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# p,q are both non-zero integers, which of the following would be the va

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Director
Status: Learning stage
Joined: 01 Oct 2017
Posts: 931
WE: Supply Chain Management (Energy and Utilities)
p,q are both non-zero integers, which of the following would be the va  [#permalink]

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14 Jul 2018, 11:55
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Difficulty:

95% (hard)

Question Stats:

25% (02:27) correct 75% (02:56) wrong based on 40 sessions

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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,II only
(D) I,III only
(E) I,Ii and III
MBA Section Director
Affiliations: GMATClub
Joined: 22 May 2017
Posts: 1468
Concentration: Nonprofit
GPA: 4
WE: Engineering (Computer Software)
Re: p,q are both non-zero integers, which of the following would be the va  [#permalink]

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14 Jul 2018, 19:03
1
$$\frac{5(pq)^3+35(pq)^2-40pq}{(p-1)(p+4)}$$=0

Since (p-1)(p+4) is in denominator = > p $$\neq$$ 1 and p $$\neq$$ -4

=> $$5(pq)^3+35(pq)^2-40pq$$=0

=> $$5pq((pq)^2+7(pq)-8$$=0

=> $$(pq)^2+7(pq)-8$$=0

=> $$(pq)^2 + 8(pq) - (pq) -8$$=0

=> $$(pq)(pq + 8) -(pq + 8)$$=0

=> $$(pq-1)(pq+8)$$=0

=> pq = 1 or pq = -8

1) q = -4 => p = 2

q = -4 is possible

2) q = 1 => p = -8

q = 1 is possible

3) q = 2 => p = -4 is not possible since (p+4) is in denominator and hence p $$\neq$$ -4

only cases 1 and 2 are possible

Hence option C
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p,q are both non-zero integers, which of the following would be the va  [#permalink]

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14 Jul 2018, 19:14
Assume pq = x
p cannot be equal to 1 and -4 as denominator cannot be equal to 0.

5x * (x^2 + 7x + 8) = 0
5x * (x + 8) * (x - 1) = 0
x = 0 or -8 or 1
But, x cannot be 0 as p and q are non zero integers.

Hence pq = -8 or 1
If pq = 1 then p = q = -1
If pq = -8 then pq can be (-1, 8), (-2, 4), (-8, 1), (2, -4), (4, -2), (8, -1).
Values of q can be 8, 4, 1, -4, -2, -1

p,q are both non-zero integers, which of the following would be the va &nbs [#permalink] 14 Jul 2018, 19:14
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