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Manager  Joined: 25 Dec 2010
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If n is a positive integer and k = 5.1*10^n, what is the value of k?  [#permalink]

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Question Stats: 67% (01:53) correct 33% (01:47) wrong based on 1484 sessions

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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) $$k^2 = 2.601 * 10^9$$

Originally posted by shashankp27 on 21 May 2011, 10:08.
Last edited by Bunuel on 06 Feb 2019, 06:06, edited 1 time in total.
Renamed the topic and edited the question.
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Re: If n is a positive integer and k = 5.1*10^n, what is the value of k?  [#permalink]

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fxsunny wrote:
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) k² = 2.601 * 10^9

Target question: What is the value of k?

Given: n is a positive integer, and k = (5.1)x(10^n)
IMPORTANT: This since n can be ANY positive integer, there are several possible values of k.
They are: 51, 510, 5100, 51000, 510000, etc

Statement 1: 6,000 < k < 500,000
If we examine the possible values of k (51, 510, 5100, 51000, 510000, etc ), we can see that only ONE value (51,000) lies within the range defined by the inequality.
So, k must equal 51,000
Since we can answer the target question with certainty, statement 1 is SUFFICIENT

Statement 2: k² = 2.601 x 10^9
If k²= 2.601 x 10^9, then EITHER k = √(2.601 x 10^9) OR k = -√(2.601 x 10^9). So, it appears that we cannot answer the target question.
HOWEVER, the question also tells us that k = 5.1 x 10^n, and since 5.1 x 10^n will always have a POSITIVE value, we know that k must be POSITIVE.
If k is POSITIVE, then k -√(2.601 x 10^9)
This means that k must equal √(2.601 x 10^9)
Since we can answer the target question with certainty, statement 2 is SUFFICIENT

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

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shashankp27 wrote:
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

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.

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

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

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

Hope it's clear.
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Re: If n is a positive integer and k = 5.1*10^n, what is the value of k?  [#permalink]

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Bunuel wrote:
fxsunny wrote:
OG12: DS/151:
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

My Response:

(1) Solving for k by trying out n = 0,1,2,3 etc. we arrive at k = 51000 for n=4. SUFFICIENT.
(2) K could be 5.1 x 10^4 or -5.1 x 10^4. NOT SUFFICIENT.

OG12 Explanation: 2nd statement implies k can only be 5.1 x 10^4. Why not (-5.1 x 10^4) ?

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.

Hope it's clear.

Hi Bunuel,

If we weren't told that "n" is positive, wouldn't B still be sufficient? Isn't it true that whenever we take a square root, we always choose the positive value. Meaning, if we take a square root of 4, isn't the answer 2 and not +/- 2?

How is that any different than the k^2 value given above? Is it because we are working with a variable in k^2
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Re: If n is a positive integer and k = 5.1*10^n, what is the value of k?  [#permalink]

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russ9 wrote:
Bunuel wrote:
fxsunny wrote:
OG12: DS/151:
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

My Response:

(1) Solving for k by trying out n = 0,1,2,3 etc. we arrive at k = 51000 for n=4. SUFFICIENT.
(2) K could be 5.1 x 10^4 or -5.1 x 10^4. NOT SUFFICIENT.

OG12 Explanation: 2nd statement implies k can only be 5.1 x 10^4. Why not (-5.1 x 10^4) ?

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.

Hope it's clear.

Hi Bunuel,

If we weren't told that "n" is positive, wouldn't B still be sufficient? Isn't it true that whenever we take a square root, we always choose the positive value. Meaning, if we take a square root of 4, isn't the answer 2 and not +/- 2?

How is that any different than the k^2 value given above? Is it because we are working with a variable in k^2

When the GMAT provides the square root sign for an even root, such as a square root, fourth root, etc. then the only accepted answer is the positive root.

That is:
$$\sqrt{9} = 3$$, NOT +3 or -3;
$$\sqrt{16} = 2$$, NOT +2 or -2;

Notice that in contrast, the equation $$x^2 = 9$$ has TWO solutions, +3 and -3. Because $$x^2 = 9$$ means that $$x =-\sqrt{9}=-3$$ or $$x=\sqrt{9}=3$$.
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GMAT 1: 760 Q50 V44 Re: If n is a positive integer and k = 5.1*10^n, what is the value of k?  [#permalink]

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fxsunny wrote:
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

Given:
n is a positive integer.
k=5.1*10^n

Required: k = ?

Statement 1: 6,000 < k < 500,000
Since n is a positive integer, k can take the values 51, 510, 5100, 51000, 510000 etc.
Of these only one value lies in the range (6000, 500000)
Hence k = 51,000
SUFFICIENT

Statement 2: $$k^2$$ = 2.601 * $$10^9$$
This will give us 2 values of k, but we are concerned with the positive value only, since k cannot be negative as per the definition k = 5.1*$$10^n$$
SUFFICIENT

Option D
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Re: If n is a positive integer and k = 5.1*10^n, what is the value of k?  [#permalink]

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fxsunny wrote:
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

We are given that n is a positive integer and k = 5.1*10^n and need to determine k.

Statement One Alone:

6,000 < k < 500,000

We see that if n = 4, then k = 5.1 x 10^ 4 = 51,000, which is between 6,000 and 500,000, If n = 3, then k = 5.1 x 10^3 = 5,100, which is less than 6,000 and if n = 5, then k = 5.1 x 10^5 = 510,000, which is greater than 500,000. So n must be 4 and k must be 51,000.

Statement one alone is sufficient to answer the question.

Statement Two Alone:

k^2 = 2.601 * 10^9

Since k = 5.1*10^n, and since n is a positive integer, we see that we can take the square root of both sides of the given equation and get a singular value for k. Thus, statement two is sufficient to answer the question.

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