vk_vinayak wrote:Is the integer n ODD?
1. (n^2) - n is NOT a multiple of 4
2. n is a multiple of 3
Target question:
Is the integer n ODD?
Statement 1: (n^2) - n is NOT a multiple of 4
Important: When it comes to integer properties questions such as this, it's useful to know that expressions like
n^2 - n are a tricky way of hiding some helpful information about the variable.
In this case, we can rewrite
n^2 - n as
n(n-1) or
(n-1)(n)
Now notice that
n-1 and
n are two consecutive integers.
So, statement 1 is telling us that the product of two consecutive integers is not divisible by 4.
Given this, we can consider two cases (among many)
case a:
n-1 = 2 and
n = 3, in which case
n is odd.
case b:
n-1 = 5 and
n = 6, in which case
n is not odd.
Since we cannot answer the
target question with certainty, statement 1 is NOT SUFFICIENT
Statement 2: n is a multiple of 3
Given this information, we can consider two cases (among many)
case a:
n-1 = 2 and
n = 3, in which case
n is odd.
case b:
n-1 = 5 and
n = 6, in which case
n is not odd.
Since we cannot answer the
target question with certainty, statement 2 is NOT SUFFICIENT
Statements 1 & 2:
Even when we combine the two statements, we can still have conflicting answers to the target question. Here are two possible cases (among many)
case a:
n-1 = 2 and
n = 3, in which case
n is odd.
case b:
n-1 = 5 and
n = 6, in which case
n is not odd.
Since we cannot answer the
target question with certainty, statements 1 & 2 combined are NOT SUFFICIENT
Answer =
E
Cheers,
Brent
