OG DS 151

[mundasingh123]

151. 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 × 109
Why is answer D.
In option 2

(2) k^2 = 2.601 × 109

, k can be positive or negative

[vineeshp]

Cos problem says k = 5.1 * 10 ^ n. This is positive right?

[Anurag@Gurome]

151. 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 × 109

As n is a positive integer, possible values of k are 51, 510, 5100, ... etc
Hence k is always a positive integer.

Statement 1: Only possible value of k is 51,000 --> Sufficient

Statement 2: As k is always positive, we can have an unique value of k from this expression --> Sufficient

The correct answer is D.

[mundasingh123]

But otherwise , if k^2 = 25 is stated , then can k be positive as well as negative ?

[Anurag@Gurome]

But otherwise , if k^2 = 25 is stated , then can k be positive as well as negative ?

Yes.

[Night reader]

k = 5.1 × 10^n means k is positive, as the right-hand-side (RHS) is positive. Find k-?

st(1) 6,000 < k < 500,000 can be rewritten as 6*10^3 < k < 5 *10^5. If we compare the left-hand-side (LHS) and RHS we notice that 6>5.1 BUT 5.1>5. We should deduce about 3<n<5 in expression 10^n. Because n is a positive integer n=4, Statement (1) gives us k=5.1*10^4 Sufficient

st(2) k^2 = 2.601 × 109 by using the question information can be rewritten as 26.01 × 100^n = 2.601 × 109 (remember LHS is k^2, so we need to multiply our result by 2 for k^1 OR k); It's easy to notice that n is slight more than 2 for the equality 26.01 × 100^n = 2.601 × 109 be valid, BUT we need to multiply by factor 2 and n=4. Statement (2) gives us k=5.1 *10^4 Sufficient;

answer is D (cleared the previous query)

151. 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 × 109
Why is answer D.
In option 2

(2) k^2 = 2.601 × 109

, k can be positive or negative