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# Is 5^k less than 1,000? (1) 5^(k-1) > 3,000 (2) 5^(k-1) =

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Is 5^k less than 1,000? (1) 5^(k-1) > 3,000 (2) 5^(k-1) = [#permalink]

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24 Apr 2007, 07:30
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Is 5^k less than 1,000?

(1) 5^(k-1) > 3,000

(2) 5^(k-1) = 5^k - 500

Hmmm...

I somehow disagree with the OA.

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Director
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24 Apr 2007, 08:23
It should be 'D'.

Statement1: 5^(k-1) > 3000
Multiplying both sides by 5
5^k > 15000
SUFF

Statement2: 5^(k-1) = 5^k - 500
5^k - 5^(k-1) = 500
5^k(1- 5^-1) = 500
5^k(4/5) = 500
5^k = 2500/4 = 625
so 5^k < 1000
SUFF

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24 Apr 2007, 09:58
Is 5^k less than 1,000?

(1) 5^(k-1) > 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^(k-1) = 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

What is OA ?

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24 Apr 2007, 12:04
I agree with D...

5^K>1000?

1) 5^k/5>3000; 5^k>15000 suff

2) 5^(k-1) - 5^k =500

5^(k-1)(5-1)=500

5^(k-1) (4)=500; = 2500/4;

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24 Apr 2007, 18:24

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.

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24 Apr 2007, 19:56
hmmm.... D?
St1:
5^(k-1) > 3000
(5^k)/5 > 3000
5^k > 15,000

Sufficient.

St2:
5^(k-1) = 5^k - 500
(5^k)/5 = 5^k - 500
5^k = 5^k(5) - 2500
5^k(5-1) = 2500
5^k = 625
Sufficient.

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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^(k-1) > 3,000

(2) 5^(k-1) = 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^(k-1) > 3,000 hence k-1>5 and hence k>6. So statement 1 is sufficient.

Statement2->5^(k-1) = 5^k - 500. The only value of k that will satisfy this equation is k=4 and hence this statement is also sufficient.

Javed.

Cheers!

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24 Apr 2007, 21:58
The OA is B. Congratz vijay2001!

I too thought D was the answer.

This problem is insidious.

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24 Apr 2007, 23:03
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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25 Apr 2007, 00:09
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 ?

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25 Apr 2007, 00:14
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?

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25 Apr 2007, 10:24
Guys See my edited post above. Hope this helps.

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25 Apr 2007, 12:00
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 ??

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25 Apr 2007, 12:28
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

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25 Apr 2007, 20:35
OK- may be this example helps

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

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01 May 2007, 10:35
Vijay

(1 / 5)^.0001 = 0.999839069

which does not satisfies statement 1 itself...

where am I going wrng...please explain...

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01 May 2007, 10:44
Hi Fig,

I am still getting ans as D . Please can you help on this.

Thanks

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01 May 2007, 11:26
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.

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04 May 2007, 12:18
Hello Vijay,

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04 May 2007, 13:44
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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04 May 2007, 13:44

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