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

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by BTGModeratorVI » Wed Apr 22, 2020 11:16 am

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Answers

A

B

C

D

E

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Difficulty—

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
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Source: — Data Sufficiency |

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

by Jay@ManhattanReview » Thu Apr 23, 2020 11:01 pm
BTGModeratorVI wrote: ↑
Wed Apr 22, 2020 11:16 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
Let's take each statement one by one.

(1) z is a factor of 20.

Case 1: Say z = 20, then we have z + 1 = 21, a factor of 105. The answer is yes.
Case 2: Say z = 10, then we have z + 1 = 11, not a factor of 105. The answer is no. No unique answer. Insufficient.

(2) 10 is a factor of z.

=> z = 10p => z + 1 = 10p + 1

Case 1: Say p = 2; thus, we have z + 1 = 21, a factor of 105. The answer is yes.
Case 2: Say p = 1; thus, we have z + 1 = 11, not a factor of 105. The answer is no. No unique answer. Insufficient.

Even both statements together can't help. Insufficient.

The correct answer: E

Hope this helps!

-Jay
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Re: If z is a positive integer, is z + 1 a factor of 105?

by Brent@GMATPrepNow » Fri Apr 24, 2020 7:52 am
BTGModeratorVI wrote: ↑
Wed Apr 22, 2020 11:16 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
Brent Hanneson - Creator of GMATPrepNow.com
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