test 13 #20

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dunkin77: Master | Next Rank: 500 Posts; Posts: 269; Joined: Sun Apr 01, 2007 5:41 am

test 13 #20

by dunkin77 » Mon Apr 23, 2007 2:36 pm

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

(1) S < 20
(2) s2 > 220

Hi,

The answer is C) but I can't figure out why it's C)... Can anyone help pls?

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Source: Beat The GMAT — Data Sufficiency | Mon Apr 23, 2007 2:36 pm

sanju438: Newbie | Next Rank: 10 Posts; Posts: 5; Joined: Tue Sep 05, 2006 9:33 pm

by sanju438 » Wed Oct 01, 2008 1:07 pm

S = n(n+1)/2
(1) S < 20. Insufficient. n can be 1, 2 etc
(2) S^2 > 220. Insufficient . n can be 6, 7, etc

Taking (1) and (2) together, only n = 5 is possible. Sufficient

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raju232007: Master | Next Rank: 500 Posts; Posts: 133; Joined: Sat Dec 29, 2007 2:43 am; Thanked: 12 times

by raju232007 » Fri Oct 03, 2008 9:26 am

But it is given that S is the sum of first n natural numbers....so as per the first statement S<20
This is possible only when n=5 (i.e 1+2+3+4+5)
if n=6 S becomes 21...so th only solution is n=5

if u consider the second statement S can be anything(i.e S>14.5)
so n can be 5,6,78 etc...

So I think the ans should be A..Correct me if i am wrong..

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Morgoth: Master | Next Rank: 500 Posts; Posts: 316; Joined: Mon Sep 22, 2008 12:04 am; Thanked: 36 times; Followed by:1 members

by Morgoth » Fri Oct 03, 2008 9:35 am

raju232007 wrote:But it is given that S is the sum of first n natural numbers....so as per the first statement S<20
This is possible only when n=5 (i.e 1+2+3+4+5)
if n=6 S becomes 21...so th only solution is n=5

if u consider the second statement S can be anything(i.e S>14.5)
so n can be 5,6,78 etc...

So I think the ans should be A..Correct me if i am wrong..

First statement is insufficient.

if n=2
S = 2+1 = 3 <20

if n=3
S=1+2+3=6 <20

if n=4
S=1+2+3+4=10 <20

if n=5
S=1+2+3+4+5=15 <20

therefore, 0 < n < 6. Insufficient.

Hope this helps.