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# If n > 0, which is greater, 20 percent of n or 10 percent

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Manager
Joined: 25 Mar 2008
Posts: 106
Followers: 1

Kudos [?]: 11 [0], given: 0

If n > 0, which is greater, 20 percent of n or 10 percent [#permalink]  12 Apr 2008, 11:49
If n > 0, which is greater, 20 percent of n or 10 percent of the sum of n and 0.5 ?

(1) n < 0.1

(2) n > 0.01

i dont know the oa
Director
Joined: 10 Sep 2007
Posts: 949
Followers: 7

Kudos [?]: 205 [0], given: 0

Re: integer [#permalink]  12 Apr 2008, 14:13
Very first thing in this question you should do is to pre-phrase the question.
Original question says which is greater, 20 percent of n or 10 percent of the sum of n and 0.5 ?
So first numerically denote 20 percent of n and 10 percent of the sum of n and 0.5.
20 percent of n = n*20/100 = 0.2n
10 percent of the sum of n and 0.5 = n*10/100 + 0.5 = .1n + 0.5

We need to see if 0.2n > .1n + 0.5
Or .1n > .5
Or n > 5 (I did not reverse the sign of inequality as all the terms involved are +ve)

Now go to the statements.

Statement 1:
Tells us n < 0.1, so n is not greater than 5 and question is answered negatively.

Statement 2:
Tells us n > 0.01, but it does not gives us exact value of n. So n can any value less than, more than 5 or even 5 itself. So this statement alone is insufficient.

SVP
Joined: 28 Dec 2005
Posts: 1583
Followers: 2

Kudos [?]: 88 [0], given: 2

Re: integer [#permalink]  12 Apr 2008, 16:20
same approach as above to get A
Manager
Joined: 16 Sep 2007
Posts: 215
Followers: 1

Kudos [?]: 11 [0], given: 0

Re: integer [#permalink]  12 Apr 2008, 20:18
alternative method:

1)
.1>n>0
estimate using boundary conditions:
.1*.2=.02 and (.1+.5)*.1=.06
second case larger
0*.2=0 and (0+.5)*.1=.05
second case larger
Therefore 10% of (n+.5) I estimate is always larger. Therefore 1 passes

2)
n>.01
estimate using boundary conditions (let infinity = 100)
(.01)*.2=.002 and (.01+.5)*.1=.051
second case larger
(100)*.2=20 and (100+.5)*.1=10.05
first case larger
No agreement. Therefore 2 does not pass.

Re: integer   [#permalink] 12 Apr 2008, 20:18
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