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08 May 2023, 09:30
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C
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Difficulty:
15%
(low)
Question Stats:
84% (01:18) correct
16%
(01:02)
wrong
based on 32
sessions
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What is the value of \((p-q)(p+q)\)?
(1) \(p-q=5\)
(2) \(p\) and \(q\) are prime numbers
(1) \(p-q=5\)
(2) \(p\) and \(q\) are prime numbers
08 May 2023, 10:27
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Bunuel
Statement 1
(1) \(p-q=5\)
We are given the difference between p and q. We can infer that the value of p is greater than the value of q as the difference is positive, however, we cannot find a unique value of \((p-q)(p+q)\).
Ex:
Case 1) p = 5, q = 0
5 * 5 = 25
Case 2) p = 6, q = 1
5 * 7 = 35
Hence, we can eliminate A and D.
Statement 2
(2) \(p\) and \(q\) are prime numbers
As there is no specific constraint we can have multiple values \((p-q)(p+q)\)
Case 1) p = 7, q = 2
5 * 9 = 45
Case 2) p = 7, q = 5
2 * 12 = 24
Eliminate B.
Combined
From statement 2, we know that both p and q are prime numbers. From statement 1, we have inferred that p is greater than q and the difference between p and q is 5.
As the difference is an odd integer, one of the prime numbers should be even. Hence, q should be even.
Therefore q = 2.
p = 2 + 5 = 7
As we now have a single possible value of p and q, we can find a unique value of \((p-q)(p+q)\).
The statements combined are sufficient.
Option C
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