NEW HERE? LEARN MORE
closeclose
Last visit was: 24 Apr 2024, 13:16 It is currently 24 Apr 2024, 13:16
Decision Tracker
My Rewards
New posts
New comers' posts

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.
Go to My Error Log Learn more
Close
Request Expert Reply
Confirm Cancel

Adam tears off a page from his textbook. The sum of the remaining page

SORT BY:
Date
Kudos
Tags:
Find Similar Topics 
Show Tags
Hide Tags
User avatar
L
DisciplinedPrep
VP
VP
Joined: 15 Jan 2018
Posts: 1345
Own Kudos [?]: 1920 [8]
Given Kudos: 628
Concentration: Marketing, Leadership
Send PM
Adam tears off a page from his textbook. The sum of the remaining page [#permalink] New post   02 Jan 2020, 03:00
8
Bookmarks
00:00
A
B
C
D
E

Difficulty:

95% (hard)

Question Stats:

34% (02:19) correct 66% (02:14) wrong based on 35 sessions
Hide Show timer Statistics
Adam tears off a page from his textbook. The sum of the remaining page numbers is 10000. What are the two page-numbers on the torn-off pages of his textbook?

A. 8 and 9

B. 33 and 34

C. 77 and 78

D. 97 and 98

E. 76 and 77
ShowHide Answer
Official Answer
E
User avatar
L
chetan2u
RC & DI Moderator
Joined: 02 Aug 2009
Status:Math and DI Expert
Posts: 11169
Own Kudos [?]: 31890 [1]
Given Kudos: 290
Send PM
Reviews Badge
Re: Adam tears off a page from his textbook. The sum of the remaining page [#permalink] New post   02 Jan 2020, 03:20
1
Kudos
Expert Reply
DisciplinedPrep wrote:
Adam tears off a page from his textbook. The sum of the remaining page numbers is 10000. What are the two page-numbers on the torn-off pages of his textbook?

A. 8 and 9 or 76 and 77

B. 33 and 34 or 5 and 6

C. 77 and 78 or 8 and 9

D. 97 and 98 or 77 and 78

E. 76 and 77 or 5 and 6



Let the numbers be a and b, and total pages be n, so sum of n pages = \(\frac{n(n+1)}{2}=10000+a+b....n(n+1)=20000+2(a+b)\)
Thus 20000+2(a+b) should be the product of two consecutive numbers n and n+1..

You can check from choices or look for the squareroot of 20000, which is closer to 140..
So if 140 pages are there..14*141=19740<20000, so take next value of n as 141
141*142=20022, so look for 2(a+b) = 22...a+b=11...From choices 5 and 6 fit in
Answer is B or E
Take next value of n as 142, so 142*143=20306...look for 2(a+b)=306...a+b=153...Only 76+77=153 fits in

E
avatar
B
akanksha10899
Intern
Intern
Joined: 30 Apr 2019
Posts: 6
Own Kudos [?]: 2 [0]
Given Kudos: 79
Send PM
Re: Adam tears off a page from his textbook. The sum of the remaining page [#permalink] New post   05 Jan 2020, 22:12
chetan2u wrote:
DisciplinedPrep wrote:
Adam tears off a page from his textbook. The sum of the remaining page numbers is 10000. What are the two page-numbers on the torn-off pages of his textbook?

A. 8 and 9 or 76 and 77

B. 33 and 34 or 5 and 6

C. 77 and 78 or 8 and 9

D. 97 and 98 or 77 and 78

E. 76 and 77 or 5 and 6



Let the numbers be a and b, and total pages be n, so sum of n pages = \(\frac{n(n+1)}{2}=10000+a+b....n(n+1)=20000+2(a+b)\)
Thus 20000+2(a+b) should be the product of two consecutive numbers n and n+1..

You can check from choices or look for the squareroot of 20000, which is closer to 140..
So if 140 pages are there..14*141=19740<20000, so take next value of n as 141
141*142=20022, so look for 2(a+b) = 22...a+b=11...From choices 5 and 6 fit in
Answer is B or E
Take next value of n as 142, so 142*143=20306...look for 2(a+b)=306...a+b=153...Only 76+77=153 fits in

E


Hi, I did not get your explanation like how you solved it and what approach you used. Can you explain me a different approach?
User avatar
L
rajatchopra1994
VP
VP
Joined: 16 Feb 2015
Posts: 1080
Own Kudos [?]: 1024 [0]
Given Kudos: 30
Location: United States
Send PM
Re: Adam tears off a page from his textbook. The sum of the remaining page [#permalink] New post   06 Jan 2020, 01:19
akanksha10899 wrote:
chetan2u wrote:
DisciplinedPrep wrote:
Adam tears off a page from his textbook. The sum of the remaining page numbers is 10000. What are the two page-numbers on the torn-off pages of his textbook?

A. 8 and 9 or 76 and 77

B. 33 and 34 or 5 and 6

C. 77 and 78 or 8 and 9

D. 97 and 98 or 77 and 78

E. 76 and 77 or 5 and 6



Let the numbers be a and b, and total pages be n, so sum of n pages = \(\frac{n(n+1)}{2}=10000+a+b....n(n+1)=20000+2(a+b)\)
Thus 20000+2(a+b) should be the product of two consecutive numbers n and n+1..

You can check from choices or look for the squareroot of 20000, which is closer to 140..
So if 140 pages are there..14*141=19740<20000, so take next value of n as 141
141*142=20022, so look for 2(a+b) = 22...a+b=11...From choices 5 and 6 fit in
Answer is B or E
Take next value of n as 142, so 142*143=20306...look for 2(a+b)=306...a+b=153...Only 76+77=153 fits in

E


Hi, I did not get your explanation like how you solved it and what approach you used. Can you explain me a different approach?


Dear akanksha10899 ,

This Approach is called Average.
Below URL contains the concept & related questions like this.
https://mba.hitbullseye.com/cat/Average-Questions.php

Regards,
Rajat Chopra
User avatar
L
nick1816
Retired Moderator
Joined: 19 Oct 2018
Posts: 1878
Own Kudos [?]: 6296 [2]
Given Kudos: 704
Location: India
Send PM
Re: Adam tears off a page from his textbook. The sum of the remaining page [#permalink] New post   06 Jan 2020, 02:21
1
Kudos
1
Bookmarks
n(n+1)/2= 10000+x+x+1

n^2+n= 20000+4x+2

n^2+n- (20002+4x)=0

As n is a real number and an integer; hence, b^2-4ac must be a perfect square

b^2-4ac=1+4(20002+4x)= 16x+80009

We can use the options to get to the answer.

16*76+80009= 285^2

E




DisciplinedPrep wrote:
Adam tears off a page from his textbook. The sum of the remaining page numbers is 10000. What are the two page-numbers on the torn-off pages of his textbook?

A. 8 and 9

B. 33 and 34

C. 77 and 78

D. 97 and 98

E. 76 and 77
User avatar
bumpbot
Non-Human User
Joined: 09 Sep 2013
Posts: 32653
Own Kudos [?]: 821 [0]
Given Kudos: 0
Send PM
Re: Adam tears off a page from his textbook. The sum of the remaining page [#permalink] New post   10 Jul 2023, 09:52
Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
GMAT Club Bot
gmatclubot
Re: Adam tears off a page from his textbook. The sum of the remaining page [#permalink]
10 Jul 2023, 09:52
Moderators:
Bunuel
Math Expert
92902 posts
yashikaaggarwal
Senior Moderator - Masters Forum
3137 posts

Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne
Main navigation
GMAT Resources
Partners
MBA Resources
www.gmac.com|www.mba.com | | GMAT Club Rules | Terms and Conditions