Data Sufficiency

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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