Evenly spaced integers - Kaplan Problem - The Beat The GMAT Forum

Evenly spaced integers - Kaplan Problem

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iikarthik: Senior | Next Rank: 100 Posts; Posts: 57; Joined: Sun Jul 06, 2008 10:52 am; Thanked: 1 times; GMAT Score:640

by iikarthik » Fri Jun 04, 2010 9:02 am

What is the sum of 5 evenly spaced integers?

1. The middle integer is zero
2. Exactly 2 of the integers are negative

what is an evenly spaced integer? are they consecutive/ consecutive odd or consecutive even / Arithmetic progression series nos.Need assistance to understand this one

OA is A

Thanks
karthik

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Source: Beat The GMAT — Data Sufficiency | Fri Jun 04, 2010 9:02 am

boazkhan: Master | Next Rank: 500 Posts; Posts: 135; Joined: Tue Oct 13, 2009 10:27 am; Thanked: 3 times

by boazkhan » Fri Jun 04, 2010 9:09 am

correct, A is the answer...if i understand the question correctly..here is an example of 5 evenly spaced integers:

-4, -2, 0, 2, 4 or -10, -5, 0, 5, 10 or -6, -3, 0, 3, 6.....basically 0 (Zero) is the middle term and you have the exact number of positive and negative of same magnitude on both sides.

hope this helps.

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Haaress: Master | Next Rank: 500 Posts; Posts: 151; Joined: Thu Apr 22, 2010 4:07 pm; Thanked: 14 times

by Haaress » Fri Jun 04, 2010 9:17 am

Evenly spaced integer set can either be a consecutive set ( eg 1, 2 , 3, 4 ) or a sequence ( 1, 4,7,10) . In a nutshell, If the difference between any two integers in a sequence is a constant , then it is evenly spaced.

Stmt 1... The middle integer is zero
There are a few example of evenly spaced integers.

-10, -5 , 0 , 5, 10 ... common difference is 5 and the median is 0. The sum is also zero.
2, 1, 0, 1 , 2....common difference is 1 and the median is 0. The sum is also zero.

So 1 is sufficient

Stmt. 2. Exactly 2 of the integers are negative.

Here are examples of set for stmt 2.

-9,-5,0,5,9...Yes its evenly spaced
-10,-2,6,14No its not evely spaced. So it is Insuff.

Last edited by Haaress on Fri Jun 04, 2010 11:04 am, edited 1 time in total.

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krazy800: Master | Next Rank: 500 Posts; Posts: 136; Joined: Sun Sep 28, 2008 8:20 pm; Location: fssf; Thanked: 17 times

by krazy800 » Fri Jun 04, 2010 9:24 am

iikarthik wrote:What is the sum of 5 evenly spaced integers?

1. The middle integer is zero
2. Exactly 2 of the integers are negative

what is an evenly spaced integer? are they consecutive/ consecutive odd or consecutive even / Arithmetic progression series nos.Need assistance to understand this one

OA is A

Thanks
karthik

Evenly spaced integers are in Arithmetic Progression, i.e. with a same common difference.

They could be consecutive even or cosecutive odd numbers or succesive numbers

for example, 0, 2, 4, 6 are consequtive odd integers (evenly spaced - i.e. having a same common difference -2)

for example, 0, 3, 5, 7 are consequtive even integers (evenly spaced - i.e. having a same common difference-2)

Now in the above problem

Statement 1: says middle integers is 0.

therefore, 2 integers will be negative and 2 integers will be positive

to exemplify, consider -2,-1, 0, 1, 2

sum =0

for any set of evenly spaced integers with middle number as 0, the sum is zero. so statement 1- sufficient

Staement 2: Exactly 2 integers are negative. since the numbers are evenly spaced, middle number should be 0. an other two numbers will be positive.

so statement 2 - sufficient.

unless I am missing something OA is D

Aiming High

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Haaress: Master | Next Rank: 500 Posts; Posts: 151; Joined: Thu Apr 22, 2010 4:07 pm; Thanked: 14 times

by Haaress » Fri Jun 04, 2010 9:57 am

@krazy800 ..Statement 2 only states that - Exactly 2 integers are negative. So where is the following extra piece coming from (I guess from info provided in Stmt 1) since the numbers are evenly spaced, middle number should be 0. an other two numbers will be positive. .

Sometime, I guess GMAT strategically place the correct answer in stmt 2 so as to confuse the test takers.

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krazy800: Master | Next Rank: 500 Posts; Posts: 136; Joined: Sun Sep 28, 2008 8:20 pm; Location: fssf; Thanked: 17 times

by krazy800 » Fri Jun 04, 2010 10:06 am

Haaress wrote:@krazy800 ..Statement 2 only states that - Exactly 2 integers are negative. So where is the following extra piece coming from (I guess from info provided in Stmt 1) since the numbers are evenly spaced, middle number should be 0. an other two numbers will be positive. .

Sometime, I guess GMAT strategically place the correct answer in stmt 2 so as to confuse the test takers.

its is given that the 5 numbers are evenly spaced.

In statement 2 its says Exactly two numbers are negative.

The above two statements are leading to the extra piece of info I was getting to.

Now try out any series of numbers that are evenly spaced and that has exactly two negative integers. Probably u will agree with me that statement 2 is sufficient.

Aiming High

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iikarthik: Senior | Next Rank: 100 Posts; Posts: 57; Joined: Sun Jul 06, 2008 10:52 am; Thanked: 1 times; GMAT Score:640

by iikarthik » Fri Jun 04, 2010 10:19 am

krazy800 wrote:
Haaress wrote:@krazy800 ..Statement 2 only states that - Exactly 2 integers are negative. So where is the following extra piece coming from (I guess from info provided in Stmt 1) since the numbers are evenly spaced, middle number should be 0. an other two numbers will be positive. .

Sometime, I guess GMAT strategically place the correct answer in stmt 2 so as to confuse the test takers.
its is given that the 5 numbers are evenly spaced.

In statement 2 its says Exactly two numbers are negative.

The above two statements are leading to the extra piece of info I was getting to.

Now try out any series of numbers that are evenly spaced and that has exactly two negative integers. Probably u will agree with me that statement 2 is sufficient.

Hi,

Thanks for ur inputs.I was of the same opinion till i bumped into this one...

-4,-1,2,5,8,...This is an evenly spaced series with only two negative numbers.

Hope this is correct

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Haaress: Master | Next Rank: 500 Posts; Posts: 151; Joined: Thu Apr 22, 2010 4:07 pm; Thanked: 14 times

by Haaress » Fri Jun 04, 2010 10:21 am

@Krazy800.. its is given that the 5 numbers are evenly spaced. In statement 2 its says Exactly two numbers are negative.

Here is a set that covers both of your stmts below but is still insuff...

-10, -2, 6, 14, 22.... the set is evenly spaced ( with a common diff. of 8)..sum is 30.
-3, -1, 1,3 ,5 is also an evenly spaced set ( with a common diff. of 2).. but the sum is 5.

So, an evenly spaced set with 2 negatives and ZERO as it median always yields a Zero sum and thats why stmt 1. is suff.

I hope this clears any confusion. Please let me know. Thanks!

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krazy800: Master | Next Rank: 500 Posts; Posts: 136; Joined: Sun Sep 28, 2008 8:20 pm; Location: fssf; Thanked: 17 times

by krazy800 » Fri Jun 04, 2010 1:05 pm

Haaress wrote:@Krazy800.. its is given that the 5 numbers are evenly spaced. In statement 2 its says Exactly two numbers are negative.

Here is a set that covers both of your stmts below but is still insuff...

-10, -2, 6, 14, 22.... the set is evenly spaced ( with a common diff. of 8)..sum is 30.
-3, -1, 1,3 ,5 is also an evenly spaced set ( with a common diff. of 2).. but the sum is 5.

So, an evenly spaced set with 2 negatives and ZERO as it median always yields a Zero sum and thats why stmt 1. is suff.

I hope this clears any confusion. Please let me know. Thanks!

@Haaress. agree with you & Thank you! I have overlooked the problem.

Aiming High

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