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# PROBLEM 2

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PROBLEM 2 [#permalink]  14 Oct 2018, 08:35
$$p + |k| > |p| + k$$

 Quantity A Quantity B p k
Director
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Re: PROBLEM 2 [#permalink]  14 Oct 2018, 11:27
ruposh6240 wrote:
p + |k| > |p| + k
21.
Quantity A
p
Quantity B
k

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Re: PROBLEM 2 [#permalink]  15 Oct 2018, 06:36
Expert's post

We have $$p + |k| > |p| + k$$

rearranging it we get $$p - |p| > k - |k|$$

If p and k are both positive then $$p - |p| = k - |k|=0$$

However, if p and k are both negative then $$p - |p|= 2p$$ and $$k - |k| =2k$$ So $$p > k$$.

Example p= -2 and k =-5 $$-2 + |-5| > |2| -5$$

If p is positive and k is negative then $$p - |p| > k - |k|$$ or $$0 > k - |k|$$ or $$k <0$$. The inequality still holds.

Finally, if p is negative and k is positive $$p - |p| > 0$$ or $$p > 0$$ which is not possible as p is negative.

Hence p has to be greater than k. Option A is correct.
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Re: PROBLEM 2   [#permalink] 15 Oct 2018, 06:36
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