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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] New post   05 Feb 2020, 03:01
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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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B
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Re: If p and q are not 0, what is the value of p^3*q^3 ? [#permalink] New post   05 Feb 2020, 03:33
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If p and q are not 0, what is the value of \(p^3*q^3\) ?

(1) \(p^2 – (\frac{4}{q})^2 = 0\)
\(p^2 = (\frac{4}{q})^2 \)
\(p^2 * q^2 = 4^2 \)
Square roots both sides, we get -> \(p * q = +/- (2) \)
Insufficient because it will give the result of \(p^3*q^3\) = +8 / -8

A D / B C E

(2) \(p^3 – (\frac{4}{q})^3 = 0\)
\(p^3 = (\frac{4}{q})^3 \)
\(p^3 * q^3 = 4^3 \)
Sufficient

'B' is the winner
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Re: If p and q are not 0, what is the value of p^3*q^3 ? [#permalink] New post   05 Feb 2020, 03:52
If p and q are not 0, what is the value of \(p3∗q3\) ?


(1) \(p^2\)-\((\frac{4}{q})^2\)=0
\((p+\frac{4}{q})*(p-\frac{4}{q})\)=0 -> \(p=\frac{4}{q}\); \(p=\frac{-4}{q}\)

-> pq = 4; pq=-4 -> \(p^3* q^3 \)=+-64 -> Not Sufficient

(2)\( p^3–(\frac{4}{q})^3\)=0 -> \(p^3 = (\frac{4}{q})^3\) -> \(p^3*q^3\) = \(4^3\) -> Clearly Sufficient
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If p and q are not 0, what is the value of p^3*q^3 ? [#permalink] New post   Updated on: 06 Feb 2020, 01:28
#1
p2–(4/q)2=0

(p+4/q) * ( p-4/q)=0
p,q = 2 each or ; 4,1 or 16 , 1/4 , -4,1
in all cases ; p3∗q3 = 64 or -64 ; insufficient
#2
p3–(4q)3=0
(p^3*q^3- 64 )/ q^3 = 0
possible at p=q=2 and p=16 and q= 1/4
p^3*q^3 = 64
sufficient
IMO B


If p and q are not 0, what is the value of p3∗q3 ?


(1) p2–(4q)2=0

(2) p3–(4q)3=0

Originally posted by Archit3110 on 05 Feb 2020, 03:58.
Last edited by Archit3110 on 06 Feb 2020, 01:28, edited 1 time in total.
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Re: If p and q are not 0, what is the value of p^3*q^3 ? [#permalink] New post   05 Feb 2020, 04:36
IMO D

We need to find the value of p^3×q^3.

Statement 1

p^2= (4÷q)^2
p^2×q^2 =16
value of p and q can be 2 or -2
But we r asked the value of p3q3.Donot get the idea that we should eliminate the statement bcoz p & q are negative .
Even if both of them r negative product of 2 negatives
p^3&q^3 will give us positive value 64.
So statement 1 is alone sufficient.

Statement 2 alone is sufficient 2 and gives us the value 64.

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Re: If p and q are not 0, what is the value of p^3*q^3 ? [#permalink] New post   05 Feb 2020, 07:08
Quote:
If p and q are not 0, what is the value of pˆ3∗qˆ3?

(1) pˆ2–(4/q)ˆ2=0
(2) pˆ3–(4/q)ˆ3=0


(1) pˆ2–(4/q)ˆ2=0 insufic

pˆ2=16/qˆ2…pˆ2qˆ2=16=2ˆ4
pˆ2qˆ2: 4*4, -4*4, 16*1, 16*-1

(2) pˆ3–(4/q)ˆ3=0 sufic

pˆ3=64/qˆ3…pˆ3qˆ3=64

Ans (B)
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Re: If p and q are not 0, what is the value of p^3*q^3 ? [#permalink] New post   05 Feb 2020, 08:27
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If p and q are not 0, what is the value of \(p^3 ∗ q^3\)?


(1) \(p^2–(\frac{4}{q})^2=0\)

=> p*q = -4 or p*q =4
=> \(p^3 * q^3 = -4^3\) or \(p^3 * q^3 = 4^3\)
Not Suff

(2) \(p^3–(\frac{4}{q})^3=0\)
=> p*q =4
=> \(p^3 * q^3 = 4^3\)

Suff

=> Choice B
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Re: If p and q are not 0, what is the value of p^3*q^3 ? [#permalink] New post   05 Feb 2020, 11:40
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From statement (1), p^2 – (4/q)^2 = 0
or,p^2 = (4/q)^2
or,p^2 q^2 = 16 = 4^2
or, pq =±4

(pq)^3= 64 or -64

Therefore, Statement (1) is insufficient.

From statement (2), p^3-(4/q)^3 = 0
or,p^3=(4/q)^3
or, (pq)^3 = 64

Therefore, statement (2) is sufficient.
Answer:B
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Re: If p and q are not 0, what is the value of p^3*q^3 ? [#permalink] New post   05 Feb 2020, 20:00
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(1) \(p^2*q^2 = 16\)

Possible value of (p, q) = (1, 4), (1, -4), (2, 2), (2, -2), . . .
—> Different values of \(p^3*q^3\) are possible —> Insufficient

(2) \(p^3*q^3= 64\)
—> Sufficient

Option B

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Re: If p and q are not 0, what is the value of p^3*q^3 ? [#permalink] New post   05 Feb 2020, 20:20
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1. <=> p^2 = (4/q)^2 <=> (p*q)^2 = 4^2 <=> pq = +/-4 => insufficient
2. <=> (p*q)^3 = 4^3 => sufficient

=> Answer: B
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Re: If p and q are not 0, what is the value of p^3*q^3 ? [#permalink] New post   05 Feb 2020, 22:29
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We are given that p and q are not zero. We are to determine p^3 * q^3, in other words, what is (pq)^3?

Statement 1: p^2 - (4/q)^2=0
Not sufficient, because pq=4 or pq=-4. When pq=4, (pq)^3=64 and when pq=-4, (pq)^3 = -64.

Statement 2: p^3 - (4/q)^3 = 0
p^3 - (4/p)^3 = 0 implies p^3=(4/q)^3 since factoring p^3 - (4/q)^3 = (p-4/p)(p^2+(4/q)^2 + 4p/q)=0
Either (p-4/p)=0 or (p^2+(4/q)^2 + 4p/q)=0
for (p^2+(4/q)^2 + 4p/q)=0, p must be zero and 4/q must be equal to zero. but p and q are not zero per the question stem, hence only p-4/q=0, hence pq=4.
So (pq)^3 = 64.
Statement 2 is sufficient.

the answer is B imo.
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Re: If p and q are not 0, what is the value of p^3*q^3 ? [#permalink] New post   06 Feb 2020, 00:21
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p,q — not equal to zero
What is the value of \(p^{3}q^{3} =\) ?

(Statement1): \(p^{2} —(4/q)^{2} = 0\)
—> \(p^{2}q^{2}—16 = 0\)
\((pq)^{2} = 16\)
pq= 4 and pq = —4
—> \(p^{3}q^{3} \) — could be —64 and 64
Insufficient


(Statement2): \(p^{3} —(4/q)^{3} = 0\)
\((pq)^{3} —64 = 0\)
\( (pq)^{3} = 64 \)
Sufficient

The answer is B

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Re: If p and q are not 0, what is the value of p^3*q^3 ? [#permalink] New post   06 Feb 2020, 06:35
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1)\( p^2 * q^2 = 16\)

Many possible values
Insufficient

2) \(p^3 * q^3 = 64\)
Sufficient

Hence, option B
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Re: If p and q are not 0, what is the value of p^3*q^3 ? [#permalink]
06 Feb 2020, 06:35
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