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If P + |k| > |P| + k then which of the following is true of Inqual

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If P + |k| > |P| + k then which of the following is true of Inqual [#permalink]

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If P + |k| > |P| + k then which of the following is true of Inequalities ?

A. P=K
B. P<=k
C. P<k
D. P>k
E. Can't determined

Again strucked with Inequalities ? Need Help.

Bunuel and VeritasPrepKarishma ?
[Reveal] Spoiler: OA

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Re: If P + |k| > |P| + k then which of the following is true of Inqual [#permalink]

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New post 21 Nov 2014, 08:33
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I am neither of two you asked to help, but I am retaking the GMAT soon, so here is how I approached this problem:

Assuming that P and k and both sides have the absolute value, the only way we will have an inequality is when when one or more numbers have negative signs, and thus change their value when an absolute value is taken. We already know that P on the left side equals |P| on the right side because the left side of the inequality is larger (and therefore, there is no way P is negative). So, what truly shifts the equation here is the sign flip when we take an absolute value of k. In other words, k must be negative, otherwise |k| would be equal to k and P+|k| would be equal to |P|+k. Hence, P (which is positive) must be larger than k (which is negative).
I know it's somewhat conceptual and may not be easy to follow, but that's how I looked at it.

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Re: If P + |k| > |P| + k then which of the following is true of Inqual [#permalink]

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New post 21 Nov 2014, 12:12
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sunny3011 wrote:
If P + |k| > |P| + k then which of the following is true of Inequalities ?

A. P=K
B. P<=k
C. P<k
D. P>k
E. Can't determined

Again strucked with Inequalities ? Need Help.

Bunuel and VeritasPrepKarishma ?


let's assume that p=k and k>0

then P + |k| > |P| + k becomes

k+k>k+k , 2k>2k, which is false. hence this inequality doesn't hold good.

lets try p=k, and k<0

-k+k>k-k or 0>0 which is false. hence option a is out.

similarly we can reject option b, because of the equality sign

let's try option C

P<k

let's pick numbers, say p=2 and k=8
then we have

2+8>2+8
which doesn't hold valid.

lets say p=-1 and k=1

then -1+1>1+1
0>2 , which is false.

say p=-2 and k=-1

then, -2+1> 2-1
-1>1, which is again false. hence option c is out.

let's try option D

P>k

p=3 and k=-1
3+1>3-1
4>2, bingo.

hence answer is option D

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Re: If P + |k| > |P| + k then which of the following is true of Inqual [#permalink]

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New post 22 Nov 2014, 02:42
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given that P + |k| > |P| + k.................1

lets square both sides : p^2+k^2+2p|k| > p^2+k^2+2k|p|

so, p|k|>k|p| ;
Clearly, the above statement is valid only if p>k

Answer is D

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Re: If P + |k| > |P| + k then which of the following is true of Inqual [#permalink]

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sunny3011 wrote:
If P + |k| > |P| + k then which of the following is true of Inequalities ?

A. P=K
B. P<=k
C. P<k
D. P>k
E. Can't determined

Again strucked with Inequalities ? Need Help.

Bunuel and VeritasPrepKarishma ?


There are four potential scenarios.
1. P<0 and K<0
2. P<0 and K>0
3. P>0 and K<0
4. P>0 and K >0

Since |P| + K is less than zero, then P must be greater than zero, or else the statement would be invalid: [negative] + [positive] is never greater than [positive] + [positive]. If P>0 then K must be less than zero, or else the statement would be invalid: [positive] + [positive] equals [positive] + [positive].

Remember absolute value of some expression is always non-negative.

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If P + |k| > |P| + k then which of the following is true of Inqual [#permalink]

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New post 11 Jul 2015, 02:44
Say p >0 and K>0.
then p+k>p+k, doesn't hold.

Say p<0 and k<0.

then P-K > -P+K----> 2p>2k------> P>K .

we can try for different values. P>0 and K<0 or P<0 and K>0, but we can not get relation we wanted.

Ans. D

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Re: If P + |k| > |P| + k then which of the following is true of Inqual [#permalink]

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New post 13 Jul 2015, 03:24
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sunny3011, could you please mention the source ?

Also, is this a may be true question ?. If it is a must be true question like all the other gmat questions the answer would go only one way either true or false, but this question is bit different.

For ex: if we choose p=3 and k=2, then the main equation will not hold good, as it will be equal. And there is no condition as such to pick the numbers.

So either the OA should be E or the question is not of the Gmat standards or i might be entirely wrong. Bunuel, could you help solve this question.

Thanks.

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Re: If P + |k| > |P| + k then which of the following is true of Inqual [#permalink]

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New post 13 Jul 2015, 03:49
Swaroopdev wrote:
sunny3011, could you please mention the source ?

Also, is this a may be true question ?. If it is a must be true question like all the other gmat questions the answer would go only one way either true or false, but this question is bit different.

For ex: if we choose p=3 and k=2, then the main equation will not hold good, as it will be equal. And there is no condition as such to pick the numbers.

So either the OA should be E or the question is not of the Gmat standards or i might be entirely wrong. Bunuel, could you help solve this question.

Thanks.


A must be true question will always call it out as must be true. For this question, if you can find a set of values for P,K that satisfy the given inequality, you have your answer.

I tried the following:

P,K = (-4,3), (-4,-3), (4,-3) (this was the only one satisfying the given inequality and gave P>K). Thus D is the correct answer.

From the given inequality, it is clear that you will have 4 cases (I agree that there are no restriction on whether the numbers need to be integers. But luckily for this question, integers were able to satisfy the given inequality. Had this question called it out as a "must be true question", I would have been left with D and E and then once I had checked for integers, I would have to go to fractions to rule out 1 of the 2 (D orE)):

P>0, K>0
P>0, K<0
P<0,K>0
P<, K<0

Once you realise this, it becomes a matter of picking the values and checking with what values does the given inequality hold true.

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If P + |k| > |P| + k then which of the following is true of Inqual [#permalink]

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New post 13 Jul 2015, 04:39
Engr2012 My doubt is regarding the ambiguity of the question not the method to solve the actual question. I agree of all options only D can be proven right but if it can also be proven wrong, then perhaps the best answer is option E don't you think ? Gmat standard questions doesn't allow for ambiguity in the options, there is always a definite answer which will hold good as per the question.

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Re: If P + |k| > |P| + k then which of the following is true of Inqual [#permalink]

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New post 25 Jul 2015, 11:11
I'm not sure if it is the correct way to solve this, but I did get the correct answer.

Rearranging the inequality, we get: P+|P| > k+|k|

There are 4 states that could exist:
P+P>k+k --> 2P>2k --> P>k, answer choice D
P-P>k+k --> 0>2k not in the answer choices
P+P>k-k --> 2P>0 not in the answer choices
P-P>k-k --> 0>0 not possible

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Re: If P + |k| > |P| + k then which of the following is true of Inqual [#permalink]

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jgcanada wrote:
I'm not sure if it is the correct way to solve this, but I did get the correct answer.

Rearranging the inequality, we get: P+|P| > k+|k|

There are 4 states that could exist:
P+P>k+k --> 2P>2k --> P>k, answer choice D
P-P>k+k --> 0>2k not in the answer choices
P+P>k-k --> 2P>0 not in the answer choices
P-P>k-k --> 0>0 not possible


You were lucky to get to correct answer but the correct way is to look at 4 cases:

If p>0, k>0 --> |p| =p , |k|=k
If p>0, k<0 --> |p| =p , |k|=-k
If p<0, k>0 --> |p| =-p , |k|=k
If p<0, k<0 --> |p| =-p , |k|=-k

Once you apply the above cases, you will see that cases 2 and provide you p>k. Thus, D is the correct answer.

You can also get to the correct answer by testing a few values as shown in my earlier post: if-p-k-p-k-then-which-of-the-following-is-true-of-inqual-188860.html#p1548563

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Re: If P + |k| > |P| + k then which of the following is true of Inqual [#permalink]

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akumar5 wrote:
given that P + |k| > |P| + k.................1

lets square both sides : p^2+k^2+2p|k| > p^2+k^2+2k|p|

so, p|k|>k|p| ;
Clearly, the above statement is valid only if p>k

Answer is D


In equality we can square only when both the sides are +ve. How could you deduce that both sides are +ve?

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Re: If P + |k| > |P| + k then which of the following is true of Inqual [#permalink]

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New post 12 Aug 2015, 09:31
If P + |k| > |P| + k then which of the following is true of Inequalities ?

A. P=K
B. P<=k
C. P<k
D. P>k
E. Can't determined


1. Rearrange constraint:

P - k > |P| - |k|

4 cases:
++ (p positive, k positive)
+-
-+
--

++ =>P - k > P - k => impossible

+- => P - k > P - (-k) => P - k > P + k, for P > 0, k < 0

remove the P from both sides, and we are left with -k > k, for k < 0 which is always true.

no need to continue, since positive P & negative k always satisfies constraint, we know that P > k is correct

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If P + |k| > |P| + k then which of the following is true of Inqual [#permalink]

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New post 15 Aug 2015, 04:21
sunny3011 wrote:
If P + |k| > |P| + k then which of the following is true of Inequalities ?

A. P=K
B. P<=k
C. P<k
D. P>k
E. Can't determined

Again strucked with Inequalities ? Need Help.

Bunuel and VeritasPrepKarishma ?

option D is wrong
when p =3 and k=2
3+2 = 3+2
Hence, the correct option is E
please check your answer.
It is true when p=1 and k=-1

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If P + |k| > |P| + k then which of the following is true of Inqual [#permalink]

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New post 16 Aug 2015, 01:21
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Here's how i approached the problem.
Attachment:
Inequality_Matrix.PNG
Inequality_Matrix.PNG [ 5.93 KiB | Viewed 5145 times ]

For case 3 and 4, the inequality given in the problem is true and in both the cases, P>K.
Answer D.

Please note: the question clearly states that, "If P + |k| > |P| + k is true, which of the following inequalities is true" and not the other way round. So you should not expect all the values that satisfy the right answer choice to satisfy the given statement as well.

Hope it helps.

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Re: If P + |k| > |P| + k then which of the following is true of Inqual [#permalink]

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New post 06 Sep 2015, 02:46
sunny3011 wrote:
If P + |k| > |P| + k then which of the following is true of Inequalities ?

A. P=K
B. P<=k
C. P<k
D. P>k
E. Can't determined

Again strucked with Inequalities ? Need Help.

Bunuel and VeritasPrepKarishma ?


HI,

p + |K| > |p|+ K

Can be written as
p-|p|>k -|K|

now think of this logically
This can be possible onlly if both p and k are negative
because if they will be postive
p-|p| will be zero , same the case with k-|k|

so p and k are negative
and now for them to hold this inequality
P>K
Try plugging in some numbers and you will get this.

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Re: If P + |k| > |P| + k then which of the following is true of Inqual [#permalink]

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sunny3011 wrote:
If P + |k| > |P| + k then which of the following is true of Inequalities ?

A. P=K
B. P<=k
C. P<k
D. P>k
E. Can't determined

Again strucked with Inequalities ? Need Help.

Bunuel and VeritasPrepKarishma ?


This is how I solved:
P + |k| > |P| + k
=> P - |P| > k - |k|
=> Now, if P & K is positive, then |P| = P & |k| = k => P -P > k - k => 0 > 0 => Invalid scenario
This can only be possible only if both P & k are negative
=> P - (-P) > k - (-k)
=> 2P > 2k
=> P > k

Option D
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If P + |k| > |P| + k then which of the following is true of Inqual [#permalink]

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New post 13 Sep 2015, 06:58
neeti041190 wrote:
akumar5 wrote:
given that P + |k| > |P| + k.................1

lets square both sides : p^2+k^2+2p|k| > p^2+k^2+2k|p|

so, p|k|>k|p| ;
Clearly, the above statement is valid only if p>k

Answer is D


In equality we can square only when both the sides are +ve. How could you deduce that both sides are +ve?


Hey there,

The inequality holds true only for p>k .One can get this relation by thorough inspection of each scenarios such as
1) k>p
2)k=p
3)p>k

Each of the above three cases further extends to four different scenarios in terms of -ve,+ve and equal values for k & p.
One can evaluate these cases by placing different values for p & k in the inequality given.
For instance : Lets check p>k
p=2 & k=-1
The inequality holds true.
Similarly, as you go through each cases, you will find that only the above relation(p>k) satisfies the inequality of the three cases.

Let me thank you for pointing out the error ,which i accidentally put into my previous solution. Undoubtedly,You have raised a valid point & indeed its true.
Hope my current solution helps .

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Re: If P + |k| > |P| + k then which of the following is true of Inqual [#permalink]

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New post 03 Oct 2015, 22:44
p + |K| > |p| + K can be arranged into |K| - K > |p| - p

|K| - K > |p| - p implies that K has to be negative (so that |K| - - K is a greater number than |k|) and P has to be positive (so that |p| - p is a lower number than |p|) in order for the equation to be valid.

Given K is negative and P is positive, K<P

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Re: If P + |k| > |P| + k then which of the following is true of Inqual [#permalink]

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New post 29 Oct 2016, 10:59
sunny3011 wrote:
If P + |k| > |P| + k then which of the following is true of Inequalities ?

A. P=K
B. P<=k
C. P<k
D. P>k
E. Can't determined

Again strucked with Inequalities ? Need Help.

Bunuel and VeritasPrepKarishma ?


from stem

p-/p/ > k-/k/ , p-/p/ = 0 if p is +ve and 2p if p is -ve , k-/k/ = 0 if k is +ve and 2k if k is -ve , but since we cant have 0>0 therefore

p is +ve and k -ve or or p is -ve and k -ve but 2p>2k in either case p>k

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Re: If P + |k| > |P| + k then which of the following is true of Inqual   [#permalink] 29 Oct 2016, 10:59

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