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crimson2283: Senior | Next Rank: 100 Posts; Posts: 84; Joined: Fri Jan 07, 2011 8:29 amFollowed by: 1 member; Thanked: 5 times

by crimson2283 » Sat Feb 26, 2011 9:34 am

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

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Source: Beat The GMAT — Problem Solving | Sat Feb 26, 2011 9:34 am

anshumishra: Legendary Member; Posts: 543; Joined: Tue Jun 15, 2010 7:01 pmFollowed by: 3 members; Thanked: 147 times

by anshumishra » Sat Feb 26, 2011 9:40 am

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

Thanks
Anshu

(Every mistake is a lesson learned )

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crimson2283: Senior | Next Rank: 100 Posts; Posts: 84; Joined: Fri Jan 07, 2011 8:29 amFollowed by: 1 member; Thanked: 5 times

by crimson2283 » Sat Feb 26, 2011 10:12 am

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: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

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anshumishra: Legendary Member; Posts: 543; Joined: Tue Jun 15, 2010 7:01 pmFollowed by: 3 members; Thanked: 147 times

by anshumishra » Sat Feb 26, 2011 10:23 am

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.

Thanks
Anshu

(Every mistake is a lesson learned )

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crimson2283: Senior | Next Rank: 100 Posts; Posts: 84; Joined: Fri Jan 07, 2011 8:29 amFollowed by: 1 member; Thanked: 5 times

by crimson2283 » Sat Feb 26, 2011 10:38 am

Very well explained. Thanks once again.

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.

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GMATGuruNY: GMAT Instructor; Posts: 15539; Joined: Tue May 25, 2010 12:04 pmFollowed by: 1906 members; Location: New York, NY; Thanked: 13060 times; GMAT Score:790

by GMATGuruNY » Sat Feb 26, 2011 12:16 pm

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

Try to disprove the answer choices by plugging in different values for k.

Plug in k = -8. This value works because (-8)^2 - 4 > 45.

Answer choice A:
2*(-8) > 13. No.
Elliminate A.

Answer choice B:
8(-8) > 56. No.
Eliminate B.

Answer choice C:
(-8)Â² > 64. Yes.
Hold onto C.

Answer choice D:
(-8)Â³ > 512. No.
Eliminate D.

Answer choice E:
(-8)Â² > 523. No.
Eliminate E.

The correct answer is C.[/spoiler]

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