts: 7
A page is torn from a novel. The sum of the remaining page numbers is  [#permalink]

Show Tags

New post 09 Jul 2020, 12:31
Recall that the sum of the consecutive integers from 1 to n is given by n(n + 1)/2. Let’s analyze each Roman numeral:

I: 76 and 77

If the page numbers on the torn page was 76 and 77, then the sum of the pages of the novel was 10,000 + 76 + 77 = 10,153. To determine whether 10,153 is the sum of consecutive integers, let’s solve n(n + 1)/2 = 10,153:

n(n + 1)/2 = 10153

n^2 + n = 20306

n^2 + n - 20306 = 0

(n + 143)(n - 142) = 0

n = -143 or n = 142

We see that 10,153 is the sum of the integers from 1 to 142; therefore it is possible that the page numbers on the torn page were 76 and 77.

II: 33 and 34

If the page numbers on the torn page was 33 and 34, then the sum of the pages of the novel was 10,000 + 33 + 34 = 10,067. To determine whether 10,067 is the sum of consecutive integers, let’s solve n(n + 1)/2 = 10,067:

n(n+1)/2 = 10067

n^2 + n = 20134

n^2 + n - 20134 = 0

This equation has no integer roots. Thus, the page numbers on the torn page cannot be 33 and 34.

III: 5 and 6

If the page numbers on the torn page was 5 and 6, then the sum of the pages of the novel was 10,000 + 5 + 6 = 10,011. To determine whether 10,011 is the sum of consecutive integers, let’s solve n(n + 1)/2 = 10,011:

n(n+1)/2 = 10011

n^2 + n = 20022

n^2 + n - 20022 = 0

(n + 142)(n - 141) = 0

We see that 10,011 is the sum of the integers from 1 to 141; therefore it is possible that the page numbers on the torn page were 5 and 6.

Answer: E

[/quote]

Hi ScottTargetTestPrep,

Could you please tell how to split the middle term for such equations (n^2 + n - 20306 = 0
) in a quicker manner as I am finding difficulty in solving them.

Thanks!
GMAT Club Bot
A page is torn from a novel. The sum of the remaining page numbers is   [#permalink] 09 Jul 2020, 12:31

A page is torn from a novel. The sum of the remaining page numbers is

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





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