BTGModeratorVI wrote: ↑Wed Oct 07, 2020 7:15 am
If z is a positive integer, is z + 1 a factor of 105?
(1) z is a factor of 20.
(2) 10 is a factor of z.
Answer:
E
Source: Kaplan
Given: z is a positive integer
Target question: Is z + 1 a factor of 105?
Statement 1: z is a factor of 20
So, z COULD equal 1,2, 4, 5, 10, or 20
Case a: If z = 4, then z + 1 = 5. 5 is a factor of 105. So, the answer to the target question is
YES, z+1 is a factor of 105
Case b: If z = 10, then z + 1 = 11. 11 is not a factor of 105. So, the answer to the target question is
NO, z+1 is not a factor of 105
Since we cannot answer the
target question with certainty, statement 1 is NOT SUFFICIENT
Statement 2: 10 is a factor of z.
So, z COULD equal 10, 20, 30, 40, etc
Case a: If z = 10, then z + 1 = 11. 11 is not a factor of 105. So, the answer to the target question is
NO, z+1 is not a factor of 105
Case b: If z = 20, then z + 1 = 21. 21 is a factor of 105. So, the answer to the target question is
YES, z+1 is a factor of 105
Since we cannot answer the
target question with certainty, statement 2 is NOT SUFFICIENT
Statements 1 and 2 combined
There are two values of z that satisfy BOTH statements: z = 10 and z = 20
Case a: If z = 10, then z + 1 = 11. 11 is not a factor of 105. So, the answer to the target question is
NO, z+1 is not a factor of 105
Case b: If z = 20, then z + 1 = 21. 21 is a factor of 105. So, the answer to the target question is
YES, z+1 is a factor of 105
Since we cannot answer the
target question with certainty, the combined statements are NOT SUFFICIENT
Answer: E
Cheers,
Brent
