How would you reason the second statement?

Expert replies

rrobiinn: Junior | Next Rank: 30 Posts; Posts: 24; Joined: Tue Mar 06, 2012 5:35 am

by rrobiinn » Tue May 29, 2012 8:42 pm

Is the average of n consecutive integers equal to 1?
(1) n is even.
(2) If S is the sum of the n consecutive integers, then 0 <s <n.

Like this post

Source: Beat The GMAT — Problem Solving | Tue May 29, 2012 8:42 pm

1947: Master | Next Rank: 500 Posts; Posts: 215; Joined: Sat Jun 14, 2008 4:24 pmFollowed by: 1 member; Thanked: 13 times

by 1947 » Tue May 29, 2012 9:20 pm

avg = sum/no. of term
so avg = s/n
from 2 since s<n so s/n is not 1 SUFF

from 1 try numbers -2,-1 avg = -3/2
1,2,3,4 avg 10/4 so avg is not 1 SUFF

D should be ans

rrobiinn wrote:Is the average of n consecutive integers equal to 1?
(1) n is even.
(2) If S is the sum of the n consecutive integers, then 0 <s <n.

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

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 » Wed May 30, 2012 3:07 am

rrobiinn wrote:Is the average of n consecutive integers equal to 1?
(1) n is even.
(2) If s is the sum of the n consecutive integers, then 0 < s < n.

Statement 1: Average of any even number of consecutive integers will always be the average of the central two numbers, i.e. a fraction. Hence, the average cannot be equal to 1.

Sufficient

Statement 2: Sum of n integers = s and 0 < s < n ---> 0 < s/n < 1
Hence, average of those n consecutive integers = s/n < 1

Sufficient

The correct answer is D.

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

rrobiinn: Junior | Next Rank: 30 Posts; Posts: 24; Joined: Tue Mar 06, 2012 5:35 am

by rrobiinn » Sun Jun 03, 2012 11:25 pm

Anurag@Gurome wrote:
rrobiinn wrote:Is the average of n consecutive integers equal to 1?
(1) n is even.
(2) If s is the sum of the n consecutive integers, then 0 < s < n.
Statement 1: Average of any even number of consecutive integers will always be the average of the central two numbers, i.e. a fraction. Hence, the average cannot be equal to 1.

Sufficient

Statement 2: Sum of n integers = s and 0 < s < n ---> 0 < s/n < 1
Hence, average of those n consecutive integers = s/n < 1

Sufficient

The correct answer is D.

Just above your post 1947 reasoned:

avg = sum/no. of term
so avg = s/n
from 2 since s<n so s/n is not 1 SUFF

from 1 try numbers -2,-1 avg = -3/2
1,2,3,4 avg 10/4 so avg is not 1 SUFF

D should be ans

* I understood his reasoning where yours has made it complex for me to understand. Could you make your explanation bit more easy to comprehend?

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 » Mon Jun 04, 2012 1:00 am

rrobiinn wrote:...yours has made it complex for me to understand. Could you make your explanation bit more easy to comprehend?

Let me try.

Statement 1: Average of any even number of consecutive integers will always be the average of the central two numbers, i.e. a fraction.

For example, say we have four consecutive integers: a, (a + 1), (a + 2), and (a + 3)
Average of this four consecutive integers = (4a + 6)/4 = (2a + 3)/2
Which is same as the average of central two numbers = [(a + 1) + (a + 2)]/2 = (2a + 3)/2 = (a + 1.5) --> A fraction

Let's take another example
Say we have ten consecutive integers: a, (a + 1), (a + 2), (a + 3), (a + 4), (a + 5), (a + 6), (a + 7), (a + 8), and (a + 9)
Average of this four consecutive integers = (10a + 45)/10 = (2a + 9)/2
Which is same as the average of central two numbers = [(a + 4) + (a + 5)]/2 = (2a + 9)/2 = (a + 4.5) --> A fraction

The average will always be a fraction as the sum of central two integers will always be odd as they are consecutive integers.

Hence, the average cannot be equal to 1.

Sufficient

Statement 2: Sum of n integers = s and 0 < s < n ---> 0 < s/n < 1

We know, s is less than n. Hence, the average, i.e. the ratio of s and n cannot be equal to n. This is just saying in words. I have shown it mathematically as 0 < s < n implies 0 < s/n < 1

Hence, average of those n consecutive integers = s/n < 1

Sufficient

I could've picked some number and shown that the statements do not help to conclude that average is not equal to 1 but that does not mean that they won't for any other set of numbers. If the question was "Is the average of n consecutive integers always equal to 1?" Then by picking some numbers and showing that average is not equal to 1, we could've concluded for sure that the average is not always equal to 1.

Picking number is great for showing exceptions or different scenarios but we can't pick number and prove some general case.

Like this post

amit28it: Senior | Next Rank: 100 Posts; Posts: 82; Joined: Fri Nov 04, 2011 12:35 amFollowed by: 2 members

by amit28it » Mon Jun 04, 2012 4:11 am

The answer given by Anurag@Gurome I always love his style of explaining the problem and the answer is D as mentioned by him.
Circumference of a Circle Formula

Like this post

rrobiinn: Junior | Next Rank: 30 Posts; Posts: 24; Joined: Tue Mar 06, 2012 5:35 am

by rrobiinn » Mon Jun 04, 2012 4:11 am

Thanks for the excellent explanation.

Like this post

Post new topic Post Reply

• Page 1 of 1

GMAT Course Reviews

559 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