K a positive

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sanju09: GMAT Instructor; Posts: 3650; Joined: Wed Jan 21, 2009 4:27 amFollowed by: 80 members; Location: India; Thanked: 267 times; GMAT Score:760

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

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Source: Beat The GMAT — Data Sufficiency | Tue Aug 28, 2012 1:43 am

vk_vinayak: Legendary Member; Posts: 502; Joined: Tue Jun 03, 2008 11:36 pmFollowed by: 21 members; Thanked: 99 times

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)

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sanju09: GMAT Instructor; Posts: 3650; Joined: Wed Jan 21, 2009 4:27 amFollowed by: 80 members; Location: India; Thanked: 267 times; 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

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Anurag@Gurome: GMAT Instructor; Posts: 3835; Joined: Fri Apr 02, 2010 10:00 pmFollowed by: 523 members; Location: Milpitas, CA; Thanked: 1854 times; 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

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Brent@GMATPrepNow: GMAT Instructor; Posts: 16207; Joined: Mon Dec 08, 2008 6:26 pmFollowed by: 1268 members; Location: Vancouver, BC; Thanked: 5254 times; 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

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neelgandham: Community Manager; Posts: 1060; Joined: Fri May 13, 2011 6:46 amFollowed by: 52 members; Location: Utrecht, The Netherlands; Thanked: 318 times

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.

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sanju09: GMAT Instructor; Posts: 3650; Joined: Wed Jan 21, 2009 4:27 amFollowed by: 80 members; Location: India; Thanked: 267 times; 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

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Ganesh hatwar: 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

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