GMAT Question of the Day: Daily via email | Daily via Instagram New to GMAT Club? Watch this Video

 It is currently 28 Jan 2020, 16:50

### 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 (5(pq)^3 + 35(pq)^2 - 40pq)/((p - 1)(p + 4)) = 0 and p, q are both

Author Message
TAGS:

### Hide Tags

Math Expert
Joined: 02 Sep 2009
Posts: 60727
If (5(pq)^3 + 35(pq)^2 - 40pq)/((p - 1)(p + 4)) = 0 and p, q are both  [#permalink]

### Show Tags

12 Nov 2019, 04:15
00:00

Difficulty:

85% (hard)

Question Stats:

34% (02:32) correct 66% (02:38) wrong based on 32 sessions

### HideShow timer Statistics

If $$\frac{5(pq)^3+35(pq)^2-40pq}{(p-1)(p+4)}=0$$ and p, q are both non-zero integers, which of the following would be the value of q?

I. -4
II. 1
III. 2

(A) I only
(B) II only
(C) I and II only
(D) I and III only
(E) I, II and III

Are You Up For the Challenge: 700 Level Questions

_________________
Intern
Joined: 09 Feb 2017
Posts: 2
Re: If (5(pq)^3 + 35(pq)^2 - 40pq)/((p - 1)(p + 4)) = 0 and p, q are both  [#permalink]

### Show Tags

12 Nov 2019, 04:47
if you divide both sides of the equation by "pq" you have 5(pq)2+35pq−40/((p−1)(p+4))=0 and then dividing everything by 5 we have (pq)2+7pq−8/((p−1)(p+4))=0

we know that p cant be 1 and it cant be -4 because the denominator can't be 0

the numerator of the function can be written as (pq-1)(pq+8) which means that pq should be equal to either 1 or -8

if q=-4 we can have a 0 in the numerator by using p=2, which doesn't lead to a 0 in the denominator
if q=1 we can have a 0 in the numerator by using p=1 or p=-8, p=1 can't be used but p=-8 can be used
if q=2 we can have a 0 in the numerator by using p=-4 which can't be used

in conclusion, answer C both I and II can be used
Math Expert
Joined: 02 Aug 2009
Posts: 8327
Re: If (5(pq)^3 + 35(pq)^2 - 40pq)/((p - 1)(p + 4)) = 0 and p, q are both  [#permalink]

### Show Tags

12 Nov 2019, 04:59
If $$\frac{5(pq)^3+35(pq)^2-40pq}{(p-1)(p+4)}=0$$ and p, q are both non-zero integers, which of the following would be the value of q?

$$\frac{5(pq)^3+35(pq)^2-40pq}{(p-1)(p+4)}=0$$ means $$5(pq)^3+35(pq)^2-40pq=0......(pq)^2+7pq-8=0....(pq+8)(pq-1)=0....pq=-8..or..pq=1$$
But p cannot be 1 or -4 as (p-1)(p+4) cannot be 0

I. -4 ..........pq=-8..p*-4=8...p=2 Possible
II. 1 .........pq=-8.....p=-8.......Possible
III. 2 ........pq=-8....p=-4...or..pq=-1...p=-1/2...Both NOT possible

I and II possible

C
_________________
Re: If (5(pq)^3 + 35(pq)^2 - 40pq)/((p - 1)(p + 4)) = 0 and p, q are both   [#permalink] 12 Nov 2019, 04:59
Display posts from previous: Sort by