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p + |k| > |p| + k

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p + |k| > |p| + k [#permalink] New post 09 Aug 2018, 03:44
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Question Stats:

64% (00:57) correct 35% (00:58) wrong based on 126 sessions
\(p + |k| > |p| + k\)

Quantity A
Quantity B
p
k


A) Quantity A is greater.
B) Quantity B is greater.
C) The two quantities are equal.
D) The relationship cannot be determined from the information given.

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[Reveal] Spoiler: OA

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Re: p + |k| > |p| + k [#permalink] New post 09 Aug 2018, 15:27
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Carcass wrote:
\(p + |k| > |p| + k\)

Quantity A
Quantity B
p
k


A) Quantity A is greater.
B) Quantity B is greater.
C) The two quantities are equal.
D) The relationship cannot be determined from the information given.

Kudos for R.A.E



Given ,

\(p + |k| > |p| + k\)


Both sides include the same variable but p + |k| is greater. Why ?

let assume some values.

p = 5 / -5

k = - 100

In this case and only in this case inequality is true.

Thus p is greater than k.

The best answer is A.
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Re: p + |k| > |p| + k [#permalink] New post 04 Mar 2020, 03:15
Can someone explain some more?
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Re: p + |k| > |p| + k [#permalink] New post 04 Mar 2020, 11:20
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Expert's post
Carcass wrote:
\(p + |k| > |p| + k\)

Quantity A
Quantity B
p
k


A) Quantity A is greater.
B) Quantity B is greater.
C) The two quantities are equal.
D) The relationship cannot be determined from the information given.

Kudos for R.A.E


Warning: This is a long solution, but there are some key properties/strategies that some students may find useful

Useful properties:
#1: If x is POSITIVE, then |x| = x
#2: If x is NEGATIVE, then |x| = -x


For example, if x = 3, then |x| = |3| = 3 = x
Conversely, if x = -3, then |x| = |-3| = 3 = -(-3) = -x

Okay, first notice that p and k cannot be equal.
IF it were the case that p = k, then we can replace p with k to get: \(k + |k| > |k| + k\)
This makes no sense. So, we can be sure that p and k are not equal

Now let's examine 4 possible cases:

case i: p is POSITIVE and k is POSITIVE
Applying property #1, we get: \(p + k > p + k\)
This makes no sense. \(p + k = p + k\)
So, case i is impossible.

case ii: p is POSITIVE and k is NEGATIVE
Applying properties #1 and 2, we get: \(p + (-k) > p + k\)
Subtract p from both sides of the inequality to get: \(-k > k\)
Add k to both sides to get: \(0 > 2k\)
Since k is NEGATIVE in this case, the inequality \(0 > 2k\) is true.
So, case ii is possible

case iii: p is NEGATIVE and k is POSITIVE
Applying properties #1 and 2, we get: \(p + k > (-p) + k\)
Subtract k from both sides of the inequality to get: \(p > -p\)
Add p to both sides to get: \(2p > 0\)
Since p is NEGATIVE in this case, the inequality \(2p > 0\) is NOT true.
So, case iii is impossible.

case iv: p is NEGATIVE and k is NEGATIVE
Applying property #2, we get: \(p + (-k) > (-p) + k\)
Add p to both sides to get: \(2p - k > k\)
Add k to both sides to get: \(2p > 2k\)
Divide both sides by 2 to get: \(p > k\)
This tells us that, if p is NEGATIVE and k is NEGATIVE, then \(p > k\)
case iv is possible

At this point, we can see that there are only two possible cases, and for each case, we can be certain that \(p > k\)

Answer: A

Cheers,
Brent
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Re: p + |k| > |p| + k [#permalink] New post 25 May 2020, 09:44
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another way could be to square both sides of the inequality

you would be left with P|K| > |P|K.....this can only be true when P>K.....

Therefore A..

Cheers.
Re: p + |k| > |p| + k   [#permalink] 25 May 2020, 09:44
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