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) k^2 = 2.601 x 10^9

Can anyone help me out ? I'm perplexed......

Hi Goldie,

Okay, lets look at the statement of the problem first. In order to determine the value of k, without looking at either proposition, we need to know the value of n.

Lets look at (1). If we let n vary from 1, we have:
n=1, k = 51
n=2, k = 510
n=3, k = 5100
n=4, k = 51000
n=5, k = 510000

The only k that is between 6,000 and 500,000 is the value of k that corresponds to n=4. So it is very easy to determine the value of k. k = 51,000.

Lets look at (2). Since k must be a positive number (there is no way it can be otherwise based on the statement of the problem), we can find the positive square root of k to determine its value. Remember data sufficiency doesn't require you to solve the problem. It requires you to determine if the information present is sufficient to solve the problem if you have to. Clearly, if you had the patience, you could indeed determine the square root of 2601000000. (It's actually 51,000 surprise surprise)

Both propositions are sufficient to solve the problem. The correct answer is D.

Take care,
Steve

hello....
oh my god.that is really tough question for me.i can not answer this.but if you get the answer must reply me......