BREAKING: Target Test Prep releases Brand New 2026 On Demand GMAT prep course

Redeem

K a positive

This topic has expert replies
Post new topic Post Reply
Previous Topic Next Topic
User avatar
GMAT Instructor
Posts: 3650
Joined: Wed Jan 21, 2009 4:27 am
Location: India
Thanked: 267 times
Followed by:80 members
GMAT Score:760

K a positive

by sanju09 » Tue Aug 28, 2012 1:43 am
Is K a positive number?

(1) |K^3| + 1 > K.
(2) K + 1 > |K^3|.

[spoiler]OA E[/spoiler]

Source: gmatclub
The mind is everything. What you think you become. -Lord Buddha



Sanjeev K Saxena
Quantitative Instructor
The Princeton Review - Manya Abroad
Lucknow-226001

www.manyagroup.com
Top
Source: — Data Sufficiency |
User avatar
Legendary Member
Posts: 502
Joined: Tue Jun 03, 2008 11:36 pm
Thanked: 99 times
Followed by:21 members

by vk_vinayak » Tue Aug 28, 2012 2:56 am
sanju09 wrote:Is K a positive number?

(1) |K^3| + 1 > K.
(2) K + 1 > |K^3|.

[spoiler]OA E[/spoiler]

Source: gmatclub
Do you have a solution for this? I tried but it was very lengthy. If only some one could help with efficient solution.
- VK

I will (Learn. Recognize. Apply)
Top
User avatar
GMAT Instructor
Posts: 3650
Joined: Wed Jan 21, 2009 4:27 am
Location: India
Thanked: 267 times
Followed by:80 members
GMAT Score:760

by sanju09 » Wed Aug 29, 2012 1:48 am
vk_vinayak wrote:
sanju09 wrote:Is K a positive number?

(1) |K^3| + 1 > K.
(2) K + 1 > |K^3|.

[spoiler]OA E[/spoiler]

Source: gmatclub
Do you have a solution for this? I tried but it was very lengthy. If only some one could help with efficient solution.

(1) This statement is true for all integers K, negatives, zero and positives, hence insufficient.

(2) This statement is not true for an integer K, except K = 0, 1, hence insufficient.

Taken together

K = [spoiler]0, 1 or a non integer. Insufficient

Win E[/spoiler]
The mind is everything. What you think you become. -Lord Buddha



Sanjeev K Saxena
Quantitative Instructor
The Princeton Review - Manya Abroad
Lucknow-226001

www.manyagroup.com
Top

GMAT/MBA Expert

User avatar
GMAT Instructor
Posts: 3835
Joined: Fri Apr 02, 2010 10:00 pm
Location: Milpitas, CA
Thanked: 1854 times
Followed by:523 members
GMAT Score:770

by Anurag@Gurome » Wed Aug 29, 2012 2:57 am
sanju09 wrote:
Is K a positive number?

(1) |K^3| + 1 > K.
(2) K + 1 > |K^3|.

OA E

Source: gmatclub
In the question it is not mentioned whether k is integer. So, we should not assume it to be an integer.

consider 1st option:
if k > 1, K^3 will be greater than k, so |k^3| + 1 > k.
if 0 < k < 1, k will be less than 1, so it will be less than |k^3| + 1.
if k = 1 or 0, |K^3| + 1 > K
if k < 0. k will be less than positive number (|k^3| + 1).
hence, it will satisfy for all numbers. So , we can`t answer with this option.

consider 2nd option:
k + 1 > |k^3|
if 0 < k < 1, k will be greater than |k^3|. so , the range will satisfy k + 1 > |k^3|
this will also satisfy for some negative values greater than -1. for example take -1/10 as k. it will satisfy the condition.
k + 1 = -k^3 (for exact value of k, we can solve the equation and get it. but it would be waste of our time when we are giving the exam)
so, with this condition also we got a range, which lies in both positive and negative numbers.

considering 1 and 2 together,
it will be the range matching for both the equations. Which will be the range of 2nd option taken alone. As the 1st option is true for all numbers.

hence, it is E
Anurag Mairal, Ph.D., MBA
GMAT Expert, Admissions and Career Guidance
Gurome, Inc.
1-800-566-4043 (USA)

Join Our Facebook Groups
GMAT with Gurome
https://www.facebook.com/groups/272466352793633/
Admissions with Gurome
https://www.facebook.com/groups/461459690536574/
Career Advising with Gurome
https://www.facebook.com/groups/360435787349781/
Top

GMAT/MBA Expert

User avatar
GMAT Instructor
Posts: 16207
Joined: Mon Dec 08, 2008 6:26 pm
Location: Vancouver, BC
Thanked: 5254 times
Followed by:1268 members
GMAT Score:770

by Brent@GMATPrepNow » Wed Aug 29, 2012 7:24 am
sanju09 wrote:Is K a positive number?

(1) |K^3| + 1 > K.
(2) K + 1 > |K^3|.

[spoiler]OA E[/spoiler]

When plugging in numbers, it's often useful to try 0, 1, -1, 1/2, -1/2, 10 and -10, since they represent a nice corss-section of values.

Target question: Is K a positive?

Statement 1: |K^3| + 1 > K
Lots of cases are possible here.
case a) K=0, in which case K is not positive
case b) K=1, in which case K is positive
Since we cannot answer the target question with certainty, statement 1 is NOT SUFFICIENT

Statement 2: K + 1 > |K^3|.
case a) K=0, in which case K is not positive
case b) K=1, in which case K is positive
Since we cannot answer the target question with certainty, statement 2 is NOT SUFFICIENT

Statements 1 + 2:
case a) K=0, in which case K is not positive
case b) K=1, in which case K is positive
Since we cannot answer the target question with certainty, the combined statements are NOT SUFFICIENT

Answer = E

Cheers,
Brent

For more information on plugging in numbers, you can watch this free video: https://www.gmatprepnow.com/module/gmat- ... cy?id=1102
Brent Hanneson - Creator of GMATPrepNow.com
Image
Top
User avatar
Community Manager
Posts: 1060
Joined: Fri May 13, 2011 6:46 am
Location: Utrecht, The Netherlands
Thanked: 318 times
Followed by:52 members

by neelgandham » Wed Aug 29, 2012 8:54 am
If you are really good at plotting graphs then you can solving by plotting the same.

Is K a positive number?
(1)|K^3| + 1 > K.

The graph in blue is the graph of Y = |K^3| + 1. You can see from the graph that the condition |K^3| + 1 > K is true for all K. Since we cannot determine the sign of K, statement I is insufficient to answer the question
(2)K + 1 > |K^3|.
K > |K^3| - 1. The graph in red is the graph of Y = |K^3| - 1. You can see from the graph that the condition K > |K^3| - 1 is satisfied for some values between -1 and 0, at 0 and some values between 0 and 1. Since we cannot determine the sign of K, statement II is insufficient to answer the question
From I and II
From I and II, the conditions |K^3| + 1 > K and K > |K^3| - 1 are satisfied for some values between -1 and 0, at 0 and some values between 0 and 1. Since we cannot determine the sign of K, statement I + II combined is insufficient to answer the question.

Answer E
Experts - Correct me if I am wrong.
Attachments
BTG-1.jpg
Anil Gandham
Welcome to BEATtheGMAT | Photography | Getting Started | BTG Community rules | MBA Watch
Check out GMAT Prep Now's online course at https://www.gmatprepnow.com/
Top
User avatar
GMAT Instructor
Posts: 3650
Joined: Wed Jan 21, 2009 4:27 am
Location: India
Thanked: 267 times
Followed by:80 members
GMAT Score:760

by sanju09 » Wed Aug 29, 2012 11:28 am
Anurag@Gurome wrote:
sanju09 wrote:
Is K a positive number?

(1) |K^3| + 1 > K.
(2) K + 1 > |K^3|.

OA E

Source: gmatclub
In the question it is not mentioned whether k is integer. So, we should not assume it to be an integer.

consider 1st option:
if k > 1, K^3 will be greater than k, so |k^3| + 1 > k.
if 0 < k < 1, k will be less than 1, so it will be less than |k^3| + 1.
if k = 1 or 0, |K^3| + 1 > K
if k < 0. k will be less than positive number (|k^3| + 1).
hence, it will satisfy for all numbers. So , we can`t answer with this option.

consider 2nd option:
k + 1 > |k^3|
if 0 < k < 1, k will be greater than |k^3|. so , the range will satisfy k + 1 > |k^3|
this will also satisfy for some negative values greater than -1. for example take -1/10 as k. it will satisfy the condition.
k + 1 = -k^3 (for exact value of k, we can solve the equation and get it. but it would be waste of our time when we are giving the exam)
so, with this condition also we got a range, which lies in both positive and negative numbers.

considering 1 and 2 together,
it will be the range matching for both the equations. Which will be the range of 2nd option taken alone. As the 1st option is true for all numbers.

hence, it is E
K may be an integer, and the assumption serves the purpose as well.
The mind is everything. What you think you become. -Lord Buddha



Sanjeev K Saxena
Quantitative Instructor
The Princeton Review - Manya Abroad
Lucknow-226001

www.manyagroup.com
Top
Senior | Next Rank: 100 Posts
Posts: 97
Joined: Sun Jun 24, 2012 11:23 pm

by Ganesh hatwar » Thu Aug 30, 2012 1:15 am
Failed both statements for zero

So E

PS : Considering 0 to be not positive
Top
Post new topic Post Reply
• Page 1 of 1