GMAT Question of the Day - Daily to your Mailbox; hard ones only

 It is currently 23 Oct 2019, 13:56

### GMAT Club Daily Prep

#### Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History

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

Author Message
TAGS:

### Hide Tags

Intern
Joined: 29 Dec 2018
Posts: 31
If 0 < q ≤ p, then for all possible values of p and q, p must be great  [#permalink]

### Show Tags

04 Mar 2019, 05:28
4
00:00

Difficulty:

65% (hard)

Question Stats:

42% (01:49) correct 58% (02:11) wrong based on 31 sessions

### HideShow timer Statistics

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. $$\frac{pq+q^2}{p}$$
Manager
Joined: 21 Feb 2019
Posts: 125
Location: Italy
Re: If 0 < q ≤ p, then for all possible values of p and q, p must be great  [#permalink]

### Show Tags

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.
_________________
If you like my post, Kudos are appreciated! Thank you.

MEMENTO AUDERE SEMPER
Re: If 0 < q ≤ p, then for all possible values of p and q, p must be great   [#permalink] 04 Mar 2019, 06:43
Display posts from previous: Sort by