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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.

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

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 \(x=\sqrt{9}=3\). _________________

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

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

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

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03 Sep 2017, 22:42

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