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# Tricky DS Question - Can't understand why it's sufficient

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Intern
Joined: 28 Jun 2009
Posts: 9
Tricky DS Question - Can't understand why it's sufficient [#permalink]

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25 Jul 2009, 07:29
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Hi there, can someone help me with this question (OG DS 144)

If n is a positive integer, is (1/10)^n < 0.01?
I. n > 2
II. (1 / 10)^(n-1) < 0.1

First, I check that if n=3, then (1/10)^n = 1/1000 = 0.001 < 0.01 (holds for all n >2) - SUFFICIENT.

Second, check II.

If n = 1, then (1/10)^(1-1) = 1 => Not < 0.1 (false)
If n = 2, then (1/10)^(2-1) = 0.1 => Not < 0.1 (false)
If n = 3, then (1/10)^(3-1) = 0.01 => < 0.1 (true)

So in this case, wouldn't it be NOT SUFFICIENT, since n can be any positive integer and would not conclusively indicate whether the inequality was true or false.

In this case, the answer key says D. Both are sufficient. Can someone explain this to me?

Thanks,
Senior Manager
Joined: 18 Jun 2009
Posts: 351
Location: San Francisco
Re: Tricky DS Question - Can't understand why it's sufficient [#permalink]

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25 Jul 2009, 08:34
You are confused between question and the stm2)

From stmt2 we should pick up a value for n which satisfies stmt2)

The question is not asking you to prove stmt2). It says stmt2 s already true so for what cases of n is stmt2 true ?

If n = 3, then (1/10)^(3-1) = 0.01 => < 0.1 (true)
If n = 4, then (1/10)^(4-1) = 0.001 => < 0.1 (true)

in other words for n >=3 we have stmt2 true so substituting n>=3 in the question "is (1/10)^n < 0.01"

yes it is true in all cases of n >= 3 ... therefore 2 is suff

Intern
Joined: 28 Jun 2009
Posts: 9
Re: Tricky DS Question - Can't understand why it's sufficient [#permalink]

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25 Jul 2009, 10:27
Thanks. I understand now. Sometimes I get caught up/confused with the question and just need someone to point it out to me.

These inequality questions can be very tricky! Especially those where the question stem and the statements are both inequalities! Any tips for those types of questions?
Retired Moderator
Joined: 05 Jul 2006
Posts: 1741
Re: Tricky DS Question - Can't understand why it's sufficient [#permalink]

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25 Jul 2009, 13:28
Hi there, can someone help me with this question (OG DS 144)

If n is a positive integer, is (1/10)^n < 0.01?
I. n > 2
II. (1 / 10)^(n-1) < 0.1

is 10^-n< 10^-2

ie: is -n<-2 ie: is n>2

from 1 ...........suff

from 2

1-n<-2 ie: -n<-3 ie: n>3........suff

D
Re: Tricky DS Question - Can't understand why it's sufficient   [#permalink] 25 Jul 2009, 13:28
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