What is the value of the integer n? (1) n(n + 2) = 15 (2) (n

but talking about statement 2), cant value of N be 3 or ANY decimal number? Since it is NOT stated in the question that "N is an integer". Correct me if I am wrong.

Question is: What is the value of the integer n? So the stem explicitly says that n is an integer.

Forget conventional ways of solving math questions. In DS, Variable approach is the easiest and quickest way to find the answer without actually solving the problem.
Remember equal number of variables and independent equations ensures a solution.

What is the value of the integer n?

(1) n(n + 2) = 15
(2) (n + 2)^n = 125

In the original condition there is 1 variable (n) and thus we need 1 equation to match the number of variable and equation. Since there is 1 each in 1) and 2), D has high probability of being the answer.
In case of 1), n^2+2n-15=0, (n+5)(n-3)=0 and thus n=-5,3. The answer is not unique, therefore the condition is not sufficient.
In case of 2), n=3, therefore the answer is unique and the condition is sufficient. Therefore the answer is B.

Normally for cases where we need 1 more equation, such as original conditions with 1 variable, or 2 variables and 1 equation, or 3 variables and 2 equations, we have 1 equation each in both 1) and 2). Therefore D has a high chance of being the answer, which is why we attempt to solve the question using 1) and 2) separately. Here, there is 59 % chance that D is the answer, while A or B has 38% chance. There is 3% chance that C or E is the answer for the case. Since D is most likely to be the answer according to DS definition, we solve the question assuming D would be our answer hence using 1) and 2) separately. Obviously there may be cases where the answer is A, B, C or E.

In statement one: n(n+2)=15 can we say that either n = 15 or n+2=15 n =13. Am i wrong?? Or is this method too correct??

Nope.
if you say that, you're meaning to say that 15*13 = 15 which is not possible.
You can only say that when n(n+2) = 0
i.e. n = 0,-2 <= 2 solutions for the equation.

n^{2} + 2n -15 = 0
n = -5,3

Alternatively
You can plug in values.
n(n+2) = 15
15 = 1*15 or 3*5

n = 3
3*5 =15

But if n = -5
n+2 = -3
-3*(-5) = 15

2 values so the statement is not sufficient.

Hope this helps.

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