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06 May 2021, 10:36
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Difficulty:
25%
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Question Stats:
74% (01:10) correct
26%
(01:14)
wrong
based on 50
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Is integer a a prime number?
(1) 2a has exactly three factors.
(2) a is an even number
(1) 2a has exactly three factors.
(2) a is an even number
06 May 2021, 10:45
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Bunuel
Question: Is integer a = Prime?
Statement 1: 2a has exactly three factors.
CONCEPT: Number of Factors
For a Number \(N=a^p*b^q*c^r*... \)where a, b, c etc are distinct prime factors of n and p, q r are their respective exponents
The number of factors of \(N = (p+1)*(q+1)*(r+1)*...\) and so on
ie. for a number to have 3 factors it must be of type \(Prime^2\)
i.e. a must be 2
@a = 2, 2a = 4 which has 3 factors
but for any other value of a, 2a will not have 3 factors hence
a = 2
SUFFICIENT
Statement 2: a = even
a could be 2 or 4 or 8 etc, hence
NOT SUFFICIENT
Answer: Option A
WannaManaConsult
06 May 2021, 10:45
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1) The only way to get 3 factors is for a number to be a perfect square of a prime number.
2 is a factor of 2a. That means the factors must be 1, 2, 4 and 2a=4. a=2 and is prime. Sufficient
2) a can be any multiple of 2, including 2 itself. 2 itself is prime, no other multiple of 2 is. Insufficient.
2 is a factor of 2a. That means the factors must be 1, 2, 4 and 2a=4. a=2 and is prime. Sufficient
2) a can be any multiple of 2, including 2 itself. 2 itself is prime, no other multiple of 2 is. Insufficient.
