Data Sufficiency

silverlining wrote:is 5^k less than 1000 ?

1) 5^k+1 > 3000
2) 5^k-1 = 5^k - 500

can somebody please help me with this !! this sum is from og 13
i found few explanations for this already , but iam still not clear with them


thanx in advance

Statement 1: 5^(k + 1) > 3000 --> (5^k)*5 > 3000 --> 5^k > 600
Now 5^k can be more than or less than 1000.

Not sufficient

Statement 2: 5^(k - 1) = 5^k - 500
--> 5^k/5 = 5^k - 500
--> 5^k = 5*5^k - 2500
--> 4*5^k = 2500
--> 5^k = 625 < 1000

Sufficient

The correct answer is B.

Note: We don't have to calculate the value of 5^k for statement 2. From the statement we can see that a definite value of 5^k can obtained. Hence, we can tell whether that value will be less than 1000 or not.

silverlining wrote:is 5^k less than 1000 ?
1) 5^(k+1) > 3000
2) 5^(k-1) = 5^k - 500

Note: I should mention that silverlining's original wording is possibly misleading. 5^k+1 could be interpreted (5^k)+1, when the expression is meant to read 5^(k+1). ome brackets (added above) will help avoid confusion.

Target question: Is 5^k less than 1000?

Statement 1: 5^(k+1) > 3000
First notice that 5^(k+1) = (5^k)(5^1)
So, we can take 5^(k+1) > 3000 and divide both sides by 5 to get: 5^k > 600
There are several possible cases to consider. Here are two:
case a: 5^k = 601, in which case 5^k is less than 1000.
case b: 5^k = 1001, in which case 5^k is not less than 1000.
Since we cannot answer the target question with certainty, statement 1 is NOT SUFFICIENT.

Statement 2: 5^(k-1) = 5^k - 500
Rearrange to get the k's on one side: (5^k) - 5^(k-1) = 500
Factor the left side: 5^(k-1)[5 - 1] = 500
Simplify: 5^(k-1)[4] = 500
Divide both sides by 4 to get: 5^(k-1) = 125
Since 5^3 = 125, we know that (k-1) = 3, which means k=4.
If k=4, then 5^k = 5^4 = 625, in which case 5^k is definitely less than 1000.
Since we can answer the target question with certainty, statement 2 is SUFFICIENT.

Answer = B

Cheers,
Brent