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Senior Manager  S
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If n is a positive integer and k = 5.1 x 10^n , what is the  [#permalink]

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

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

_________________

Originally posted by Baten80 on 09 Mar 2011, 07:52.
Last edited by Bunuel on 18 Dec 2012, 08:21, edited 2 times in total.
Renamed the topic and edited the question.
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Posts: 58340
Re: Arithmetic properties  [#permalink]

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Baten80 wrote:
If n is a positive integer and k = 5.1 x^n , what is the value of k ?
(1) 6,000 < k < 500,000
(2) k^2 = 2.601 * 10^9

I understand the official explanation. is there any other easy way?

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.

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Senior Manager  S
Status: No dream is too large, no dreamer is too small
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Re: Arithmetic properties  [#permalink]

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Bunuel wrote:
Baten80 wrote:
If n is a positive integer and k = 5.1 x^n , what is the value of k ?
(1) 6,000 < k < 500,000
(2) k^2 = 2.601 * 10^9

I understand the official explanation. is there any other easy way?

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.

I corrected the original post.
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If n is a positive integer and k = 5.1 x 10^n , what is the valu  [#permalink]

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Actually the answer D is correct.

Allow me to explain. As n is a positive integer. The values of k will be

n=1 --> 51
n+2 --> 510
n+3 --> 5,100
n+4 --> 51,000
n+5 --> 510,000

The inequality,although very wide,tells us about the only possible value of k which is 51,000. As 5100 is less than 6000 and 510,000 is more than 500,000.

Statement B is sufficient on its own. Should give a positive and negative value of K. But the question stem tells us that K is positive.

Hope this helps
Intern  Joined: 13 Dec 2015
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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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Bunuel wrote:
Baten80 wrote:
If n is a positive integer and k = 5.1 x^n , what is the value of k ?
(1) 6,000 < k < 500,000
(2) k^2 = 2.601 * 10^9

I understand the official explanation. is there any other easy way?

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.

could you please explain the solution of statement 2
Math Expert V
Joined: 02 Sep 2009
Posts: 58340
Re: If n is a positive integer and k = 5.1 x 10^n , what is the  [#permalink]

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Maruf Iqbal wrote:
Bunuel wrote:
Baten80 wrote:
If n is a positive integer and k = 5.1 x^n , what is the value of k ?
(1) 6,000 < k < 500,000
(2) k^2 = 2.601 * 10^9

I understand the official explanation. is there any other easy way?

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.

could you please explain the solution of statement 2

$$k^2 = 2.601 * 10^9 = 2601*10^6 = 51^2*(10^3)^2$$

$$k= \sqrt{51^2*(10^3)^2}=51*10^3=51000$$
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If n is a positive integer and k = 5.1 x 10^n , what is the  [#permalink]

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D is the correct answer. Here's why:

(1) 6,000 < k < 500,000 --> n=4 because other values would put k outside of its 'bounds' that we are given with (1).

SUFFICIENT

(2) k^2 = 2.601 * 10^9 --> square root both sides to get k alone and set RHS equal to main equation and solve for n.

SUFFICIENT
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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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Prompt analysis
K is a positive integer

Superset
The value of n could be any positive integer

Translation
In order to the value on n, we need:
1# exact value of n
2# range of k
3# any equation to find the value of n

Statement analysis
St 1: from the range, the value of n comes out to be 4. ANSWER. Hence option b,c,e eliminated
St 2: from the statement we get k = 5.1 x 10^4. Since k is positive, we can say that the value of n is 4. ANSWER

Option D.
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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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Bunnel,

This might sound very basic..but I had to ask to be a 100% about my understanding..

So u have mentioned in the highlighted text below that no matter the value of n, k is always positive..
Could please explain that?
Values means = + or - or do u mean the power of 10?

Shirai

Bunuel wrote:
Baten80 wrote:
If n is a positive integer and k = 5.1 x^n , what is the value of k ?
(1) 6,000 < k < 500,000
(2) k^2 = 2.601 * 10^9

I understand the official explanation. is there any other easy way?

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.

Math Expert V
Joined: 02 Sep 2009
Posts: 58340
Re: If n is a positive integer and k = 5.1 x 10^n , what is the  [#permalink]

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shinrai15 wrote:
Bunnel,

This might sound very basic..but I had to ask to be a 100% about my understanding..

So u have mentioned in the highlighted text below that no matter the value of n, k is always positive..
Could please explain that?
Values means = + or - or do u mean the power of 10?

Shirai

Bunuel wrote:
Baten80 wrote:
If n is a positive integer and k = 5.1 x^n , what is the value of k ?
(1) 6,000 < k < 500,000
(2) k^2 = 2.601 * 10^9

I understand the official explanation. is there any other easy way?

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.

Don't know what you mean by the highlighted part...

We are given that k = 5.1 * 10^n and that n is a positive integer. k could be: 51, 510, 5,100, 51,000, ... as you can see k is always a positive integer.
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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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I solved first statement this way. Not sure if this is correct.

6*10^3<51*10^(n-1)<5*10^5

So I assumed that the value of n (in order to find k) will come from the 10s. So I just considered 10s while solving further.

n has to be 5 for the above inequality to be true.

6*10^3<51*10^4<5*10^5

But figured out that this does not make sense as the inequality is not more true.

6000<510000<500000

so n= 4

I prefer what Bunuel has posted. Way better method. This is just something..........
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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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