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Is the average of X consecutive numbers odd? (1) The first

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Is the average of X consecutive numbers odd? (1) The first [#permalink] New post 19 Jun 2008, 03:35
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Is the average of X consecutive numbers odd?

(1) The first number in the series is odd.

(2) The sum of the numbers is odd.
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Re: DS-Numbers [#permalink] New post 19 Jun 2008, 05:36
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durgesh79 wrote:
Value wrote:
Is the average of X consecutive numbers odd?

(1) The first number in the series is odd.

(2) The sum of the numbers is odd.


The average of consecutive numbers is nothing but middle number (if X is odd) or average of middle two numbers (if X is even)

Statement 1 : tells nothing about X, set could be, 1,2,3 - Avg = 2 OR just 1,2 - Avg = 1.5
Statement 2 : sum of X consecutive integers = X * Avg
As per statement its Odd.
Odd * Odd = Odd.

So we know both X and Avg should be Odd. Suff.

Answer B.


hi durgesh79,
u said that sum of X consecutive integers = X * Avg correct

(2) The sum of the numbers is odd.

if x=2
i.e even+odd=odd
average is in decimals its not a integer as a result it cannot be odd or even
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Re: DS-Numbers [#permalink] New post 19 Jun 2008, 03:47
Value wrote:
Is the average of X consecutive numbers odd?

(1) The first number in the series is odd.

(2) The sum of the numbers is odd.


ok m no expert at this but i m goin to try


let us say X = 5

and first number is 1 and -1
so average of 5 numbers is 3 and 1

hence statement 1 is sufficent

statement 2 on the other hand is not sufficent because depending upon the starting number the average will either be odd or be in decimals

therefore statement 1 is sufficent and A is the answer
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Re: DS-Numbers [#permalink] New post 19 Jun 2008, 04:02
Value wrote:
Is the average of X consecutive numbers odd?

(1) The first number in the series is odd.

(2) The sum of the numbers is odd.


E for me

1) clearly insuff, consider 3,4 result is fraction, then consider 1,2,3 average is even
2) for sum to be odd there should be odd number of odd numbers in the sequence. 2,3 OR 3,4 result is fraction, -1,0,1,2,3 average is odd. so insuff

together, insuff,
consider sequences in 2 above (3,4)(-1,0,1,2,3)
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Re: DS-Numbers [#permalink] New post 19 Jun 2008, 04:04
i think it is C

for stat 1, try 3,4,5 which gives an even average, or 3,4,5,6 which gives an non-integer average
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Re: DS-Numbers [#permalink] New post 19 Jun 2008, 04:05
Value wrote:
Is the average of X consecutive numbers odd?

(1) The first number in the series is odd.

(2) The sum of the numbers is odd.


The average of consecutive numbers is nothing but middle number (if X is odd) or average of middle two numbers (if X is even)

Statement 1 : tells nothing about X, set could be, 1,2,3 - Avg = 2 OR just 1,2 - Avg = 1.5
Statement 2 : sum of X consecutive integers = X * Avg
As per statement its Odd.
Odd * Odd = Odd.

So we know both X and Avg should be Odd. Suff.

Answer B.
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Re: DS-Numbers [#permalink] New post 19 Jun 2008, 05:54
rohit929 wrote:
hi durgesh79,
u said that sum of X consecutive integers = X * Avg correct

(2) The sum of the numbers is odd.

if x=2
i.e even+odd=odd
average is in decimals its not a integer as a result it cannot be odd or even


My bad..... Thanks for pointing it out Rohit.
+1 to you.
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Re: DS-Numbers [#permalink] New post 19 Jun 2008, 06:51
Ok so this is a Yes/No Q

Statement 1

Even set of terms results in a decimal= NO
Odd set of terms results in an odd or even integer= YES & NO
Therefore is insufficent

Statement 2

odd number of terms results in a odd integer using 1+2+3+4+5/2= ODD= YES maybe
odd number of terms results in a odd integer using 1+2+3+4+5+6+7/2= EVEN= NO maybe
Therefore is insufficent

When I combined them, Still not consistent
19:27=ODD/9=ODD=YES
1:6=ODD/6= decimal= NO

So I go with "E"
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Re: DS-Numbers [#permalink] New post 19 Jun 2008, 07:09
I did a quick chart with the simplest of choices. I will try to sum up the chart without one.

1: Take the odd start to be 1.
X = 1 => odd
X = 2 => (1 + 2)/2 => decimal
Insufficient.

2: Though it may not be suggestible I decided to use above examples so both figuring out if it was B as well as if it was either C or E.
X = 1 => odd
X = 2 => (1 + 2)/2 => decimal
B is Insufficient and because I used examples that started with an odd number both together are also insufficient.

Therefore E is the answer.
Re: DS-Numbers   [#permalink] 19 Jun 2008, 07:09
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