GMAT Question of the Day - Daily to your Mailbox; hard ones only

 It is currently 15 Oct 2019, 16:46

### GMAT Club Daily Prep

#### Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History

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

Author Message
TAGS:

### Hide Tags

Senior Manager
Status: No dream is too large, no dreamer is too small
Joined: 14 Jul 2010
Posts: 426
If n is a positive integer and k = 5.1 x 10^n , what is the  [#permalink]

### Show Tags

Updated on: 18 Dec 2012, 08:21
1
1
30
00:00

Difficulty:

45% (medium)

Question Stats:

68% (01:51) correct 32% (01:53) wrong based on 1232 sessions

### HideShow timer Statistics

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.
Math Expert
Joined: 02 Sep 2009
Posts: 58340

### Show Tags

09 Mar 2011, 08:07
3
4
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.

_________________
##### General Discussion
Senior Manager
Status: No dream is too large, no dreamer is too small
Joined: 14 Jul 2010
Posts: 426

### Show Tags

09 Mar 2011, 08:31
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.
_________________
Intern
Joined: 21 Oct 2014
Posts: 6
If n is a positive integer and k = 5.1 x 10^n , what is the valu  [#permalink]

### Show Tags

23 Jul 2015, 13:47
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
Posts: 3
Re: If n is a positive integer and k = 5.1 x 10^n , what is the  [#permalink]

### Show Tags

16 Jul 2016, 06:34
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
Joined: 02 Sep 2009
Posts: 58340
Re: If n is a positive integer and k = 5.1 x 10^n , what is the  [#permalink]

### Show Tags

16 Jul 2016, 08:38
1
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

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

$$k= \sqrt{51^2*(10^3)^2}=51*10^3=51000$$
_________________
Current Student
Status: DONE!
Joined: 05 Sep 2016
Posts: 358
If n is a positive integer and k = 5.1 x 10^n , what is the  [#permalink]

### Show Tags

23 Sep 2016, 09:35
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
Director
Status: Come! Fall in Love with Learning!
Joined: 05 Jan 2017
Posts: 535
Location: India
Re: If n is a positive integer and k = 5.1 x 10^n , what is the  [#permalink]

### Show Tags

23 Feb 2017, 06:01
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.
_________________
GMAT Mentors
Intern
Joined: 08 Sep 2016
Posts: 32
Re: If n is a positive integer and k = 5.1 x 10^n , what is the  [#permalink]

### Show Tags

12 Sep 2017, 10:14
Bunnel,

So u have mentioned in the highlighted text below that no matter the value of n, k is always positive..
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
Joined: 02 Sep 2009
Posts: 58340
Re: If n is a positive integer and k = 5.1 x 10^n , what is the  [#permalink]

### Show Tags

12 Sep 2017, 10:23
1
shinrai15 wrote:
Bunnel,

So u have mentioned in the highlighted text below that no matter the value of n, k is always positive..
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.
_________________
Director
Joined: 02 Sep 2016
Posts: 649
Re: If n is a positive integer and k = 5.1 x 10^n , what is the  [#permalink]

### Show Tags

12 Sep 2017, 12:26
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..........
_________________
Help me make my explanation better by providing a logical feedback.

If you liked the post, HIT KUDOS !!

Don't quit.............Do it.
Non-Human User
Joined: 09 Sep 2013
Posts: 13167
Re: If n is a positive integer and k = 5.1 x 10^n , what is the  [#permalink]

### Show Tags

31 Jan 2019, 23:13
Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
_________________
Re: If n is a positive integer and k = 5.1 x 10^n , what is the   [#permalink] 31 Jan 2019, 23:13
Display posts from previous: Sort by