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Is 5^k less than 1,000? (1) 5^(k1) > 3,000 (2) 5^(k1) = [#permalink]
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24 Apr 2007, 07:30
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This topic is locked. If you want to discuss this question please repost it in the respective forum. Is 5^k less than 1,000?
(1) 5^(k1) > 3,000
(2) 5^(k1) = 5^k  500
Hmmm...
I somehow disagree with the OA.



Director
Joined: 14 Jan 2007
Posts: 774

It should be 'D'.
Statement1: 5^(k1) > 3000
Multiplying both sides by 5
5^k > 15000
SUFF
Statement2: 5^(k1) = 5^k  500
5^k  5^(k1) = 500
5^k(1 5^1) = 500
5^k(4/5) = 500
5^k = 2500/4 = 625
so 5^k < 1000
SUFF
So answer is 'D'



Director
Joined: 30 Nov 2006
Posts: 591
Location: Kuwait

Is 5^k less than 1,000?
(1) 5^(k1) > 3,000
5^k x 5^1 > 3,000
5^k > 3,000 x 5
Therefore, 5^k > 15,000
Statement 1 is sufficient
(2) 5^(k1) = 5^k  500
5^k x 5^1 = 5^k  500
5^k = 5(5^k)  2500
5^k  5(5^k) =  2500
4(5^k) = 2500
5^k =  2500/4 = 625
statement 2 is sufficient
Answer: D
What is OA ?



Current Student
Joined: 28 Dec 2004
Posts: 3357
Location: New York City
Schools: Wharton'11 HBS'12

I agree with D...
5^K>1000?
1) 5^k/5>3000; 5^k>15000 suff
2) 5^(k1)  5^k =500
5^(k1)(51)=500
5^(k1) (4)=500; = 2500/4;



Manager
Joined: 28 Aug 2006
Posts: 160

Answer B
Since Statement 1 basically says 5^k/5>3000 which means
(5^k/5) value can be anything from 3001 to infinity as k can take any value not neccessarly an integer value.
From Statement II we get K=4 Hence answer is 4
VJ
Last edited by vijay2001 on 25 Apr 2007, 10:27, edited 3 times in total.



GMAT Club Legend
Joined: 07 Jul 2004
Posts: 5043
Location: Singapore

hmmm.... D?
St1:
5^(k1) > 3000
(5^k)/5 > 3000
5^k > 15,000
Sufficient.
St2:
5^(k1) = 5^k  500
(5^k)/5 = 5^k  500
5^k = 5^k(5)  2500
5^k(51) = 2500
5^k = 625
Sufficient.



Senior Manager
Joined: 01 Jan 2007
Posts: 322

Re: DS  familiar inequality [#permalink]
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24 Apr 2007, 20:22
ricokevin wrote: Is 5^k less than 1,000? (1) 5^(k1) > 3,000 (2) 5^(k1) = 5^k  500 Hmmm... I somehow disagree with the OA.
It always helps to find possible values of 5^k.
5^1=5
5^2=25
5^3=125
5^4=625
5^5=3125.
Statment1>5^(k1) > 3,000 hence k1>5 and hence k>6. So statement 1 is sufficient.
Statement2>5^(k1) = 5^k  500. The only value of k that will satisfy this equation is k=4 and hence this statement is also sufficient.
Answere D.
Javed.
Cheers!



Senior Manager
Joined: 11 Feb 2007
Posts: 351

The OA is B. Congratz vijay2001!
I too thought D was the answer.
This problem is insidious.



Senior Manager
Joined: 28 Aug 2006
Posts: 304

First statement is not sufficient .....for one simple reason that k need not be integer.
So 1 is not sufficient
Clearly 2 is sufficient
So B
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Director
Joined: 13 Mar 2007
Posts: 543
Schools: MIT Sloan

cicerone, can you explain the reasoning?
irrespective of whether k is an integer,
from st1,
5^k/5 > 3000,
5 is +ve, hence we can multiply both sides of inequality by 5 without altering the sign
=> 5^k > 3000 x 5 , which clearly indicates that 5^k is not lesser than 1000
What is it that I am missing here ?



Director
Joined: 29 Aug 2005
Posts: 860

I dont see why Statement 1 can't be sufficient.
5^k >15000
all we are interested in is whether 5^k<1000
What is the source of this q?
If someone thinks that it should be B, can you please explain why?



Manager
Joined: 28 Aug 2006
Posts: 160

Guys See my edited post above. Hope this helps.



Director
Joined: 13 Mar 2007
Posts: 543
Schools: MIT Sloan

well. i still dont get it ..
we are interested in 5^k alone and not (5^k/5),
from st1, 5^k > 3000 x 5
so when the above is GIVEN, is there any possibility at all  whatever the value of k, for 5^k < 1000 ??



Current Student
Joined: 22 Apr 2007
Posts: 1097

vijay2001 wrote: Guys See my edited post above. Hope this helps.
Vijay, your explanation is still not clear. I am also finding it difficult to believe that if (5^k)/5 > 3000, then that's not sufficient to say that 5^k can, in any case, be less than 1000



Manager
Joined: 28 Aug 2006
Posts: 160

OK may be this example helps
Let say k=0.999 so k1= 0.0001 => 1/5^0.0001, which will be a very big number possibilly greater than 3000. Which satisfies the condition (5^(k1))>3000 but will not satisfy that that 5^k >1000



Intern
Joined: 14 Aug 2006
Posts: 26

Vijay
(1 / 5)^.0001 = 0.999839069
which does not satisfies statement 1 itself...
where am I going wrng...please explain...



Intern
Joined: 14 Aug 2006
Posts: 26

Hi Fig,
I am still getting ans as D . Please can you help on this.
Thanks



Intern
Joined: 05 Jun 2003
Posts: 48

PPGJ wrote: Hi Fig, I am still getting ans as D . Please can you help on this. Thanks
I don't understand either. If Stmt 1 asserts that 5^k > 15,000, then how can 5^k be less than 1,000 at the same time? So I think Stmt 1 is SUFF.
Unless we're missing some information from the question.



Intern
Joined: 14 Aug 2006
Posts: 26

Hello Vijay,
Please can you explain....



Manager
Joined: 18 Apr 2007
Posts: 120

The first thing I noticed when I finished this problem is that stmt 1 and stmt 2 contradict each other. Stmt one clearly comes out to 5^k>15000, but stmt 2 clearly comes out to 5^k=625. You can't have 5^k both greater than 3000 AND less than 1000.
Anyway, I'm confused by the reasoning for B as well, although vijay's example helps.
I agree, a poorly structured question.







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