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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] New post 21 Jan 2012, 08:01
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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

[Reveal] Spoiler:
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) ?
[Reveal] Spoiler: OA
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Re: If n is a positive integer and k = 5.1 x 10^n, what is k? [#permalink] New post 21 Jan 2012, 08:17
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Expert's post
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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1 KUDOS received
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Re: If n is a positive integer and k=5.1*10^n, what is the value [#permalink] New post 21 Jan 2012, 21:41
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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] New post 31 Oct 2014, 13:30
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] New post 01 Nov 2014, 04:21
Expert's post
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 MATH FORUM? PLEASE READ THIS: ALL YOU NEED FOR QUANT!!!

PLEASE READ AND FOLLOW: 11 Rules for Posting!!!

RESOURCES: [GMAT MATH BOOK]; 1. Triangles; 2. Polygons; 3. Coordinate Geometry; 4. Factorials; 5. Circles; 6. Number Theory; 7. Remainders; 8. Overlapping Sets; 9. PDF of Math Book; 10. Remainders; 11. GMAT Prep Software Analysis NEW!!!; 12. SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) NEW!!!; 12. Tricky questions from previous years. NEW!!!;

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.


What are GMAT Club Tests?
25 extra-hard Quant Tests

GMAT Club Premium Membership - big benefits and savings

Re: If n is a positive integer and k=5.1*10^n, what is the value   [#permalink] 01 Nov 2014, 04:21
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