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# The sum of n consecutive positive integers is 45. What is

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The sum of n consecutive positive integers is 45. What is [#permalink]

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31 Jan 2012, 17:42
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The sum of n consecutive positive integers is 45. What is the value of n?

(1) n is even
(2) n < 9
[Reveal] Spoiler: OA

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Last edited by Bunuel on 12 Jun 2013, 03:33, edited 2 times in total.
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31 Jan 2012, 17:55
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enigma123 wrote:
The sum of n consecutive positive integers is 45. What is the value of n?
(1) n is even
(2) n < 9

For me its C. Any thoughts guys?

The sum of n consecutive positive integers is 45. What is the value of n?

(1) n is even --> n can be 2: 22+23=45. But it also can be 6 --> x+(x+1)+(x+2)+(x+3)+(x+4)+(x+5)=45 --> x=5. At least two values of n are possible. Not sufficient.

(2) n<9 --> the above example is also valid for this statement, hence not sufficient.

(1)+(2) Still at least two values of n are possible. Not sufficient.

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Re: The sum of n consecutive positive integers is 45. What is [#permalink]

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23 Sep 2012, 22:51
Bunuel

my question is hovv do you knovv vvhere to stop there could have been an 8 too
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Re: The sum of n consecutive positive integers is 45. What is [#permalink]

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24 Sep 2012, 04:12
Expert's post
venmic wrote:
Bunuel

my question is hovv do you knovv vvhere to stop there could have been an 8 too

When a DS question asks about the value of some variable, then the statement(s) is sufficient ONLY if you can get the single numerical value of this variable.

Now, when we consider the two statements together we have that n can be 2 or 6, so we don't have single numerical value of n, which means that the answer is E. We don't need to find whether n can be some other number, since two values are enough to tell that the statements taken together are not sufficient.

Hope it's clear.
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Re: The sum of n consecutive positive integers is 45. What is [#permalink]

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24 Sep 2012, 08:30
The sum of n consecutive positive integers is 45. What is the value of n?
(1) n is even
(2) n < 9

First the quick maths.... consecutive numbers added together to make 45..
N + N+1 + N+2 all the way to N +i

The quickest way for me was to disprove both.

With two numbers N + N + 1 = 45 so 2n + 1 = 45, 2n = 44 n = 22 (2 numbers)
With six numbers 6N + 15 = 45, 6N=30 N=5 (6 numbers)

Even if we take both 1 and 2, n could be 2 or 6. Therefore E
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Re: The sum of n consecutive positive integers is 45. What is [#permalink]

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06 Oct 2012, 05:52
Bunuel wrote:
venmic wrote:
Bunuel

my question is hovv do you knovv vvhere to stop there could have been an 8 too

When a DS question asks about the value of some variable, then the statement(s) is sufficient ONLY if you can get the single numerical value of this variable.

Now, when we consider the two statements together we have that n can be 2 or 6, so we don't have single numerical value of n, which means that the answer is E. We don't need to find whether n can be some other number, since two values are enough to tell that the statements taken together are not sufficient.

Hope it's clear.

Hey Bunuel,

The sum of n consecutive numbers is n (n+1)/2=45
Therefore- n(n+1)=90
...> n^2+n-90=0
....> n-9=0 or n=-10

so both 1 and 2 are sufficient to answer. So the answer must be D right??
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Re: The sum of n consecutive positive integers is 45. What is [#permalink]

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06 Oct 2012, 08:09
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rajathpanta wrote:
Bunuel wrote:
venmic wrote:
Bunuel

my question is hovv do you knovv vvhere to stop there could have been an 8 too

When a DS question asks about the value of some variable, then the statement(s) is sufficient ONLY if you can get the single numerical value of this variable.

Now, when we consider the two statements together we have that n can be 2 or 6, so we don't have single numerical value of n, which means that the answer is E. We don't need to find whether n can be some other number, since two values are enough to tell that the statements taken together are not sufficient.

Hope it's clear.

Hey Bunuel,

The sum of n consecutive numbers is n (n+1)/2=45
Therefore- n(n+1)=90
...> n^2+n-90=0
....> n-9=0 or n=-10

so both 1 and 2 are sufficient to answer. So the answer must be D right??

The sum of n consecutive numbers is n (n+1)/2=45 NO
The sum of the first n consecutive positive integers 1, 2, 3,..., n is n(n + 1)/2.
Nowhere is stated that we have some number of the first positive integers.
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Re: The sum of n consecutive positive integers is 45. What is [#permalink]

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06 Oct 2012, 09:20
Thanks EVa... got it
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The sum of n consecutive positive integers is 45 [#permalink]

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18 May 2013, 23:50
The sum of n consecutive positive integers is 45. What is the value of n?

(1) n is even

(2) n < 9

Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.
Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.
Both statements TOGETHER are sufficient, but NEITHER one ALONE is sufficient.
EACH statement ALONE is sufficient.
Statements (1) and (2) TOGETHER are NOT sufficient.

Hi Everyone this problem is from Manhattan Practise test 4. This problem looked very simple to me but I am stuck with it. Despite looking at the explanation which is long and hard to understand, I couldn't understand what so ever. However while I was giving exam I thought that there is a formula for the sum of n consecutive positive integers which is n(n+1)/2 and this problem could be solved easily. But that doesn't apply to this problem. Can someone please help me with this.

OA is E.

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Re: The sum of n consecutive positive integers is 45 [#permalink]

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19 May 2013, 00:06
Hi tk1tez7777

The sum of n consecutive integers is 45.

one simple short cut:- as the numbers are consecutive look for the numbers around 45/n

statement 1:- for n = 2 (22 and 23) we will get the sum as 45
for n = 6 (5,6,7,8,9,10) we will get sum as 45

So we cannot decide the value of n. Statement 1 alone is not sufficient.

statement 2:- n>9.

For both n = 2 and n = 6 the sum of the numbers is 45.

So statement 2 alone is not sufficient.

Combining both statements n<9 and n is even.

Again for both n = 2 and n=3 the sum is 45 so combined they are not sufficient.

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Re: The sum of n consecutive positive integers is 45 [#permalink]

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19 May 2013, 00:34
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tk1tez7777 wrote:
The sum of n consecutive positive integers is 45. What is the value of n?

(1) n is even

(2) n < 9

Let the first term be a, which is a positive integer. Thus, given that$$\frac{n}{2}[2a+(n-1)]$$ = 45

From F.S 1, we know that n=even, thus 2a+(n-1) = even+odd=odd.

Thus,$$\frac{n}{2}*odd$$ =$$\frac{10}{2}*9$$. It could also be =$$\frac{6}{2}*15$$
Insufficient.

From F.S 2, we know that n<9. Thus, $$\frac{90}{n}$$ must be an integer.We have n=1 or 2 or 3 or 5 or 6.Insufficient.
Taking both together , we have n = 2 or 6. Insufficient.
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Re: The sum of n consecutive positive integers is 45 [#permalink]

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19 May 2013, 03:18
Expert's post
tk1tez7777 wrote:
The sum of n consecutive positive integers is 45. What is the value of n?

(1) n is even

(2) n < 9

Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.
Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.
Both statements TOGETHER are sufficient, but NEITHER one ALONE is sufficient.
EACH statement ALONE is sufficient.
Statements (1) and (2) TOGETHER are NOT sufficient.

Hi Everyone this problem is from Manhattan Practise test 4. This problem looked very simple to me but I am stuck with it. Despite looking at the explanation which is long and hard to understand, I couldn't understand what so ever. However while I was giving exam I thought that there is a formula for the sum of n consecutive positive integers which is n(n+1)/2 and this problem could be solved easily. But that doesn't apply to this problem. Can someone please help me with this.

OA is E.

Merging similar topics. Please refer to the solutions above.
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Re: The sum of n consecutive positive integers is 45. What is [#permalink]

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Re: The sum of n consecutive positive integers is 45. What is [#permalink]

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Re: The sum of n consecutive positive integers is 45. What is   [#permalink] 08 Apr 2016, 05:41
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