14:I[5014,["/_next/static/chunks/11d1gk4m2o846.js","/_next/static/chunks/14mrh2-p_w84d.js","/_next/static/chunks/40y9lkvta2o_p.js"],"default"] 15:I[38392,["/_next/static/chunks/11d1gk4m2o846.js","/_next/static/chunks/14mrh2-p_w84d.js","/_next/static/chunks/40y9lkvta2o_p.js"],"PracticeCard"] 17:I[70570,["/_next/static/chunks/11d1gk4m2o846.js","/_next/static/chunks/14mrh2-p_w84d.js","/_next/static/chunks/40y9lkvta2o_p.js"],"ExamAppearanceBadge"] 16:T53c,Question: If n is a positive integer, then n(n + 1)(n + 2) is-

Solution:
There's a nice rule says:
The product of k consecutive integers is divisible by k, k - 1, k - 2, ..., 2, and 1
So, for example, the product of any 5 consecutive integers will be divisible by 5, 4, 3, 2 and 1
Likewise, the product of any 11 consecutive integers will be divisible by 11, 10, 9, . . . 3, 2 and 1
NOTE: the product may be divisible by other numbers as well, but these divisors are guaranteed.

Notice that n, n + 1, and n + 2 are three consecutive integers.
This means the product of n, n + 1, and n + 2 will be divisible by 3, 2 and 1

Since n(n + 1)(n + 2) is divisible by 2, then the product is ALWAYS EVEN.
This means we can eliminate answer choices A and B, because they put restrictions on when the product is even.
We can also eliminate C because it suggests that the product can be odd.

Likewise, since n(n + 1)(n + 2) is ALWAYS divisible by 3, we can eliminate answer choice D, because it puts a restriction on when the product is divisible by 3

If n is even ⇒ even × odd × even (Prod of two even numbers always divisible by 2 × 2 = 4)