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When a positive integer n is divided by 29, what is the rema

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by Max@Math Revolution » Thu Jul 14, 2016 12:14 am
When a positive integer n is divided by 29, what is the remainder?
1) n-5 is divisible by 29
2) n-29 is divisible by 5

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Source: — Data Sufficiency |

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by Brent@GMATPrepNow » Sat Jul 16, 2016 2:03 pm
Max@Math Revolution wrote:When a positive integer n is divided by 29, what is the remainder?

1) n-5 is divisible by 29
2) n-29 is divisible by 5
Target question: When a positive integer n is divided by 29, what is the remainder?

Statement 1: n-5 is divisible by 29
This tells us that n-5 = 29k for some integer k.
Add 5 to both sides to get n = 29k + 5
In other words, n is 5 GREATER than some multiple of 29
So, if we divide n by 29, the remainder will be 5
Since we can answer the target question with certainty, statement 1 is SUFFICIENT

Statement 2: n-29 is divisible by 5
There are several values of n that satisfy statement 2. Here are two:
Case a: n = 34 (34-29 = 5, and 5 is divisible by 5). In this case if we divide n by 29, the remainder will be 5
Case b: n = 39 (39-29 = 10, and 10 is divisible by 5). In this case if we divide n by 29, the remainder will be 10
Since we cannot answer the target question with certainty, statement 2 is NOT SUFFICIENT

Answer = A

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Brent
Brent Hanneson - Creator of GMATPrepNow.com
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by Max@Math Revolution » Mon Jul 18, 2016 3:05 am
If we use direct substitution, in case of con 1), the remainder is always 5. The answer is unique and the condition is sufficient. Thus, the correct answer is A.
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