Data Sufficiency

BTGmoderatorDC wrote:What is the value of integer z?

(1) z is the remainder when positive integer x is divided by positive integer (x - 1)
(2) x is not a prime number

OA C

Source: Veritas Prep

Target question: What is the value of integer z?

Statement 1: z represents the remainder when positive integer x is divided by positive integer (x - 1)
In almost all cases, we will get a remainder of 1 when we divide x by (x-1).
For example, 6 divided by 5 equals 1 with remainder 1 (in other words z = 1)
9 divided by 8 equals 1 with remainder 1 (in other words z = 1)
22 divided by 21 equals 1 with remainder 1 (in other words z = 1)
.
.
.
and so on.,

The only time we don't get a remainder of 1 is when x = 2
If x = 2, then x divided by (x-1) becomes 2 divided by 1, in which case the remainder is 0 (in other words z = 0)
Since we cannot answer the target question with certainty, statement 1 is NOT SUFFICIENT

Statement 2: x is not a prime number
No information about z
Statement 2 is NOT SUFFICIENT

Statements 1 and 2 combined
From statement 1, we learned that the remainder will always be 1 AS LONG as x does not equal 2
Statement 2 tells us that x does not equal 2
If x does not equal 2, then dividing x by (x-1) will always leave remainder 1
In other words, z must equal 1
Since we can answer the target question with certainty, the combined statements are SUFFICIENT

Answer: C

Cheers,
Brent