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

It is currently 18 Jul 2018, 09:38

Close

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
Your Progress

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

Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.

Close

Request Expert Reply

Confirm Cancel

If p>5 and q>-2, then which of the following is always true?

  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics  
Author Message
TAGS:

Hide Tags

Intern
Intern
avatar
B
Joined: 23 Mar 2014
Posts: 16
If p>5 and q>-2, then which of the following is always true? [#permalink]

Show Tags

New post Updated on: 04 Jan 2018, 19:27
4
00:00
A
B
C
D
E

Difficulty:

  65% (hard)

Question Stats:

50% (01:10) correct 50% (00:53) wrong based on 105 sessions

HideShow timer Statistics

If p > 5 and q > -2, then which of the following is always true?

A) pq > -10
B) pq < -10
C) -p < 2q
D) -p > 2q
E) pq > 10

Originally posted by Rocky1304 on 03 Jan 2018, 23:53.
Last edited by Bunuel on 04 Jan 2018, 19:27, edited 1 time in total.
Edited the question.
Expert Post
2 KUDOS received
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 47080
If p>5 and q>-2, then which of the following is always true? [#permalink]

Show Tags

New post 04 Jan 2018, 01:41
2
Rocky1304 wrote:
If p > 5 and q > -2, then which of the following is always true?

A) pq > -10
B) pq < -10
C) -p < 2q
D) -p > 2q
E) pq > 10


If p > 5 and q > -2, then which of the following is always true?

A) pq > -10. If p = 100 and q = -1, then pq = -100 < -10. So, this option is not always true.

B) pq < -10. If p = 100 and q = 0, then pq = 0 > -10. So, this option is not always true.

C) -p < 2q. This is the same as p + 2q > 0.

We have p > 5 and 2q > -4 (multiplied by 2)
Add: p + 2q > 1. So, p + 2q is greater than 0.
So, this option is always true.

D) -p > 2q. Above we got that -p < 2q, so this is not true.

E) pq > 10. If p = 100 and q = 0, then pq = 0 < 10. So, this option is not always true.

Answer: C.
_________________

New to the Math Forum?
Please read this: Ultimate GMAT Quantitative Megathread | All You Need for Quant | PLEASE READ AND FOLLOW: 12 Rules for Posting!!!

Resources:
GMAT Math Book | Triangles | Polygons | Coordinate Geometry | Factorials | Circles | Number Theory | Remainders; 8. Overlapping Sets | PDF of Math Book; 10. Remainders | GMAT Prep Software Analysis | SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) | Tricky questions from previous years.

Collection of Questions:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


What are GMAT Club Tests?
Extra-hard Quant Tests with Brilliant Analytics

Expert Post
GMAT Club Legend
GMAT Club Legend
User avatar
P
Joined: 16 Oct 2010
Posts: 8127
Location: Pune, India
Re: If p>5 and q>-2, then which of the following is always true? [#permalink]

Show Tags

New post 04 Jan 2018, 11:39
Rocky1304 wrote:
If p > 5 and q > -2, then which of the following is always true?

A) pq > -10
B) pq < -10
C) -p < 2q
D) -p > 2q
E) pq > 10


p > 5
p = 6, 7, 8, 9, 10, 11, 12, ...
q > -2
q = -1, 0, 1, 2, 3, 4, 5, ...

A) pq > -10
If p = 11, q = -1, then pq = -11. Not always true.

B) pq < -10
If p = 6, q = -1, then pq = -6. Not always true.

E) pq > 10
If p = 6, q = 0, then pq = 0. Not always true.

C) -p < 2q
p is positive. Divide both sides by 2p to get -1/2 < q/p
Looks like it might be true based on some values of p and q we have taken above. Let's hold on to it and check the leftover option.

D) -p > 2q
Divide both sides by 2p to get -1/2 > q/p
If q = -1 and p = 6, we get -1/2 > -1/6 which is not true.

So (C) must always be true. We don't need to worry about non-integer values of p and q.
_________________

Karishma
Private Tutor for GMAT
Contact: bansal.karishma@gmail.com

Director
Director
User avatar
S
Joined: 08 Jun 2015
Posts: 518
Location: India
GMAT 1: 640 Q48 V29
GMAT 2: 700 Q48 V38
Premium Member CAT Tests
Re: If p>5 and q>-2, then which of the following is always true? [#permalink]

Show Tags

New post 16 Apr 2018, 01:50
+1 for option C.
In addition to solutions above , one could also arrive at C in the following way:
-p<-5; -2q<4
-p-2q<-1 --> -p<2q-1 which means , -p<2q.
Hence option C
_________________

" The few , the fearless "

Re: If p>5 and q>-2, then which of the following is always true?   [#permalink] 16 Apr 2018, 01:50
Display posts from previous: Sort by

If p>5 and q>-2, then which of the following is always true?

  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics  

Events & Promotions

PREV
NEXT


GMAT Club MBA Forum Home| About| Terms and Conditions and Privacy Policy| GMAT Club Rules| Contact| Sitemap

Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne

Kindly note that the GMAT® test is a registered trademark of the Graduate Management Admission Council®, and this site has neither been reviewed nor endorsed by GMAC®.