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# If n is a positive integer and k=5.1 x 10^n , what is the

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If n is a positive integer and k=5.1 x 10^n , what is the [#permalink]  21 May 2011, 09:08
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If n is a positive integer and k=5.1 x 10^n , what is the value of k ?
1. 6000<k<500,000
2. k^2= 2.601 x 10^9.

Please give the answer with explanation.
[Reveal] Spoiler: OA
Senior Manager
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Re: Value of K [#permalink]  21 May 2011, 10:22
k=5.1 x 10^n

Stmt1: 6000<k<500,000
Take n=3
k=5100 but it is not in the interval 6000<k<500,000
Take n=4
k=51000 it is in the interval 6000<k<500,000..Hold on to n=4
Take n=5
k=510,000 again it is not in the interval 6000<k<500,000.
Hence n=4
Sufficient

Stmt2: k^2= 2.601 x 10^9.
Substitute k=5.1 x 10^n in above eqn
(5.1*10^n)^2=2.601*10^9
10^2n=2.601*10^9 / 5.1^2
10^2n=10^9/10
10^2n=10^8
2n=8
n=4
k=5.1*10^4
k=51000
Sufficient.

OA. D
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Re: Value of K [#permalink]  21 May 2011, 13:25
Expert's post
shashankp27 wrote:
If n is a positive integer and k=5.1 x 10^n , what is the value of k ?
1. 6000<k<500,000
2. k^2= 2.601 x 10^9.

Please give the answer with explanation.

Given: k = 5.1 * 10^n
n is a positive integer which means it is at least 1. Hence k's value can be anything from 51 to 5100000000...infinite zeroes

Statement 1: 6,000<k<500,000
So 5,100 is not in this range. 51,000 is in this range. 510,000 is not in this range. Therefore, k must be 51,000. Sufficient.

Statement 2: k^2= 2.601*10^9

k^2 = 2.601 * 10^9 = 2601 * 10^6

Since k is an integer, we are certain that 2601 must be the square of an integer. It is the square of 51.

If k^2 = 2601 * 10^6, k = 51*10^3 OR -51*10^3
Since from the question stem, we know that k must be positive,
k should be 51*10^3 = 51,000. Sufficient.

Answer (D)
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Manager
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Kudos [?]: 12 [0], given: 2

Re: Value of K [#permalink]  21 May 2011, 15:38
Actually , i missed the given fact that k is +ve and considered the -ve value as well for the second statement.
But the Q stem itself says that k=5.1 x 10^n.
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Re: Value of K [#permalink]  21 May 2011, 18:24
Expert's post
shashankp27 wrote:
Actually , i missed the given fact that k is +ve and considered the -ve value as well for the second statement.
But the Q stem itself says that k=5.1 x 10^n.

Yes, for most DS questions, before you move on to the statements, break down the question stem and analyze it properly. It should be very clear in your head what data the stem has given you and what has it asked you.
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Re: Value of K [#permalink]  23 May 2011, 23:27
6000< 51000<500,000 hence n = 4.

k = 26.01^(1/2) * 10^(8/2) = 5.1 * 10^4 n = 4

thus D.
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Re: Value of K [#permalink]  08 Nov 2011, 11:13
Thanks for the great explanation karishma.
I too initially missed the fact that k can only be positive but caught it later on.
Re: Value of K   [#permalink] 08 Nov 2011, 11:13
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