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# If p and q are not 0, what is the value of p^3*q^3 ?

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If p and q are not 0, what is the value of p^3*q^3 ? [#permalink]

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19 Oct 2017, 05:39
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Difficulty:

25% (medium)

Question Stats:

72% (01:06) correct 28% (01:11) wrong based on 74 sessions

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If p and q are not 0, what is the value of $$p^3*q^3$$ ?

1. $$p^2 – (\frac{4}{q})^2 = 0$$

2. $$p^3 – (\frac{4}{q})^3 = 0$$

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Re: If p and q are not 0, what is the value of p^3*q^3 ? [#permalink]

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19 Oct 2017, 08:11
nkmungila wrote:
If p and q are not 0, what is the value of $$p^3*q^3$$ ?

1. $$p^2 – (\frac{4}{q})^2 = 0$$

2. $$p^3 – (\frac{4}{q})^3 = 0$$

Hi...

1. $$p^2 – (\frac{4}{q})^2 = 0$$..
$$\frac{p^2*q^2-4^2}{q^2}=0$$..
Means $$p^2q^2-4^2=0.....p^2q^2=4^2...$$
pq can be -4 or 4, so p^3*q^3=-4^3 or 4^3
Insufficient

2. $$p^3 – (\frac{4}{q})^3 = 0$$..
$$\frac{p^3q^3-4^3}{q^3}=0$$...
This means $$p^3*q^3=4^3$$
Sufficient

B
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Re: If p and q are not 0, what is the value of p^3*q^3 ? [#permalink]

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20 Oct 2017, 01:46
S1 => $$p^2 –(\frac{4}{q})^2$$ =0
$$p^2 = (\frac{4}{q})^2$$
|p|=|$$\frac{4}{q}$$|
p=$$\frac{4}{q} or \frac{-4}{q}$$
pq can be 4 or -4. Not sufficient.

S2 =>$$p^3 –(4/q)^3$$=0
$$p^3 = (\frac{4}{q})^3$$
p=$$\frac{4}{q}$$
pq = 4
$$p^3 * q^3 = 4^3$$
Sufficient.

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If p and q are not 0, what is the value of p^3*q^3 ? [#permalink]

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20 Oct 2017, 03:01
nkmungila wrote:
If p and q are not 0, what is the value of $$p^3*q^3$$ ?

1. $$p^2 – (\frac{4}{q})^2 = 0$$

2. $$p^3 – (\frac{4}{q})^3 = 0$$

Statement 1: $$p^2=(\frac{4}{q})^2$$, multiply both sides of the equation by $$pq^3$$

$$p^3q^3=16pq$$

$$p^3q^3-16pq=0=>pq(p^2q^2-16)=0$$, $$pq$$ cannot be $$0$$ as $$p$$ & $$q$$ are not $$0$$ or $$pq=±\sqrt{16}$$ or $$pq=±4$$.

there is no unique value. Hence Insufficient

Statement 2: $$p^3=(\frac{4}{q})^3$$. multiply both sides of the equation by $$q^3$$

$$p^3q^3=64$$. Sufficient

Option B
If p and q are not 0, what is the value of p^3*q^3 ?   [#permalink] 20 Oct 2017, 03:01
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