If z is a positive integer, is z + 1 a factor of 105?

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

If z is a positive integer, is z + 1 a factor of 105?
So let us find the factors of 105 =3*5*7, so factors are \(1, 3, 5, 7, 15, 21, 35, 105\)
So we are asked if z is any of \(1-1, 3-1, 5-1, 7-1, 15-1, 21-1, 35-1, 105-1\), that is \(2, 4, 6, 14, 20, 34 or 104\).....

(1) z is a factor of 20.
z can be 1, 2, 4, 5, 10 or 20.
If z is 2, 4 or 20..Yes
If z is 1, 5 or 10..No
Insuff

(2) 10 is a factor of z
So z can be 10, 20, 30...
If z is 20..Yes
If z is 10, 30 and so on, No
Insuff

Combined z can be 10 or 20 ( Common values of z from both the statements..
If z is 20..Yes
If z is 10, No
Insuff

E
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