phoenix9801 wrote:Hi, can someone please help to explain by step-by-step instructions (in detail) in the most simplest way and clear to understand. Would Greatly appreciate it.

1-

Is 5^k less than 1,000

(1) 5^k+1 > 3,000

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


st 1:

(1) 5^k+1 > 3,000

( 5^k ) * 5 > 3000

( 5^k ) > 3000/5

= ( 5^k ) > 600

Not sufficient as it can be greater than or less than or equal to 1000.

st 2:

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

5^k/5 = 5^K - 500

5^k = 625

So its clear 5^K < 1000

Sufficient

Pick B







2-

If x is an integer, is 9^x + 9 ^-x = b

(1) 3^x + 3^-x = √ b+c

(2) x > 0

Rahul@gurome wrote:

phoenix9801 wrote:Hi, can someone please help to explain by step-by-step instructions (in detail) in the most simplest way and clear to understand. Would Greatly appreciate it.



2-

If x is an integer, is 9^x + 9 ^-x = b

(1) 3^x + 3^-x = √ b+c

(2) x > 0

(1) 3^x + 3^-x = √ b+c implies (3^x + 3^-x)^2 = b + c
(3^x + 3^-x)^2 = 3^2x + 3^(-2x) + 2(3^x)(3^-x)
= 3^2x + 3^(-2x) + 2.(3^x-x) = 3^2x + 3^(-2x) + 2 [Since 3^x-x = 3^0 = 1]
So, 3^2x + 3^(-2x) + 2 = b + c
Now, 3^2x = 9^x and 3^-2x = 9^-x
Hence 9^x + 9^-x = b + c - 2, which implies answer to the main question is "no".
So, (1) Is SUFFICIENT to answer the question.

(2) This statement is NOT SUFFICIENT to answer the question as we don't know the relation between x and b.

[spoiler]The correct answer is (A).[/spoiler]