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# Can someone explains this Math to me 1. If S is the sum of

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Can someone explains this Math to me 1. If S is the sum of [#permalink]

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18 Jan 2007, 08:59
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Can someone explains this Math to me

1. If S is the sum of the first n positive integers, what is the value of n ?

(1) S < 20
(2) s^2 > 220

Ans. C
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18 Jan 2007, 10:20
from (1) and (2)

sqrt(220)< S < 20

14.8 < S < 20

sum of the first n positive integers = 1+2+3+4+5 = 15

n =5

Ans =c
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19 Jan 2007, 00:02
S= n(n+1)/2 <20
Possible values of n=1,2,3,4,5 -----------insufficient

S^2 > 220
n=5,6,7, .... upto +infinity ------------ insufficient

n=5 satisfies both.
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19 Jan 2007, 01:02
Can anyone explain where Swagatalakshmi's equation came from?
S= n(n+1)/2 <20

and AK, how did you go from this:
14.8 < S < 20

to this:
sum of the first n positive integers = 1+2+3+4+5 = 15
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19 Jan 2007, 03:50
Let me try
The sum of n +ve integers can be calculated using the formula n*(n+1)/2
For example, 5*6/2=15
1+2+3+4+5=15
S1:s<20 - insuff
S2:15^2 =225, 14^2=196
Since s^2>220 s should be min closer to 15 - insuff
(since < and > has more than one possibility)
Together:
'closer to 15'<s<20 suff
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19 Jan 2007, 22:52
Thanks Sumithra,

One more question. What was the significance of "if S is the sum of the first n positive integers" in the original prob?
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20 Jan 2007, 06:29
Q asks for n and s is the sum of all the integers upto n.
since we are able to find that s is between say 14.8 and 20, we can calculate n:
if n=6, 6*7/2=21 should be s,
since it is little more than the given s, n must be 5
let's try, we just can't assume, s=5*6/2=15 so n=5

20 Jan 2007, 06:29
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