K a positive

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

So E

PS : Considering 0 to be not positive