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What is the value of the positive integer n?

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by BTGmoderatorDC » Mon Oct 16, 2017 2:05 pm
What is the value of the positive integer n?

$$\left(1\right)\ n^2\ +\ 2n\ has\ four\ distinct\ positive\ factors.$$

$$\left(2\right)\ n^2\ +\ 6n\ +\ 8\ has\ four\ distinct\ positive\ factors.$$

Isn't statement 1 sufficient? I think the best Option is Option E, but why isn't it the correct Option?

OA C
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by vaibhav101 » Tue Oct 17, 2017 4:52 am
statement 1 is not sufficient because it will give two values,

if we simplify statement 1, then it could be rewritten as n(n+2)=0
which means n=0 and n= -2

statement 2 will also give two values, if we factorize the given equation we will get
(n+2)(n+4) which means n= -2 and n= -4

if we combine both the statement then we will get a unique solution, n= -2
so answer should be C
but since the question asks for positive value for n
so answer is E.
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by [email protected] » Tue Oct 17, 2017 10:44 am
Hi leihannie07,

We're told that N is a positive integer. We're asked for the value of N. This question can be solved by TESTing VALUES.

1) N^2 + 2N has 4 distinct positive factors.

IF....
N=3, then N^2+2N = 15 (factors are 1, 3, 5 and 15)
N=5, then N^2+2N = 35 (factors are 1, 5, 7 and 35)
Fact 1 is INSUFFICIENT

2) N^2 + 6N + 8 has 4 distinct positive factors.

IF....
N=3, then N^2+6N+8 = 35 (factors are 1, 5, 7 and 35)
N=5, then N^2+6N+8 = 63 (factors are 1, 7, 9 and 63)
Fact 2 is INSUFFICIENT

Combined, we already have two different values for N that 'fit' both Facts.
Combined, INSUFFICIENT

Final Answer: E

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