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05 May 2023, 09:00
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C
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
75%
(hard)
Question Stats:
31% (00:56) correct
69%
(00:56)
wrong
based on 107
sessions
History
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Not Attempted Yet
m and n are positive integers. If p and q are prime numbers, how many factors does \(p^mq^n\) have?
(1) \(m=2\) and \(n=3\)
(2) \(p=11\) and \(q=13\)
(1) \(m=2\) and \(n=3\)
(2) \(p=11\) and \(q=13\)
05 May 2023, 09:16
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A.
You know p and q are prime. Calculate (2+1)(3+1)= 12 1 sufficient. A or D
You don’t know anything about exponent values which will impact factors. 2 insufficient eliminate D
Answer A
Posted from my mobile device
You know p and q are prime. Calculate (2+1)(3+1)= 12 1 sufficient. A or D
You don’t know anything about exponent values which will impact factors. 2 insufficient eliminate D
Answer A
Posted from my mobile device
05 May 2023, 12:21
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Bunuel
Given
- p and q are prime numbers
- m and n are positive integers
Statement 1
(1) \(m=2\) and \(n=3\)
We don't know if p and q are the same prime numbers.
Case 1: If p and q are the same prime numbers, the number of factors of \(p^mq^n\) is 6
Case 2: If p and q are different prime numbers, the number of factors of \(p^mq^n\) is 12
As we have two different answers for the target question, this statement is not alone sufficient.
Statement 2
(2) \(p=11\) and \(q=13\)
While we know that p and q are different prime numbers, we don't know the value of the powers. Hence, the statement alone is not sufficient.
Combined
From statement 2, we know that p and q are not the same, and from statement 1 we know the value of the powers.
The statements combined can answer the target question.
Option C
