Problem Solving

crimson2283 wrote:If k is an integer and k^2 -4 > 45 , then which of the following inequalities must be true?

2k > 13
8k > 56
k^2 > 62
k^3 > 512
k^2 > 523

anshumishra wrote:

crimson2283 wrote:If k is an integer and k^2 -4 > 45 , then which of the following inequalities must be true?

2k > 13
8k > 56
k^2 > 62
k^3 > 512
k^2 > 523

k^2 > 49
So, k < -7 or k > 7
Since K is an integer , so K could be any integer <= -8 Or >=8.

2k > 13 -> Wrong if k =-8
8k > 56 -> wrong if k =-8
k^2 > 62 - Always right
k^3 > 512 - wrong for any -ve value of K
K^2 > 523 - wrong if K=8

C

crimson2283 wrote:Thanks so much. I get confused when a question uses inequalities.
Can you please explain this?

If - k^2 > 49, I thought k>7 or k>-7. Since k is an integer, I assumed k could be 8 and -6.
But you say, k<-7 (which is correct as per the OA), please explain why.

anshumishra wrote:

crimson2283 wrote:Thanks so much. I get confused when a question uses inequalities.
Can you please explain this?

If - k^2 > 49, I thought k>7 or k>-7. Since k is an integer, I assumed k could be 8 and -6.
But you say, k<-7 (which is correct as per the OA), please explain why.

Sure.
First Check -6^2 = 36, -5^2 = 25 (less than 49), but -7^2 = 49 , -8^2 = 64 (greater than 49)

Here is the graph for (x^2 > 49) showing the same thing. The area in blue is what we are interested here.
https://www3.wolframalpha.com/Calculate/ ... =360&h=242

Whenever you see something like x^2 > 49 => x^2 > 7^2
reduce it to |x| > 7 , which is the same as x > 7 and x < -7.

crimson2283 wrote:If k is an integer and k^2 -4 > 45 , then which of the following inequalities must be true?

2k > 13
8k > 56
k^2 > 62
k^3 > 512
k^2 > 523