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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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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 x 10^n, what is k? [#permalink]
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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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21 Jan 2012, 22:41
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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]
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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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01 Nov 2014, 05:21
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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.
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 \(x=\sqrt{9}=3\).
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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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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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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*10^n, what is the value [#permalink]
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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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