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

It is currently 16 Dec 2018, 11:52

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
Events & Promotions in December
PrevNext
SuMoTuWeThFrSa
2526272829301
2345678
9101112131415
16171819202122
23242526272829
303112345
Open Detailed Calendar
  • Free GMAT Prep Hour

     December 16, 2018

     December 16, 2018

     03:00 PM EST

     04:00 PM EST

    Strategies and techniques for approaching featured GMAT topics
  • FREE Quant Workshop by e-GMAT!

     December 16, 2018

     December 16, 2018

     07:00 AM PST

     09:00 AM PST

    Get personalized insights on how to achieve your Target Quant Score.

If P and Q are non-zero integers, is the equation Py + Qx = 7, exactly

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

Hide Tags

DS Forum Moderator
avatar
P
Joined: 21 Aug 2013
Posts: 1412
Location: India
Premium Member
If P and Q are non-zero integers, is the equation Py + Qx = 7, exactly  [#permalink]

Show Tags

New post 04 Jul 2018, 22:34
00:00
A
B
C
D
E

Difficulty:

  55% (hard)

Question Stats:

45% (02:08) correct 55% (01:22) wrong based on 14 sessions

HideShow timer Statistics

If P and Q are non-zero integers, is the equation Py + Qx = 7, exactly the same equation as 9x - 6y = 21 ?

(1) P + Q = 1

(2) P*Q = -6
examPAL Representative
User avatar
G
Joined: 07 Dec 2017
Posts: 841
Re: If P and Q are non-zero integers, is the equation Py + Qx = 7, exactly  [#permalink]

Show Tags

New post 04 Jul 2018, 22:44
amanvermagmat wrote:
If P and Q are non-zero integers, is the equation Py + Qx = 7, exactly the same equation as 9x - 6y = 21 ?

(1) P + Q = 1

(2) P*Q = -6


Two equations are equal if and only if all of their coefficients are equal.
We'll look for statements that give us this information, a Logical approach.

Rewriting our equations so they both equal 7 gives:
Py + Qx = 7
3x - 2y = 7

So our equations are equal when P = -2 and Q = 3.

(1) One equation, two variables --> infinite solutions.
Insufficient.

(2) One equation, two variables --> infinite solutions.
Insufficient

Combined:
Two equations, two variables usually gives one unique solution but in this case both of our equations are symmetrical.
So, while we can find the right numbers (they happen to be 3 and -2), we don't know which is P and which is Q.
Insufficient

(E) is our answer.
_________________

Image
Sign up for 7-day free trial
Image

Director
Director
User avatar
P
Status: Learning stage
Joined: 01 Oct 2017
Posts: 931
WE: Supply Chain Management (Energy and Utilities)
Premium Member
If P and Q are non-zero integers, is the equation Py + Qx = 7, exactly  [#permalink]

Show Tags

New post 05 Jul 2018, 04:02
amanvermagmat wrote:
If P and Q are non-zero integers, is the equation Py + Qx = 7, exactly the same equation as 9x - 6y = 21 ?

(1) P + Q = 1

(2) P*Q = -6


Given, Py + Qx = 7----------(a)
& 9x - 6y = 21 Or, 3x + -(2)y =7 ---(b)

Equating x & y co-efficient in (a) and (b) we have P=-2 & Q=3

So, when P=-2 and Q=3, both the equations become same.

Re-phrased Question stem:- Is P=-2 ,Q=3 ?

Statement-2
P + Q = 1
When P=-2 & Q=3, our answer to question stem is Yes, but there are 'n' number of combinations for which P+Q=1.
Hence, insufficient.

Statement-2
P*Q=-6
When P=-2 & Q=3, our answer to question stem is Yes, but there are 'n' number of combinations for which P*Q=-6.
Hence, insufficient.

(1)+(2), we have

\((P-Q)^2=(P+Q)^2-4*PQ\)

we know the value of P+Q & PQ from st1 & st2 respectively, therefore, we can calculate P-Q & subsequently, value of P & Q can be determined.

So, (\(P-Q)^2=1^2-4*(-6)=1+24=25\)

So, P-Q=5 Or, P-Q=-5

P-Q=5 & P+Q=1. yields P=3, Q=-2...In this case answer to question is No.

P-Q=-5 & P+Q=1. yields P=-2, Q=3...In this case answer to question is Yes.

So, insufficient.

Ans (E)
_________________

Regards,

PKN

Rise above the storm, you will find the sunshine

GMAT Club Bot
If P and Q are non-zero integers, is the equation Py + Qx = 7, exactly &nbs [#permalink] 05 Jul 2018, 04:02
Display posts from previous: Sort by

If P and Q are non-zero integers, is the equation Py + Qx = 7, exactly

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


Copyright

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®.