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# If 0 < q ≤ p, then for all possible values of p and q, p must be great

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Intern
Joined: 29 Dec 2018
Posts: 17
If 0 < q ≤ p, then for all possible values of p and q, p must be great  [#permalink]

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04 Mar 2019, 05:28
2
00:00

Difficulty:

55% (hard)

Question Stats:

27% (00:56) correct 73% (02:04) wrong based on 15 sessions

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If 0 < q ≤ p, then for all possible values of p and q, p must be greater than which of the following?

A. $$\frac{1}{p+q}$$

B. $$\frac{1}{p-q}$$

C. $$\frac{p-q}{p+q}$$

D. $$\frac{p^2-q^2}{p+q}$$

E. $$\frac{pq+q^2}{p}$$
Intern
Joined: 21 Feb 2019
Posts: 36
Re: If 0 < q ≤ p, then for all possible values of p and q, p must be great  [#permalink]

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04 Mar 2019, 06:43
To solve this quickly you should be able to recognize as soon as possible that:

$$\frac{p^2 - q^2}{p + q} = \frac{(p + q)(p - q)}{p + q} = p - q$$

$$p > p - q$$ everytime. To be accurate,

$$- q < 0$$

$$q > 0$$

Verified.

Plug-in strategy is good to discard first options IMO.
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Re: If 0 < q ≤ p, then for all possible values of p and q, p must be great   [#permalink] 04 Mar 2019, 06:43
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