What is the value of p − q ?

Question

Competition Mode Question

(1)  16p^2 = 64 + 16q^2

(2)  p^2 = 36

GMATinsight · Answer

Question: p-q = ?

Statement 1 :  16p^2=64+16q^2

16p^2=64+16q^2 
i.e.  p^2 - q^2=4

i.e.  (p - q)*(p + q)=4

Many possibilities of p - q hence

NOT SUFFICIENT

Statement 2 : p^2=36

i.e. p =  + 6 but no information of q hence

NOT SUFFICIENT

COmbining the statements

p =  + 6 and  p^2 - q^2=4

i.e.  q^2 = 6^2 - 4 = 32

i.e. q =  + 4√2

Still values of p-q can take many values hence

NOT SUFFICIENT

Answer: Option E

eakabuah · Answer

We are to determine the value of p-q

Statement 1: 16p^2=64+16q^2
From statement 1, p^2-q^2=4
hence (p-q)=4/(p+q)
We have no idea what p+q is, we are therefore unable to find p-q. Statement 1 is insufficient.

Statement 2: p^2=36
From statement 2, p=-6, or p=6
Statement 2 is insufficient since we have no idea the value of q, and besides, since p has two possible values, it is likely to result in different values of p-q.

1+2
q^2=32 hence q=-4√2 or q=4√2
any combination of the possible values of p and q yields p^2-q^2=4 but different values of p-q. For instance when p=6 and q=4√2, p-q=6-4√2=2(3-2√2)
when p=6 and q=-4√2, p-q=6+4√2=2(3+2√2)
Hence 1+2 are still not sufficient.

The answer is E.

CareerGeek · Answer

(1)  16p^2 = 64 + 16q^2 
-->  p^2 = 4 + q^2 
-->  p^2 - q^2 = 4 
-->  (p - q)(p + q) = 4 
-->  p - q = \frac{4}{p + q}  -->  Insufficient

(2)  p^2 = 36 
-->  p = 6  or  -6 
--> No information about  q  -->  Insufficient

Combining (1) & (2),
 p^2 - 36 = 4 
-->  p^2 = 40 
-->  p = \sqrt{40}  or  -\sqrt{40} 
No unique value of  p - q  -->  Insufficient

Option E

CrackverbalGMAT · Answer

We will need unique values of p and q to be able to find the value of p-q.

From statement I alone, 16 p^2  = 64 + 16 q^2 . Taking 16 q^2  to the LHS, we have,
16 ( p^2  –  q^2 ) = 64 or  p^2  –  q^2  = 4.

p^2  –  q^2  can be simplified as (p-q)*(p+q). Therefore, (p-q)*(p+q) = 4. We cannot find a unique value of (p-q) from this equation. Statement I alone is insufficient.
Answer options A and D can be eliminated. Possible answer options are B, C or E.

From statement II alone,  p^2  = 36. This means p = ± 6. But, we do not have a value for q and hence cannot find a value for p-q.
Statement II alone is insufficient. Answer option B can be eliminated. Possible answer options are C or E.

Combining both statements I and II, we have the following:
 p^2  –  q^2  = 4 from statement I and  p^2  = 36 from statement II. Therefore,  q^2  = 32 which means q = ±4√2 and p = ± 6. 
We cannot find a unique value of (p-q) even after combining both the statements together.

The correct answer option , IMO , is E.

Hope that helps!

unraveled · Answer

What is the value of p − q ?

(1)  16p^2=64+16q^2 
 16p^2 - 16q^2 = 64 
 p^2 - q^2 = 4 
(p-q) * (p+q) = 4
Case I: (p-q) * (p+q) = 4*1; p - q = 4
Case II: (p-q) * (p+q) = 2*2; p - q = 2

INSUFFICIENT.

(2)  p^2=36 
Clearly, INSUFFICIENT.

Together 1 and 2, p = 6 OR p = -6
 36 - q^2 = 4 
 q^2 = 32 
q =  \sqrt{32}  OR q = - \sqrt{32}

Four values are possible

INSUFFICIENT.

Answer E.

MARVEL13 · Answer

1. 
Not sufficient as it leaves us with
(P+q) (p-q) =4
And this equation can have more than one solution.

2. Even if we are provided with the information that p^2=36

P could be +6 or -6
Even combininng the two- q can take value +/- √32
Which will give more than one solution for p-q

So we will not get the answer even after combining the two equations.

Posted from my mobile device

Jawad001 · Answer

What is the value of p − q ?

(1) 16p^2=64+16q^2
(2) p^2=36

Solution:
From statement (1), 
16p^2=64+16q^2
or, 16p^2-16q^2 =64
Or, 16(p^2-q^2) =64
Or, (p^2-q^2) =4
Or,(p +q)(p-q) = 4, Hence, Not Sufficient.

From statement (2), 
p^2=36
Or, p = ∓ 6
Or, p = 6/-6, Not Sufficient.
Combining both statements, value of (p-q) cannot be calculated.
Not Sufficient.

Answer: E

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What is the value of p − q ?

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