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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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New post 21 Jan 2012, 09:01
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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

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.

My Answer: A.

Official Answer (OG12): D.
OG12 Explanation: 2nd statement implies k can only be 5.1 x 10^4. Why not (-5.1 x 10^4) ?
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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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New post 26 Jul 2016, 07:35
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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

Answer =

Cheers,
Brent
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Re: If n is a positive integer and k = 5.1 x 10^n, what is k?  [#permalink]

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New post 21 Jan 2012, 09:17
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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.

My Answer: A.

Official Answer (OG12): D.
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.

Answer: D.

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  [#permalink]

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New post 21 Jan 2012, 22:41
Thanks, it is. I need to pay more attention to the question.
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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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New post 31 Oct 2014, 14:30
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.

My Answer: A.

Official Answer (OG12): D.
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.

Answer: D.

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  [#permalink]

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New post 01 Nov 2014, 05:21
2
1
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.

My Answer: A.

Official Answer (OG12): D.
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.

Answer: D.

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;
\(\sqrt[4]{16} = 2\), 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 \(x=\sqrt{9}=3\).
_________________

New to the Math Forum?
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Collection of Questions:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


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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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New post 30 Dec 2015, 04:32
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  [#permalink]

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New post 29 Mar 2018, 17:39
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.

Answer: D
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Re: If n is a positive integer and k=5.1*10^n, what is the value &nbs [#permalink] 29 Mar 2018, 17:39
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