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

 It is currently 22 May 2019, 03:54 ### 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. ### Request Expert Reply # p and q are positive integers such that 2p -10 > -q, and 3q -20 < -p.

 new topic post reply Question banks Downloads My Bookmarks Reviews Important topics
Author Message
Manager  G
Joined: 13 May 2017
Posts: 107
Location: Finland
Concentration: Accounting, Entrepreneurship
GMAT 1: 530 Q42 V22 GPA: 3.14
WE: Account Management (Entertainment and Sports)
p and q are positive integers such that 2p -10 > -q, and 3q -20 < -p.  [#permalink]

### Show Tags

4 00:00

Difficulty:   95% (hard)

Question Stats: 35% (01:43) correct 65% (02:30) wrong based on 93 sessions

### HideShow timer Statistics

p and q are positive integers such that 2p -10 > -q, and 3q -20 < -p. If m is the minimum possible value of p and n is the maximum possible value of q, then which of the following pairs accurately represents (m, n)

A (1, 6)
B (6, 2)
C (3, 6)
D (3, 5)
E No such values exist.
Manager  B
Joined: 02 Oct 2018
Posts: 57
Re: p and q are positive integers such that 2p -10 > -q, and 3q -20 < -p.  [#permalink]

### Show Tags

rencsee wrote:
p and q are positive integers such that 2p -10 > -q, and 3q -20 < -p. If m is the minimum possible value of p and n is the maximum possible value of q, then which of the following pairs accurately represents (m, n)

A (1, 6)
B (6, 2)
C (3, 6)
D (3, 5)
E No such values exist.

Could some pls post the solution?
VP  D
Joined: 09 Mar 2016
Posts: 1284
p and q are positive integers such that 2p -10 > -q, and 3q -20 < -p.  [#permalink]

### Show Tags

1
rencsee wrote:
p and q are positive integers such that 2p -10 > -q, and 3q -20 < -p. If m is the minimum possible value of p and n is the maximum possible value of q, then which of the following pairs accurately represents (m, n)

A (1, 6)
B (6, 2)
C (3, 6)
D (3, 5)
E No such values exist.

GMATPrepNow Brent, i applied your concept

KEY CONCEPT: If the inequality signs of two inequalities are facing the SAME DIRECTION, then we can ADD those inequalities to create a new inequality.

3q -20 < -p
2p -10 > -q multiply both sides by -1 so we get -2p+10<q

so now we have

3q -20 < -p
-2p+10<q ---- > rearrange -q+10<-2p

add both inequelities

3q -20 < -p
-q+10<-2p

after addition we have

2q-10<-3p

so if i plug in any of the options below, where p is first term and q is second term i.e. 1 = p, q=6 , so non of the options is TRUE

A (1, 6) 1 = p, q=6
B (6, 2) 6 = p, q=2
C (3, 6) 3 = p, q=6
D (3, 5) 3 = p, q=5

whats wrong with my reasoning now Manager  G
Joined: 14 Jun 2018
Posts: 223
Re: p and q are positive integers such that 2p -10 > -q, and 3q -20 < -p.  [#permalink]

### Show Tags

3
2p -10 > -q
=> 2p + q > 10 --- 1

3q -20 < -p
=> -p - 3q > -20 -- 2

Make coefficient of 1 & 2 same for a single variable

2p+ q > 10
-2p - 6q > - 40

-5q > - 30
q < 6 ----- 3

Now ,
m = minimum possible value of p
n = maximum possible value of q

Maximum possible value of q is 5 = n

Put 5 in the equation 1
=> 2p + 5 > 10
p >2.5

Minimum possible value of p is 3 = m

(3,5) is the required answer.

D
Manager  G
Joined: 04 Oct 2018
Posts: 167
Location: Viet Nam
Re: p and q are positive integers such that 2p -10 > -q, and 3q -20 < -p.  [#permalink]

### Show Tags

1
rencsee wrote:
p and q are positive integers such that 2p -10 > -q, and 3q -20 < -p. If m is the minimum possible value of p and n is the maximum possible value of q, then which of the following pairs accurately represents (m, n)

A (1, 6)
B (6, 2)
C (3, 6)
D (3, 5)
E No such values exist.

----
2p-10 > -q => 2p + q > 10 (*)
3q-20 <-p => -3q -p > -20 => -2p - 6q > -40 (**)
Add (*) and (**) we have: -5q > -30 => q<6 => MAX q = 5 (n=5)

2p + q > 10 & q<6 => 2p + q - q > 10-6 = 4 => 2p > 4 then p > 2

FINALLY we have q<6 (MAX q = 5 =n) & p>2 then D satisfies this condition.

***********If P>Q and R<S then (P-R)>(Q-S)
_________________
"It Always Seems Impossible Until It Is Done"
CEO  V
Joined: 12 Sep 2015
Posts: 3722
Location: Canada
Re: p and q are positive integers such that 2p -10 > -q, and 3q -20 < -p.  [#permalink]

### Show Tags

1
Top Contributor
dave13 wrote:
rencsee wrote:
p and q are positive integers such that 2p -10 > -q, and 3q -20 < -p. If m is the minimum possible value of p and n is the maximum possible value of q, then which of the following pairs accurately represents (m, n)

A (1, 6)
B (6, 2)
C (3, 6)
D (3, 5)
E No such values exist.

GMATPrepNow Brent, i applied your concept

KEY CONCEPT: If the inequality signs of two inequalities are facing the SAME DIRECTION, then we can ADD those inequalities to create a new inequality.

3q -20 < -p
2p -10 > -q multiply both sides by -1 so we get -2p+10<q

so now we have

3q -20 < -p
-2p+10<q ---- > rearrange -q+10<-2p

add both inequelities

3q -20 < -p
-q+10<-2p

after addition we have

2q-10<-3p

so if i plug in any of the options below, where p is first term and q is second term i.e. 1 = p, q=6 , so non of the options is TRUE

A (1, 6) 1 = p, q=6
B (6, 2) 6 = p, q=2
C (3, 6) 3 = p, q=6
D (3, 5) 3 = p, q=5

whats wrong with my reasoning now I have highlighted the error above, in green.

If we rearrange -2p+10<q, we don't get -q+10<-2p

Cheers,
Brent
_________________
VP  D
Joined: 09 Mar 2016
Posts: 1284
Re: p and q are positive integers such that 2p -10 > -q, and 3q -20 < -p.  [#permalink]

### Show Tags

thanks a lot Brent . have an awesome weekend !  Re: p and q are positive integers such that 2p -10 > -q, and 3q -20 < -p.   [#permalink] 30 Nov 2018, 13:53
Display posts from previous: Sort by

# p and q are positive integers such that 2p -10 > -q, and 3q -20 < -p.

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

#### MBA Resources  