Data Sufficiency

VJesus12 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

We need to determine the remainder of n/29.

Statement One Alone:

n-5 is divisible by 29

We can create the equation:

(n - 5)/29 = Q (where Q is an integer)

n - 5 = 29Q

n = 29Q + 5

Thus:

n/29 = (29Q + 5)/29 = 29Q/29 + 5/29 = Q + 5/29

Since Q is an integer, the remainder must be 5. Statement one alone is sufficient to answer the question.

Statement Two Alone:

n-29 is divisible by 5

(n - 29)/5 = Q (where Q is an integer)

n - 29 = 5Q

n = 5Q + 29

Thus:

n/29 = (5Q +29)/29 = 5Q/29 + 29/29 = 5Q/29 + 1 = 1 + 5Q/29

Since 1 is an integer, the remainder must be 5Q if 5Q < 29. However, the remainder can be 5 (if Q = 1) or 10 (if Q = 2). Therefore, statement two alone is not sufficient to answer the question.

Answer: A

VJesus12 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: What is the remainder when n is divided by 29?

Statement 1: n-5 is divisible by 29
So, we can say that: n-5 = 29k for some integer k
Add 5 to both sides of the equation to get: n = 29k + 5
We can see that n is 5 greater than some multiple of 29
So, if we divide n by 29, the remainder will equal 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 = 39. Notice that 39 - 29 = 10, and 10 IS divisible by 5. When 39 is divided by 29, the remainder is 10. In other words, when we divide n by 29, the remainder will equal 10
Case b: n = 44. Notice that 44 - 29 = 15, and 15 IS divisible by 5. When 44 is divided by 29, the remainder is 15. In other words, when we divide n by 29, the remainder will equal 15
Since we cannot answer the target question with certainty, statement 2 is NOT SUFFICIENT

Answer: A

Cheers,
Brent