Difficult Math Question #1

This topic has expert replies
Master | Next Rank: 500 Posts
Posts: 354
Joined: Tue Jun 27, 2006 9:20 pm
Thanked: 11 times
Followed by:5 members

Difficult Math Question #1

by 800guy » Sat Aug 26, 2006 8:17 am
i want to start a series of post that work through the difficult math questions doc on this forum... i really suck at math and i think it would be great if we all shared our different approaches for solving certian questions. here's question 1/123!! i'll post the OA once a few people have responded..

The sum of the even numbers between 1 and n is 79*80, where n is an odd number, then n=?

GMAT/MBA Expert

User avatar
Site Admin
Posts: 6773
Joined: Mon Feb 13, 2006 8:30 am
Location: Los Angeles, CA
Thanked: 1249 times
Followed by:994 members

by beatthegmat » Sat Aug 26, 2006 8:37 am
Great initiative, 800guy! I encourage members to answer these posts as practice for the difficult quant questions you will encounter on the GMAT.

To caveat, the document 800guy is using for these posts features questions that are more difficult than you would likely encounter on the real exam. If you can answer these questions, you are well prepped for your GMAT!

Best of luck!
Beat The GMAT | The MBA Social Network
Community Management Team

Research Top GMAT Prep Courses:
https://www.beatthegmat.com/gmat-prep-courses

Research The World's Top MBA Programs:
https://www.beatthegmat.com/mba/school

User avatar
Legendary Member
Posts: 2469
Joined: Thu Apr 20, 2006 12:09 pm
Location: BtG Underground
Thanked: 85 times
Followed by:14 members

by aim-wsc » Sat Aug 26, 2006 11:06 am
dear 800guy
would u tell me d meaning of these

OA - did u mean original answer?
1/123 - so does that mean that u hv in total 123 questions?

why hv not published options?

Master | Next Rank: 500 Posts
Posts: 354
Joined: Tue Jun 27, 2006 9:20 pm
Thanked: 11 times
Followed by:5 members

by 800guy » Sat Aug 26, 2006 12:30 pm
aim-wsc wrote:dear 800guy
would u tell me d meaning of these

OA - did u mean original answer?
1/123 - so does that mean that u hv in total 123 questions?

why hv not published options?
OA means official answer.. and yes, i do have 123 questions total.

there aren't any options to publish--it's up to you all to just find the answer.

thanks guys!!

User avatar
Legendary Member
Posts: 2469
Joined: Thu Apr 20, 2006 12:09 pm
Location: BtG Underground
Thanked: 85 times
Followed by:14 members

get the formula

by aim-wsc » Sat Aug 26, 2006 12:53 pm
take lowest value for n first.
n=5
so series is 2 + 4
sum=6
which is 2 X 3.

take next value n=7
sum=12=3 X 4

take random n=23
sum=132=11 X 12

by now one can get the TREND the pattern...
add 79 & 80.
thats it.

Newbie | Next Rank: 10 Posts
Posts: 1
Joined: Fri Jul 07, 2006 12:08 pm

by alpha_gmat » Mon Aug 28, 2006 10:46 am
First Number: a = 2
Difference: d = 2
nth number: a+(n-1)d = 2+(n-1)2 = 2+ 2n-2 = 2n

Sum 79*80 = (1/2) n (first +nth number) = (1/2) n (2+2n) = n(n+1)

n=79

Master | Next Rank: 500 Posts
Posts: 354
Joined: Tue Jun 27, 2006 9:20 pm
Thanked: 11 times
Followed by:5 members

by 800guy » Mon Aug 28, 2006 7:24 pm
here's the OA:

Sol: First term a=2, common difference d=2 since even number

therefore sum to first n numbers of Arithmetic progression would be

n/2(2a+(n-1)d)

= n/2(2*2+(n-1)*2)=n(n+1) and this is equal to 79*80

therefore n=79 which is odd...

User avatar
Legendary Member
Posts: 2469
Joined: Thu Apr 20, 2006 12:09 pm
Location: BtG Underground
Thanked: 85 times
Followed by:14 members

i c

by aim-wsc » Tue Aug 29, 2006 10:19 am
ok
i got it. :roll:
hee hee
i made a mistake there.... hv to slow down :x

Junior | Next Rank: 30 Posts
Posts: 17
Joined: Wed Jan 24, 2007 3:35 am

by amitamit2020 » Wed Feb 14, 2007 11:45 am
I think n = 159 is the correct answer. Here is the analytical support.

we are given the sum of even (remember EVEN) nos. between 1 and n (n being odd number) ; the sum is equal to 79*80.

let's write the serise : 1, 2, 3 , 4, 5 ...... n-1, n (n is odd) -- total n terms

if we take out only even nos. they are 2, 4, 6 ....,(n-1) -- total [(n-1)/2] terms

now sum of these terms = (i/2) * (a +l) where i = total no. of terms; a = first term and l = last term

putting the values, sum = ((n-1)/4)*(2+(n-1)) = 79*80

i.e. (n-1) * (n+1) = 158 * 160

i.e. n = 159.

Pl. let me know if I made a mistake somewhere. I think aim-wsc had developed a good logic for the problem (!)

Senior | Next Rank: 100 Posts
Posts: 38
Joined: Sat Dec 30, 2006 7:46 pm
Thanked: 1 times

by banona » Wed Feb 14, 2007 1:42 pm
I am sorry alpha_gmat and 800guy

you gave the same answer as in the word document of " tough math problems" and it's wrong. n is not 79. In fact, we should check the accuracy of the answers sometimes.

I got the same answer following the same path as you (amitamit2020)
In fact, I think n= 159 ( and the trick is that people try to have something like (n+1)*n at the end, so that it would be possible to guess one n is;
now, to verify, if you plug the value of n in the the sumof even numbers you will find that :
if n = 79
2+4+6+........+78 = 2*( 1+2+3+4+........38) = 2*(39/2)*38 =38 * 39

Now, if n= 159
2+4+6+........+158 = 2( 1+2+3+4+........79) = 2*(80/2)*79 = 79*80

Master | Next Rank: 500 Posts
Posts: 354
Joined: Tue Jun 27, 2006 9:20 pm
Thanked: 11 times
Followed by:5 members

by 800guy » Wed Feb 14, 2007 3:08 pm
banona wrote:I am sorry alpha_gmat and 800guy

you gave the same answer as in the word document of " tough math problems" and it's wrong. n is not 79. In fact, we should check the accuracy of the answers sometimes.

I got the same answer following the same path as you (amitamit2020)
In fact, I think n= 159 ( and the trick is that people try to have something like (n+1)*n at the end, so that it would be possible to guess one n is;
now, to verify, if you plug the value of n in the the sumof even numbers you will find that :
if n = 79
2+4+6+........+78 = 2*( 1+2+3+4+........38) = 2*(39/2)*38 =38 * 39

Now, if n= 159
2+4+6+........+158 = 2( 1+2+3+4+........79) = 2*(80/2)*79 = 79*80
yup, you're right--i do provide the "OA" that's listed in the diff math questions doc. i post these questions to promote discussion on these forums...

good catch on this one

Senior | Next Rank: 100 Posts
Posts: 38
Joined: Sat Dec 30, 2006 7:46 pm
Thanked: 1 times

by banona » Wed Feb 14, 2007 8:16 pm
That' great 800guy,
You've reached your goal making us thinking and discussing around some problems,
we are waiting for your next question

Thanks

User avatar
Legendary Member
Posts: 2469
Joined: Thu Apr 20, 2006 12:09 pm
Location: BtG Underground
Thanked: 85 times
Followed by:14 members

Re: get the formula

by aim-wsc » Thu Feb 15, 2007 9:05 pm
[quote="aim-wsc''] by now one can get the TREND the pattern...
add 79 & 80.
thats it.[/quote]
so mine was correct then :mrgreen:

btw 800guy is doing great job i must tell you about this 8)
his math question series helped many of our members.

thanks 800guy :)

Senior | Next Rank: 100 Posts
Posts: 48
Joined: Sun Nov 25, 2007 3:27 pm
Location: Colombia Southamerica
Thanked: 1 times

by andes1 » Thu Jul 03, 2008 9:01 pm
thanks
LEARNING ENGLIS H

Newbie | Next Rank: 10 Posts
Posts: 4
Joined: Thu Sep 18, 2008 10:28 am

by ttwang56 » Sun Sep 21, 2008 6:07 pm
shouldn't n = 157?

if n = 159 then the way to check would be 158+2 = 160. 160 would be able to added up all the with 4+156, etc. 160 doesn't go into the 6320 (78*80) evenly. However, if n = 157, then 2+156= 158. 158 goes evenly into 6320 with a solution of 40.

why can't u solve it by factoring 80 to being 2 x 40 and multiplying the 2 to the 79?

don't know if i explained this clearly or not.