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11 Mar 2020, 02:55
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E
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
55%
(hard)
Question Stats:
58% (02:02) correct
42%
(01:51)
wrong
based on 232
sessions
History
Date
Time
Result
Not Attempted Yet
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.
(1) z is a factor of 20.
(2) 10 is a factor of z.
11 Mar 2020, 06:35
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770GMAT
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
11 Mar 2020, 19:39
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770GMAT
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
