The given explanation is comprehensive. So the next time you see a similar question you will know many approaches to solve it and can chose the one that will work in that particular case.

The approaches are:

1. To plug in any numbers in the answer choices, until all the choices except one are eliminated.

2. To prove that one of the answer choices satisfies the terms.

NOTE, that if we plug in some specific value into one of the answer choices and the value we get satisfies the terms, it DOES NOT mean that that answer choice is correct.

E.g. if we take the answer choice B: The square of a prime number. And plug in

*x*² = 10² = 100. 100 is divisible by 5, but the answer choice is NOT correct for all possible values of

*x*.

So, if to answer your question:

**Quote:**

**This question could be easier explained, because the sum any five consecutive positive integers could be divided by 5, right?**

The shortest explanations for each approach could be:

1. (B) is wrong — many squares of primes, such as 2², are not divisible by 5.

(C) is also wrong: consider 3 + 9 = 12.

(D) is incorrect; one example is (7)(9)(11), which is not divisible by 5.

(E) can be shown to be wrong as well: For instance, the difference between 16 and 9 is 7.

Therefore the remaining answer choice A must be correct.

2. Let's consider the answer choice A. If the first of the five consecutive positive integers is

*x*, the full list is:

*x* + (

*x* +1) + (

*x* + 2) + (

*x* + 3) + (

*x* + 4) = 5

*x* + 10

Since x is an integer, 5x is divisible by 5. 10 is also divisible by 5. Then, 5x + 10 is divisible by 5. The correct answer is choice A.

Each of these two explanations is sufficient on its own.