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

Question

Competition Mode Question

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

Leadership · Answer

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

shameekv1989 · Answer

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

Archit3110 · Answer

#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

suchita2409 · Answer

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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exc4libur · Answer

(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)

ostrick5465 · Answer

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

Jawad001 · Answer

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

CareerGeek · Answer

(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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tranminh1333 · Answer

1. <=> p^2 = (4/q)^2 <=> (p*q)^2 = 4^2 <=> pq = +/-4 => insufficient 2. <=> (p*q)^3 = 4^3 => sufficient => Answer: B

eakabuah · Answer

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.

lacktutor · Answer

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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hardikajmani · Answer

1)  p^2 * q^2 = 16

Many possible values
Insufficient

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

Hence,  option B

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

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