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Difficulty:
35%
(medium)
Question Stats:
66% (01:39) correct
34%
(01:38)
wrong
based on 174
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What is the value of p − q ?
(1) \(16p^2 = 64 + 16q^2\)
(2) \(p^2 = 36\)
Pure algebraic questions like this one are no longer part of the GMAT Data Sufficiency syllabus.
For relevant Data Sufficiency questions, please check the Data Sufficiency forum:
https://gmatclub.com/forum/data-sufficiency-ds-141/
https://gmatclub.com/forum/data-sufficiency-ds-141/
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Quote:
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
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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.
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.
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(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
--> \(p^2 = 4 + q^2\)
--> \(p^2 - q^2 = 4\)
--> \((p - q)(p + q) = 4\)
--> \(p - q = \frac{4}{p + q}\) --> 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
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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!
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!
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.
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(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.
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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
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
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
(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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