Consecutive integers

Expert replies

finance: Master | Next Rank: 500 Posts; Posts: 150; Joined: Tue Mar 08, 2011 4:38 am; Thanked: 5 times

by finance » Sun Jun 05, 2011 8:05 am

If z1,z2......zn is a series of consecutive positive integers, is the sum of all the integers in this sequence odd?

(1) (z1+z2+....zn)/n is an odd integer
(2) n is odd

Like this post

Source: Beat The GMAT — Data Sufficiency | Sun Jun 05, 2011 8:05 am

cans: Legendary Member; Posts: 1309; Joined: Mon Apr 04, 2011 5:34 amFollowed by: 123 members; Location: India; Thanked: 310 times; GMAT Score:750

by cans » Sun Jun 05, 2011 8:10 am

odd+even=odd
thus z1,z2,...zn
s=z1+z2+....+zn
s is odd??
a)s/n is odd -> s=n*odd number. If n is even, s is even, if n is odd, s is odd. Insufficient
b)n is odd. insufficient. (2,3,4 sum->odd ; 3,4,5 sum->odd)
a&b) n is odd and thus sum is odd. Sufficient
IMO C

If my post helped you- let me know by pushing the thanks button

Contact me about long distance tutoring!
[email protected]

Cans!!

Like this post

finance: Master | Next Rank: 500 Posts; Posts: 150; Joined: Tue Mar 08, 2011 4:38 am; Thanked: 5 times

by finance » Sun Jun 05, 2011 8:14 am

Thank you Cans! I made the same mistake as you, but that's not the OA.

Like this post

[email protected]: Legendary Member; Posts: 934; Joined: Tue Nov 09, 2010 5:16 amFollowed by: 14 members; Location: AAMCHI MUMBAI LOCAL; Thanked: 63 times

by [email protected] » Sun Jun 05, 2011 8:26 am

If z1,z2......zn is a series of consecutive positive integers, is the sum of all the integers in this sequence odd?

(1) (z1+z2+....zn)/n is an odd integer
(2) n is odd

Statement 1 says that it is an arithmetic mean of all given values and it is odd but alone is not sufficient.

Statement 2 gives the value of n but the value of 'n' alone is not sufficient.

Both statements together will give an answer i.e odd number X odd number = odd number
eg: 7 X 9 = 63.

IT IS TIME TO BEAT THE GMAT

LEARNING, APPLICATION AND TIMING IS THE FACT OF GMAT AND LIFE AS WELL... KEEP PLAYING!!!

Whenever you feel that my post really helped you to learn something new, please press on the 'THANK' button.

Like this post

cans: Legendary Member; Posts: 1309; Joined: Mon Apr 04, 2011 5:34 amFollowed by: 123 members; Location: India; Thanked: 310 times; GMAT Score:750

by cans » Sun Jun 05, 2011 8:36 am

finance wrote:Thank you Cans! I made the same mistake as you, but that's not the OA.

found my mistake
zn=z1+(n-1)
s=(n/2)*(z1+zn)
s/n = z1 + (n-1)/2
z1 is integer. also s/n is odd integer.
Thus (n-1)/2 must be integer. or n-1 is even
or n is odd.
Thus A alone is sufficient (s=odd)
IMO A
Great question.

If my post helped you- let me know by pushing the thanks button

Contact me about long distance tutoring!
[email protected]

Cans!!

Like this post

GMAT/MBA Expert

Anurag@Gurome: GMAT Instructor; Posts: 3835; Joined: Fri Apr 02, 2010 10:00 pmFollowed by: 523 members; Location: Milpitas, CA; Thanked: 1854 times; GMAT Score:770

by Anurag@Gurome » Sun Jun 05, 2011 8:40 am

finance wrote:If z1,z2......zn is a series of consecutive positive integers, is the sum of all the integers in this sequence odd?

(1) (z1+z2+....zn)/n is an odd integer
(2) n is odd

Say, x is the first integer of the series.
Then the sum of the all integers = x + (x + 1) + (x + 2) + ... + (x + n - 1) = nx + n(n - 1)/2 = n(x + (n - 1)/2)

Statement 1: (z1 + z2 + ... + zn)/n is an odd integer
Hence, (x + (n - 1)/2) is an odd integer.
Hence, (n - 1)/2 is an integer, i.e. n is an odd integer.
Therefore, sum of all the integers in the sequence = n*(some odd integer) = odd*odd = odd

Sufficient.

Statement 2: n is odd.
Hence, sum of the integers = odd*(x + (n - 1)/2)
But we don't know whether x is odd or even. Also we don't know whether (n - 1)/2 is even or odd.

Not sufficient.

The correct answer is A.

Anurag Mairal, Ph.D., MBA
GMAT Expert, Admissions and Career Guidance
Gurome, Inc.
1-800-566-4043 (USA)

Join Our Facebook Groups
GMAT with Gurome
https://www.facebook.com/groups/272466352793633/
Admissions with Gurome
https://www.facebook.com/groups/461459690536574/
Career Advising with Gurome
https://www.facebook.com/groups/360435787349781/

Like this post

aftableo2006: Senior | Next Rank: 100 Posts; Posts: 99; Joined: Sat Oct 16, 2010 1:55 pm; Thanked: 1 times

by aftableo2006 » Mon Jun 06, 2011 9:03 pm

thanks for the explanation this was a tricky one

Like this post

gmat1978: Senior | Next Rank: 100 Posts; Posts: 35; Joined: Thu Dec 23, 2010 7:38 pm

by gmat1978 » Wed Jun 08, 2011 10:34 pm

Cans,

Can you please explain your solution below in more detail?

Thanks

cans wrote:
finance wrote:Thank you Cans! I made the same mistake as you, but that's not the OA.
found my mistake
zn=z1+(n-1)
s=(n/2)*(z1+zn)
s/n = z1 + (n-1)/2
z1 is integer. also s/n is odd integer.
Thus (n-1)/2 must be integer. or n-1 is even
or n is odd.
Thus A alone is sufficient (s=odd)
IMO A
Great question.

Like this post

cans: Legendary Member; Posts: 1309; Joined: Mon Apr 04, 2011 5:34 amFollowed by: 123 members; Location: India; Thanked: 310 times; GMAT Score:750

by cans » Wed Jun 08, 2011 11:12 pm

gmat1978 wrote:Cans,

Can you please explain your solution below in more detail?

Thanks

cans wrote:
finance wrote:Thank you Cans! I made the same mistake as you, but that's not the OA.
found my mistake
zn=z1+(n-1)
s=(n/2)*(z1+zn)
s/n = z1 + (n-1)/2
z1 is integer. also s/n is odd integer.
Thus (n-1)/2 must be integer. or n-1 is even
or n is odd.
Thus A alone is sufficient (s=odd)
IMO A
Great question.

as z1,z2,...,zn is series of consecutive integers,
z2=z1+1
z3=z2+1 = z1+2
thus zn = z1 + (n-1)
Sum = z1 + z1 + z3 + ....... + zn
also using sum of arithmetic progression series formula
sum = (n/2)(z1+zn) (sum = no. of terms * (first term + last term) / 2)
sum = (n/2)(z1+z1+(n-1))
sum=(n/2) (2z1 + (n-1))
sum/n = (2z1 + (n-1))/2
also sum/n is odd.
Thus (2z1 + (n-1))/2 is odd
multiplying that odd number with 2 will give even number
thus 2z1 + (n-1) is even
also 2z1 is even
thus (n-1) + even = even -> (n-1) has to be even
thus n is even+1 or n is odd
also given sum/n is odd
Thus sum=n*odd
as n is odd, sum=odd*odd = odd (ex: 5*3=15; 3*9=27)
Sufficient

If my post helped you- let me know by pushing the thanks button

Contact me about long distance tutoring!
[email protected]

Cans!!

Like this post

Post new topic Post Reply

• Page 1 of 1

GMAT Course Reviews

560 reviews

1168 reviews

431 reviews

359 reviews

147 reviews

5/5

5 Star (560 Reviews)

"Target Test Prep is the closest to the official version of the GMAT exam, about 99% accuracy in terms of the quality and quantity of information. The course has excellently created singular sets of focused lessons and tests for every possible topic that one could come across in the official GMAT exam."

"The TTP course maximizes the efficiency of the time you spend studying. It will take time and effort but I could almost guarantee that if you complete the course exactly as it is laid out you will get an amazing score. They also have a very responsive team willing to help with any questions you might have."

"TTP has two things that I think no other test prep company offers: A teaching approach that reinforces understanding and an attitude that will give you the mental preparedness needed to succeed on the test. TTP gives you a deep understanding of the concept you need to know while teaching you how to think."

Write a Review