This is a question on finding the number of factors of an integer.
It is therefore useful to know that Primes have exactly 2 factors, the number 1 has exactly one factor and, for a composite number N which can be expressed as N = \(a^p * b^q* c^r…..\), the number of factors = (p+1) (q+1) (r+1)….
Statement I alone says that n is the product of two different prime numbers.
It’s very important to
not interpret this as “n has exactly two prime factors”. This is what causes a lot of people to think that the first statement is insufficient, which is incorrect.
Statement I is clear and categorical in saying that n is a product of two different prime numbers. Therefore, n is a composite number which can be written as n = \(a^1 * b^1\) where a and b are the two different prime numbers.
Number of factors of n = (1+1) * (1+1) = 4.
Statement I alone is sufficient to find the number of factors of n. Answer options B, C and E can be eliminated. Possible answer options are A or D.
Statement II alone says that each of n and \(2^3\) have the same number of factors.
\(2^3\) has a total of 4 factors, so n also has 4 factors.
Statement II alone is sufficient to find the number of factors of n. Answer option A can be eliminated.
The correct answer option is D.
Hope that helps!
Aravind B T
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