770GMAT wrote:
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.
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 105Case 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 105Since 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 105Case 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 105Since 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 105Case 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 105Since we cannot answer the
target question with certainty, the combined statements are NOT SUFFICIENT
Answer: E
Cheers,
Brent
_________________
Brent Hanneson – Creator of gmatprepnow.com
Before you spend another second preparing for the GMAT, check out my article series, Are you doing it wrong?.
You’ll learn what the GMAT actually tests, and why memorizing a ton of formulas actually makes you less effective.