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
