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If x is the sum of n consecutive positive integers, and n>2, is n divi

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If x is the sum of n consecutive positive integers, and n>2, is n divi  [#permalink]

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New post 19 Sep 2016, 05:38
1
14
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A
B
C
D
E

Difficulty:

  85% (hard)

Question Stats:

48% (01:58) correct 52% (02:34) wrong based on 262 sessions

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Re: If x is the sum of n consecutive positive integers, and n>2, is n divi  [#permalink]

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New post 19 Sep 2016, 06:04
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Bunuel wrote:
If x is the sum of n consecutive positive integers, and n>2, is n divisible by 4?

(1) The smallest number among the consecutive integers is even.

(2) x is odd.


NOTE : • If n is odd, the sum of n consecutive integers is always divisible by n. Given {9,10,11}{9,10,11}, we have n=3=oddn=3=odd consecutive integers. The sum is 9+10+11=30, which is divisible by 3.

• If n is even, the sum of n consecutive integers is never divisible by n. Given {9,10,11,12}{9,10,11,12}, we have n=4=evenn=4=even consecutive integers. The sum is 9+10+11+12=42, which is NOT divisible by 4.



Stat 1: We are not sure whether we have odd number of number or even number of numbers..Insufficient.

Stat 2: we have clear information that we have odd number of numbers in the series...as it is given n > 2..let's take 4,5,6 or 2,3,4 not divisible by 4..Sufficient.

IMO option B.
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Re: If x is the sum of n consecutive positive integers, and n>2, is n divi  [#permalink]

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New post 19 Sep 2016, 06:20
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In 2nd statement it is given that x is odd ,it does not give info about n as n can be 4 or any other number say n=6 (2,3,4,5,6,7) in this x is odd x=27 but n is not divisible by 4.
i think the answer is E. :idea:
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Re: If x is the sum of n consecutive positive integers, and n>2, is n divi  [#permalink]

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New post 20 Sep 2016, 01:37
Devesh29 wrote:
In 2nd statement it is given that x is odd ,it does not give info about n as n can be 4 or any other number say n=6 (2,3,4,5,6,7) in this x is odd x=27 but n is not divisible by 4.
i think the answer is E. :idea:


n will be divisible by 4 only if n is a multiple of 4.

So, I believe n being the multiple of 4, we will always get x as even. So, B should be sufficient.
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Re: If x is the sum of n consecutive positive integers, and n>2, is n divi  [#permalink]

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New post 20 Sep 2016, 05:32
(1) The smallest number among the consecutive integers is even.

We do not know total elements in the Set.

{4,5,6} -- Not divisible by 4.
(4,5,6,7} -- Divisible by 4

--Not sufficient.

(2) x is odd.

Even + Even = Even
Odd + Odd = Even
Even + Odd = Odd


So, for sum of X to be odd. n should be odd. --Sufficient.

Ans. B
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If x is the sum of n consecutive positive integers, and n>2, is n divi  [#permalink]

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New post 20 Sep 2016, 14:11
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IMO answer is B

Statement 1 n could be anything as long as it starts with an even number. So Insufficient
Statement 2 so lets start 1,2,3,4,5,6,7,8
1+2 = 3 odd n=2
3+3 = 6 even n=3
6+4 = 10 even n=4
10+5 = 15 odd n=5
15+6 = 21 Odd n = 6
21+7 = 28 Even n =7
28+ 8 = 36 Even n= 8
36 + 9 = 45 n=9 Odd
45+10 = 55 n =10 Odd



So whenever X is odd n is not divisible by 4 Sufficient
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Re: If x is the sum of n consecutive positive integers, and n>2, is n divi  [#permalink]

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New post 20 Sep 2016, 14:27
Answer is E. 4+5+6 is not divisible by 4. Also, 2+3+4 is odd and 3 is not divisible by 4.


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Re: If x is the sum of n consecutive positive integers, and n>2, is n divi  [#permalink]

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New post 20 Sep 2016, 18:53
ProfX wrote:
Answer is E. 4+5+6 is not divisible by 4. Also, 2+3+4 is odd and 3 is not divisible by 4.


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(2) x is odd.

4+5+6 is not divisible by 4. Also, 2+3+4 is odd and 3 is not divisible by 4

We need to consider data set, whose sum of elements is odd. For option 2, we should not consider {4,5,6} but {2,3,4}
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If x is the sum of n consecutive positive integers, and n>2, is n divi  [#permalink]

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New post 22 Sep 2016, 05:44
Question is basically asking is the number of terms in the set even and multiple of 4

Statement 1 : says nothing about the number of terms
statement 2 : says that the sum of all terms in odd. which can be deduced to there are unequal odd and even terms in the list. For the sum to be even, equal number of odd and even numbers should be present. So in any case n is multiple of 4

I go with B
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If x is the sum of n consecutive positive integers, and n>2, is n divi  [#permalink]

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New post 24 Feb 2017, 03:09
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Prompt analysis
Let the numbers be a, a+1, a+2….a+n-1
x = na +n(n-1)/2

Superset
The answer will be either yes or no

Translation
In order to find the answer, we need:
1# the exact value of n
2# exact value of a and x
3# some other properties of n, a and x

Statement analysis
St 1: a is even. Cannot say anything about x and n. INSUFFICIENT
St 2: x is odd. That mean n x a is odd. That means n is odd. So it cannot be divisible by 4. ANSWER.

Option B
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Re: If x is the sum of n consecutive positive integers, and n>2, is n divi  [#permalink]

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New post 05 Apr 2018, 08:24
Should it be "is X divisible by 4?"

If it's, "is n divisible by 4?", and n represents the number of consecutive numbers, then I could say n=4 which means any 4 consecutive numbers??
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Re: If x is the sum of n consecutive positive integers, and n>2, is n divi  [#permalink]

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New post 23 Aug 2018, 18:58
msk0657 wrote:
Bunuel wrote:
If x is the sum of n consecutive positive integers, and n>2, is n divisible by 4?

(1) The smallest number among the consecutive integers is even.

(2) x is odd.


NOTE : • If n is odd, the sum of n consecutive integers is always divisible by n. Given {9,10,11}{9,10,11}, we have n=3=oddn=3=odd consecutive integers. The sum is 9+10+11=30, which is divisible by 3.

• If n is even, the sum of n consecutive integers is never divisible by n. Given {9,10,11,12}{9,10,11,12}, we have n=4=evenn=4=even consecutive integers. The sum is 9+10+11+12=42, which is NOT divisible by 4.



Stat 1: We are not sure whether we have odd number of number or even number of numbers..Insufficient.

Stat 2: we have clear information that we have odd number of numbers in the series...as it is given n > 2..let's take 4,5,6 or 2,3,4 not divisible by 4..Sufficient.

IMO option B.

although I couldn't challenge the OA, i don't agree with Stat 2. We cannot conclude n is even or odd
it can be 5 odd + 5 even:
eoeoeoeoeo
it can be eoe:
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Re: If x is the sum of n consecutive positive integers, and n>2, is n divi  [#permalink]

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New post 23 Aug 2018, 19:10
for statement 1:
2,3,4,5,6
5 not divisible by 4
2,3,4,5,6,7,8,9
8 divisible by 4
clearly insufficient
for statement 2:
x=n*(a1+an)/2
if n is odd, n is not divisible by 4
if n is even,
since x is odd, n/2 must be odd and a1+an must be odd (one odd, one even).
n/2 can be expressed as 2k+1(k is int), n=4k+2. hence n not divisible by 4 (remainder is always 2)
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Re: If x is the sum of n consecutive positive integers, and n>2, is n divi  [#permalink]

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New post 08 Oct 2018, 18:26
sum of integers = x = n*average.


(1). Clearly insufficient.
(2). If x is odd, then n*average is odd. If n*average is odd, n cannot be even, and must be odd. Thus n cannot be divisible by 4.
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Re: If x is the sum of n consecutive positive integers, and n>2, is n divi   [#permalink] 08 Oct 2018, 18:26
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