If k is an integer and k^2 - 4 45, then which of the follo

Question

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

A. 2k > 13 
B. 8k > 56 
C. k^2 > 62 
D. k^3 > 512 
E. k^2 > 523

Question Type: Problem Solving
Subject Areas: Algebra
Categories: Inequalities
TPR Strategies: Plugging In

answer given:
A. If ,k^2>49 then k could equal -8. However, -16 is not greater than 13.

B. If ,k^2>49 then k could equal -8. However, -64 is not greater than 56.

C. Yes. Sincek^2>49 , and k is an integer, it must be true that k>=8 0r k<=-8 . Therefore, you know that has to be greater than or equal to 64, so it must be greater than 62.

D. If ,k^2>49 then k could equal -10. However, -1,000 is not greater than 512.

E. If k^2>49, then k could equal -10. However, 100 is not greater than 523

Bunuel · Accepted Answer

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

k^2 - 4 > 45  --> k^2>49 -->  k<-7  or  k>7 . Since given that k is an integer then k can be ..., -10, -9, -8, OR 8, 9, 10, ...

Check each option:

A. 2k > 13. If k=-8, then this option is not true. Thus this option is not ALWAYS true. Discard.

B. 8k > 56. If k=-8, then this option is not true. Thus this option is not ALWAYS true. Discard.

C. k^2 > 62. For ANY possible values of k (..., -10, -9, -8, OR 8, 9, 10, ...) this option holds true. Thus it's always true.

D. k^3 > 512. If k=-8, then this option is not true. Thus this option is not ALWAYS true. Discard.
 
E. k^2 > 523. If k=-8, then this option is not true. Thus this option is not ALWAYS true. Discard.

Answer: C.

Hope it's clear.

TeamGMATIFY · Answer

k^2 - 4 > 45 OR  k^2 > 49

Solving an inequality with a less than sign:
The value of the variable will be greater than the smaller value and smaller than the greater value.
i.e. It will lie between the extremes.

Solving an inequality with a greater than sign:
The value of the variable will be smaller than the smaller value and greater than the greater value.
i.e. It can take all the values except the values in the range.

Therefore k>7 or k<-7
Since k is an integer, possible values are 8,9,10, ... and -8,-9,-10, ...

Checking the options:

A.   2k > 13 This is not true for all negative values of k. INCORRECT
  B.   8k > 56 This is not true for all negative values of k. INCORRECT
  C.   k^2 > 62 This will always hold true, since minimum value of k =8 and k^2 = 64. CORRECT
  D.   k^3 > 512 This will not hold true for negative values of x. INCORRECT
  E.   k^2 > 523 This is not true for k = 8,9,10 ... INCORRECT

Option C

mvictor · Answer

we are told that k is an integer.
from the given inequality, we can see that k^2 > 49
k>7 or k<-7.
suppose k=8 or -8
k^2 = 64.
since we know for sure that k^2>49, it means that k > |7|. and since k must be a integer, k must be at least |8|, and 8^2 = 64.
thus, we can see that C will always be true.

stonecold · Answer

Rule to be used => integer constraint
here the range for x is => x<-7 or x>7

saurabhsavant · Answer

desperately need help with such questions..
i went through veritasprepkarishma topic on inequalities and employing the methodology explained therein it was easy to get k>7 and k<-7. In the PS forum questions it has also been explained a number of times if x> 7 then x must definitely be greater then 8...
combining the above two concepts learnt after putting in great deal of effort I so confidently chose D...aaarrrggghhhhhh...

How can one decide when to plug in numbers and when not ...and that too with the clock ticking....
Pl help ASAP...its an SOS question...i might shun the idea of even appearing for GMAT over it.

KrishnakumarKA1 · Answer

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

A. 2k > 13
B. 8k > 56
C. k^2 > 62
D. k^3 > 512
E. k^2 > 523

Question Type: Problem Solving
Subject Areas: Algebra
Categories: Inequalities
TPR Strategies: Plugging In

Show Spoiler

answer given:
A. If ,k^2>49 then k could equal -8. However, -16 is not greater than 13.

B. If ,k^2>49 then k could equal -8. However, -64 is not greater than 56.

C. Yes. Sincek^2>49 , and k is an integer, it must be true that k>=8 0r k<=-8 . Therefore, you know that has to be greater than or equal to 64, so it must be greater than 62.

D. If ,k^2>49 then k could equal -10. However, -1,000 is not greater than 512.

E. If k^2>49, then k could equal -10. However, 100 is not greater than 523

ScottTargetTestPrep · Answer

Let’s simplify the given inequality: k^2 - 4 > 45 k^2 > 49 √(k^2) > √49 |k| > 7 Thus, k > 7 or k < -7 Let’s now simplify our answer choices to see which must be true. A) 2k > 13 k > 6.5 Using answer choice A, k could be 7; however, we know that k > 7; thus, answer choice A does not have to be true. B) 8k > 56 k > 7 Since k could be -8, this answer choice does not have to be true. C) k^2 > 62 √k^2 > √62 |k| > 7.8 k > 7.8 or k < -7.8 No matter what integer values of k we select using answer choice C, those values will always be either greater than 7 or less than -7. Thus, answer choice C must be true. Answer: C

bumpbot · Answer

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If k is an integer and k^2 - 4 > 45, then which of the follo

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