It is currently 23 Feb 2018, 00:52

### GMAT Club Daily Prep

#### Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History

# Events & Promotions

###### Events & Promotions in June
Open Detailed Calendar

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

Author Message
TAGS:

### Hide Tags

Intern
Joined: 15 Apr 2012
Posts: 6
Schools: HKU 15
If k is an integer and k^2 - 4 > 45, then which of the follo [#permalink]

### Show Tags

28 Sep 2013, 02:42
9
This post was
BOOKMARKED
00:00

Difficulty:

65% (hard)

Question Stats:

53% (01:26) correct 47% (01:17) wrong based on 354 sessions

### HideShow timer Statistics

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

[Reveal] Spoiler:
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
[Reveal] Spoiler: OA

Last edited by Bunuel on 28 Sep 2013, 03:57, edited 1 time in total.
Renamed the topic, edited the question and added the OA.
Math Expert
Joined: 02 Sep 2009
Posts: 43891
Re: If k is an integer and k^2 - 4 > 45, then which of the follo [#permalink]

### Show Tags

28 Sep 2013, 04:03
1
KUDOS
Expert's post
2
This post was
BOOKMARKED
jafeer wrote:
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

[Reveal] Spoiler:
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

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.

Hope it's clear.
_________________
Non-Human User
Joined: 09 Sep 2013
Posts: 13792
Re: If k is an integer and k^2 - 4 > 45, then which of the follo [#permalink]

### Show Tags

05 Dec 2014, 18:04
Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
_________________
Non-Human User
Joined: 09 Sep 2013
Posts: 13792
Re: If k is an integer and k^2 - 4 > 45, then which of the follo [#permalink]

### Show Tags

28 Dec 2015, 00:37
Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
_________________
Senior Manager
Joined: 20 Aug 2015
Posts: 394
Location: India
GMAT 1: 760 Q50 V44
Re: If k is an integer and k^2 - 4 > 45, then which of the follo [#permalink]

### Show Tags

28 Dec 2015, 23:06
jafeer wrote:
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

$$k^2$$- 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
Board of Directors
Joined: 17 Jul 2014
Posts: 2734
Location: United States (IL)
Concentration: Finance, Economics
GMAT 1: 650 Q49 V30
GPA: 3.92
WE: General Management (Transportation)
Re: If k is an integer and k^2 - 4 > 45, then which of the follo [#permalink]

### Show Tags

12 Feb 2016, 18:17
jafeer wrote:
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

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.
Retired Moderator
Joined: 12 Aug 2015
Posts: 2426
GRE 1: 323 Q169 V154
Re: If k is an integer and k^2 - 4 > 45, then which of the follo [#permalink]

### Show Tags

10 Mar 2016, 10:41
Rule to be used => integer constraint
here the range for x is => x<-7 or x>7
_________________

Getting into HOLLYWOOD with an MBA

Stone Cold's Mock Tests for GMAT-Quant(700+)

Non-Human User
Joined: 09 Sep 2013
Posts: 13792
Re: If k is an integer and k^2 - 4 > 45, then which of the follo [#permalink]

### Show Tags

18 Mar 2017, 21:24
Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
_________________
Manager
Joined: 27 Aug 2016
Posts: 95
Location: India
Schools: HEC Montreal '21
GMAT 1: 670 Q47 V37
GPA: 3
WE: Engineering (Energy and Utilities)
Re: If k is an integer and k^2 - 4 > 45, then which of the follo [#permalink]

### Show Tags

18 Mar 2017, 21:30
Bunuel wrote:
jafeer wrote:
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

[Reveal] Spoiler:
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

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.

Hope it's clear.

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.
Senior Manager
Joined: 05 Jan 2017
Posts: 434
Location: India
Re: If k is an integer and k^2 - 4 > 45, then which of the follo [#permalink]

### Show Tags

20 Mar 2017, 04:10
[quote="jafeer"]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

k^2 - 4>45
k^2 - 49>0
(k+7)(k-7)>0

therefore k<-7 or k>7 k =...... -10, -9, -8,8,9, 10.....

A. 2k>13 or k>6.5 rejected
B. 8k>56 or k>7. not covering the negative side the set..rejected
C. k^2>62 or k^2-62>0 or (k-7.87)(k+7.87)>0. hence k< -7.87 or k>7.87 sufficient k =...... -10, -9, -8,8,9, 10..... ANSWER
D. k^3>512 or k>8. not covering the negative side the set..rejected
E. k^2>523 or k^2-523>0 or (k-22.86)(k+22.86)>0. hence k< -22.86 or k>22.86. not covering the exact set. rejected.
Target Test Prep Representative
Status: Founder & CEO
Affiliations: Target Test Prep
Joined: 14 Oct 2015
Posts: 2192
Location: United States (CA)
Re: If k is an integer and k^2 - 4 > 45, then which of the follo [#permalink]

### Show Tags

22 Mar 2017, 08:39
1
KUDOS
Expert's post
jafeer wrote:
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

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.

_________________

Scott Woodbury-Stewart
Founder and CEO

GMAT Quant Self-Study Course
500+ lessons 3000+ practice problems 800+ HD solutions

Re: If k is an integer and k^2 - 4 > 45, then which of the follo   [#permalink] 22 Mar 2017, 08:39
Display posts from previous: Sort by