Data Sufficiency

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

Hi All,

We're told that N is a POSITIVE INTEGER and K = (5.1)(10^N). We're asked for the value of K. Before we deal with the two Facts, it's worth noting that this is essentially a 'decimal shift' question. Since we're multiplying 5.1 by some positive integer-power of 10, each value of K will be 10 times greater than the value that precedes it. For example....

N=1 --> K = (5.1)(10) = 51
N=2 --> K = (5.1)(100) = 510
N=3 --> K = (5.1)(1000) = 5100
N=4 --> K = (5.1)(10000) = 51000
etc.

We can use this pattern to our advantage to save some time as we work through the 2 Facts....

1) 6,000 < K < 500,000

Based on the pattern that we defined above, the ONLY value of K that fits this given range is 51,000.
Fact 1 is SUFFICIENT

2) K^2 = (2.601)(10^9)

Since N is a positive integer, K MUST also be a POSITIVE INTEGER. Thus, the given equation in Fact 2 has just ONE solution (whatever the square-root of (2.601)(10^9) is). We don't have to calculate it though - it's enough to know that there's just one solution.
Fact 2 is SUFFICIENT

Final Answer: D

GMAT assassins aren't born, they're made,
Rich

LulaBrazilia 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