rishabhmenon21 wrote:
If x is an integer greater than 1, what is the value of x?
I) there are x unique factors of x
II) the sum of x and all prime factors greater than x is Odd
Please explain the answer to me.
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Statement 1 I) there are x unique factors of xOnly the prime number '2' has two factors 1, and 2. Hence, the statement is sufficient to answer the question. We can eliminate B, C, and E.
Statement 2 II) the sum of x and all prime factors greater than x is OddAll prime numbers except 2 are odd and hence the sum of all prime factors greater than 2 should be even.
From the question premise, we know that x is an integer greater than 1, so the minimum value of x can be 2.
Let's assume x = 2, so 2 + even = even. Therefore x cannot be 2, or for that matter any even integer. It can however be any odd integer.
Say
x = 3 → 3 + (sum of all prime factors greater than 3) = 3 + even = odd
x = 5 → 5 + (sum of all prime factors greater than 5) = 5 + even = odd
As we do not have a unique value for x, the statement alone is not sufficient.
Option A
P.S. = IMO the verbiage of the question (esp St2) isn't great. We could have referred to them as prime integers instead of prime factors.
Edit: I see Statement 2 has been edited. A revised analysis of the Statement is below -
Statement 2 (2) The sum of x and any prime number larger than x is oddAll prime numbers except 2 are odd.
From the question premise, we know that x is an integer greater than 1, so the minimum value of x can be 2.
Let's assume x = 2, so 2 + (any prime number larger than 2) = 2 + odd = odd. Hence, x = 2 satisfies the criteria. However, x can be any even integer.
Say
x = 4 → 4 + (any prime number larger than 4) = 4 + odd = odd
As we do not have a unique value for x, the statement alone is not sufficient.
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