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

 It is currently 11 Dec 2019, 22:19

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

Author Message
TAGS:

### Hide Tags

Retired Moderator
Joined: 22 Aug 2013
Posts: 1409
Location: India
If P and Q are non-zero integers, is the equation Py + Qx = 7, exactly  [#permalink]

### Show Tags

04 Jul 2018, 23:34
2
00:00

Difficulty:

85% (hard)

Question Stats:

33% (01:49) correct 67% (01:40) wrong based on 30 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
Joined: 07 Dec 2017
Posts: 1155
Re: If P and Q are non-zero integers, is the equation Py + Qx = 7, exactly  [#permalink]

### Show Tags

04 Jul 2018, 23:44
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

_________________
Director
Status: Learning stage
Joined: 01 Oct 2017
Posts: 990
WE: Supply Chain Management (Energy and Utilities)
If P and Q are non-zero integers, is the equation Py + Qx = 7, exactly  [#permalink]

### Show Tags

05 Jul 2018, 05:02
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
Non-Human User
Joined: 09 Sep 2013
Posts: 13742
Re: If P and Q are non-zero integers, is the equation Py + Qx = 7, exactly  [#permalink]

### Show Tags

30 Nov 2019, 23:58
Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
_________________
Re: If P and Q are non-zero integers, is the equation Py + Qx = 7, exactly   [#permalink] 30 Nov 2019, 23:58
Display posts from previous: Sort by