Lets do number crunching
a=5 and b=2
1. let n=2 (even) 25-4/3 = 7 Divisible
let n=3 (odd) 125-8/3 = 39 Divisible
Insufficient
2. n=2 (even) 25+4/7 = Not divisible
n=3 (odd) 125+8/7 = 19 Divisible
That means n is even..Sufficient
OA is B

Let it B.

n is not odd.

a^n+b^n may not be divisible by (a+b) only when n is even.

Let n=2, a = 1, b = 1, then (a+b)=2 and a^2+b^2=2 and 2 is divisible by 2.

Let n=2, a = 2, b = 1, then (a+b)=3 and a^2+b^2=5 and 5 is not divisible by 3.

i.e. a^2+b^2 is divisible by a+b only when a=b.

a^n-b^n is always divisible by (a-b)

a^n+b^n is only divisible by (a+b) if n is odd

Hence, 1) isn't sufficient and 2) is sufficient

Choose B

Ganesh hatwar wrote:

harsh.champ wrote:Is n odd ?

1. a^n - b^n is divisible by a - b
2. a^n + b^n is not divisible by a + b

E bcoz i am not getting !!

Nice definition of E!

Answer is B. Second statement alone is sufficient to answer the question.

sanju09 wrote:
a^n + b^n is divisible by a + b only when n is an odd positive integer, and a and/or b are non zero numbers. You cannot take n = 2 to prove this point, fangtray.

Why can we not use n=2 in picking some numbers to check this question?

If I pick, a=6 and b=3 I get:

For n=2 (even)
36+9/9 = 45/9 = 5 = DIVISIBLE by (a+b)

For n=3 (odd)
216+27/9 = 243/9 = 27 = DIVISIBLE by (a+b)

For n=4 (even)
1296+81/9 = 1377/9 = 153 = DIVISIBLE by (a+b)


Struggling to understand this question.

Answer: B

Answer: B

Answer: B

Answer is B.

I)
n=2
(a2-b2) /a-b == a+b
n=3
(a3-b3) /(a-b) = (a2 + b2-ab) A - Not sufficient.

II)
n=2
a2+b2 not by a+b
n=3
a3+b3 is divisible by (a+b)
n=5
a5+b5 is divisible by (a+b)

B it is

B it is

B it is

I love the enthusiasm, but no need to resurrect the thread