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What is the value of k?

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LulaBrazilia Master | Next Rank: 500 Posts Default Avatar
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What is the value of k?

Post Fri Mar 07, 2014 10:58 am
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

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GMAT/MBA Expert

Post Fri Mar 07, 2014 2:44 pm
LulaBrazilia wrote:
If n is a positive integer and k = (5.1)x(10^n), what is the value of k?

1) 6,000 < k < 500,000
2) k² = 2.601 x 10^9
Target question: What is the value of k?

Given: n is a positive integer, and k = (5.1)x(10^n)0
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 = D

Cheers,
Brent

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Patrick_GMATFix GMAT Instructor
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Post Fri Mar 07, 2014 11:14 am
(1)is sufficient since k must be 51,000 (the only number between 6,000 and 500,000 that begins with 51 followed by 0s)

(2) is sufficient because we know from the prompt that k is positive (so we can ignore the negative root).

The answer is D. I go through the question in detail in the full solution below (taken from the GMATFix App).



-Patrick

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