Data Sufficiency

Q. Is 5^k less than 1,000 ?

(1) 5^k-1 > 3000

(2) 5^k-1 = 5^k - 500

OA is B. Can someone please explain?

Regards
MSD

msd_2008 wrote:Q. Is 5^k less than 1,000 ?

(1) 5^k-1 > 3000

(2) 5^k-1 = 5^k - 500

OA is B. Can someone please explain?

Regards
MSD

Statement I
5^k-1 > 3000
5^k/5 > 3000

5^k > 3000*5

Sufficient.

Statement II
5^k/5 = 5^k - 500

5^k = 5^k+1 - 2500

2500 = 5^k 4

5^k = 2500/4

5^k = 625

sufficient.

The 2 statements are contradicting each other which cannot be possible

I guess statement I should be 5^k+1 > 3000, this way

5^k * 5 >3000
5^k > 600

If this the statement I , then answer is B, if not then answer is D.

Hope this helps.

I think I had this question on a practice test. You may have gotten the direction of the inequality wrong in statement 1. Otherwise, I agree that the answer is D.

Not to mention that as written, the statements contradict one another (5^k=625 and 5^k>15000), which the GMAT does not do.

damnation, i got D too

Here is the link to the correct question

https://www.beatthegmat.com/tough-one-og ... 16616.html

Statement I

5^k+1 > 3000

Hope this helps.

I'm trying a different approach to solution 2. Please comment as to whether this is accurate; Thanks.

5^(k-1)= 5^k - 500

*5^(k-1) is the same as (5^k/5^1)* so

(5^k/5^1) = 5^k - 500

*Next move the 5^K to the left hands side from the right hand side* so

(5^k/5^1) - 5^k = -500

* Then multiply each term by 5 to get rid of the denominator*

5[(5^k/5^1) - 5^k] = 5(-500) so this becomes

5^k - (5^k * 5^1) = -2500 or

5^k - (5^k+1) = -2500

so is this correct so far? How do I then solve for k? Thanks!