Is K a positive number?
(1) |K^3| + 1 > K.
(2) K + 1 > |K^3|.
[spoiler]OA E[/spoiler]
Source: gmatclub
K a positive
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- vk_vinayak
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Do you have a solution for this? I tried but it was very lengthy. If only some one could help with efficient solution.sanju09 wrote:Is K a positive number?
(1) |K^3| + 1 > K.
(2) K + 1 > |K^3|.
[spoiler]OA E[/spoiler]
Source: gmatclub
- VK
I will (Learn. Recognize. Apply)
I will (Learn. Recognize. Apply)
- sanju09
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vk_vinayak wrote:Do you have a solution for this? I tried but it was very lengthy. If only some one could help with efficient solution.sanju09 wrote:Is K a positive number?
(1) |K^3| + 1 > K.
(2) K + 1 > |K^3|.
[spoiler]OA E[/spoiler]
Source: gmatclub
(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
Sanjeev K Saxena
Quantitative Instructor
The Princeton Review - Manya Abroad
Lucknow-226001
www.manyagroup.com
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In the question it is not mentioned whether k is integer. So, we should not assume it to be an integer.sanju09 wrote:
Is K a positive number?
(1) |K^3| + 1 > K.
(2) K + 1 > |K^3|.
OA E
Source: gmatclub
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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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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If you are really good at plotting graphs then you can solving by plotting the same.
Is K a positive number?
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
Answer E
Experts - Correct me if I am wrong.
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
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(2)K + 1 > |K^3|.
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.From I and II
Answer E
Experts - Correct me if I am wrong.
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K may be an integer, and the assumption serves the purpose as well.Anurag@Gurome wrote:In the question it is not mentioned whether k is integer. So, we should not assume it to be an integer.sanju09 wrote:
Is K a positive number?
(1) |K^3| + 1 > K.
(2) K + 1 > |K^3|.
OA E
Source: gmatclub
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
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
Sanjeev K Saxena
Quantitative Instructor
The Princeton Review - Manya Abroad
Lucknow-226001
www.manyagroup.com
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