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If S is the sum of the first n positive integers, what is

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If S is the sum of the first n positive integers, what is [#permalink] New post 10 Apr 2006, 19:12
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If S is the sum of the first n positive integers, what is the value of n?

1) S < 20
2) Sqr(S) > 220
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 [#permalink] New post 10 Apr 2006, 19:52
'C' it is.

1) S < 20 + 2) Sqr(S) > 220
give us S = 15,16,17,18 or 19
as first positive integers ar 1,2,3 etc. so
1+2+3+4+5=15 enough.
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 [#permalink] New post 10 Apr 2006, 22:10
Anwwr is C;


Sum (S) = (n/2) * n = (n^2)/2

From 1:
S <20

so n can be 1, 2, 3, 4, 5

From 2:
S>220

so n can be 5, 6, 7, ....

From 1 and 2:

The only overlapp is 5!

Hence C.

Last edited by sm176811 on 11 Apr 2006, 08:03, edited 1 time in total.
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 [#permalink] New post 11 Apr 2006, 02:35
can someone explain how the answer is "C" I still do not understand how you arrived at this answer I understand statement one

1+2+3+4+5=15 which is less than 20

but statement 2 is that Sqr(s) or S >220?
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 [#permalink] New post 11 Apr 2006, 08:08
YEah the common term shud be 5.. See updated post above!
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 [#permalink] New post 11 Apr 2006, 09:07
M8 wrote:
rhyme wrote:
Can someone reply to my question directly above this post please? Its been bugging me all night.


Look up at my answer. n=5. (1,2,3,4,5) - five intigers.


I mean as the sum of the first five intigers = 15 (1+2+3+4+5).
1) 15<20.
2) 15^2 (Sqr15) = 225 which is > 220.
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 [#permalink] New post 11 Apr 2006, 18:30
Hi rhyme, you're right, I made a mistake, statement 2 is S^2. And thanks for the explanation.

rhyme wrote:
Thats not possible.

I dont believe the GMAT ever makes questions where statements 1 and 2 contradict each other.

That is, if S < 20
then the sqr(S) CANNOT be greater than 220

Did you mean S^2 ?

Assuming so...

As for statement (1)

If S<20

n could be the first 3 positive integers, 1,2,3, or the first four, 1,2,3,4, or the first five 1,2,3,4,5 but not the first six 1,2,3,4,5,6 (that would be 21)

So (1) insuff.

As for statement 2,

that means that S could be some big #, 21, 15

again, that means n could be... 5 (1,2,3,4,5) or 1,2,3,4,5,6 or a bunch of other possibilities

so (2) insufficient

Assuming both are true,

S could be some big number, 21, 15 meaning n could be 5, 6 or some number more than that

but ... from statement 1 we know n can be 1,2,3,4,5 but not 6.

overlap is 5

hence C.
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 [#permalink] New post 11 Apr 2006, 18:34
john2005 wrote:
Hi rhyme, you're right, I made a mistake, statement 2 is S^2. And thanks for the explanation.


Do you mean that S^2 and SqrS are not the same?
  [#permalink] 11 Apr 2006, 18:34
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