BTGmoderatorDC wrote: ↑Tue Jul 21, 2020 6:24 pm
If x > 1, what is the value of x?
(1) There are x unique factors of x.
(2) The sum of x and any prime number larger than x is odd.
OA
A
Source: Manhattan Prep
Let's take each statement one by one.
(1) There are x unique factors of x.
Given that x > 1, only x = 2 is an integer whose no. of district factors is equal to the number itself, 2.
For a positive integer greater than 1 to have the same no. of distinct factors as the number itself, all positive integers from 1 to the number itself must be its factors.
Note that other than 2, any integer say y would not have its factor as (y – 1). For example, 3 does not have its factor 2; 4 does not have its factor 3; and 5 does not have its factor 4, and so on...
So, x = 2. Sufficient.
(2) The sum of x and any prime number larger than x is odd.
Case 1: Say x = 2
2 + 3 = 5, odd
Case 2: Say x = 4
4 + 3 = 7, odd
No unique value of x. Insufficient.
Correct answer:
A
Hope this helps!
-Jay
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