If n is a positive integer and k=5.1*10^n, what is the value : GMAT Data Sufficiency (DS)
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If n is a positive integer and k=5.1*10^n, what is the value

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If n is a positive integer and k=5.1*10^n, what is the value [#permalink]

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If n is a positive integer and k=5.1*10^n, what is the value of k?

(1) 6,000 < k < 500,000
(2) k^2 = 2.601 * 10^9

OPEN DISCUSSION OF THIS QUESTION IS HERE: if-n-is-a-positive-integer-and-k-5-1-10-n-what-is-the-value-126370.html
[Reveal] Spoiler: OA
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Re: Value of K [#permalink]

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New post 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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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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New post 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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New post 21 May 2011, 18:24
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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]

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New post 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]

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New post 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.
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Re: If n is a positive integer and k=5.1 x 10^n , what is the [#permalink]

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New post 20 May 2014, 02:44
Thanks for the explanation Karishma. I fell into to the trap of considering negative value in second st too. :(
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Re: If n is a positive integer and k=5.1*10^n, what is the value [#permalink]

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If n is a positive integer and k=5.1*10^n, what is the value of k?

As n is a positive integer then k could be: 51, 510, 5,100, 51,000, ... Also note that no matter the value of n, k is always a positive number.

(1) 6,000 < k < 500,000 --> only one number from above is in this range: 51,000. Sufficient.

(2) k^2 = 2.601 * 10^9 --> we can solve quadratics to get two values of k positive and negative, but since given that k is positive then only the positive value of k will be valid. Sufficient.

Answer: D.

OPEN DISCUSSION OF THIS QUESTION IS HERE: if-n-is-a-positive-integer-and-k-5-1-10-n-what-is-the-value-126370.html
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Re: If n is a positive integer and k=5.1*10^n, what is the value   [#permalink] 20 May 2014, 03:15
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