factorization

[Mani_mba]

If n and k are positive integers, is n divisible by 6?
(1) n = k(k + 1)(k - 1)
(2) k – 1 is a multiple of 3.

[pepeprepa]

C for me

[Ian Stewart]

If n and k are positive integers, is n divisible by 6?
(1) n = k(k + 1)(k - 1)
(2) k – 1 is a multiple of 3.

A. From 1), n is the product of three consecutive integers: k-1, k and k+1. So n is divisible by 3! = 6. (the product of d consecutive integers is always divisible by d!). Statement 2) is clearly insufficient on its own.

[Mani_mba]

Thanks Ian !

[Bidisha800]

I understand why stmt 1 is sufficient but do not understand how stmt 2 is NOT sufficient.

Probably I'm missing something so please help me out...

k-1 = 3m
k=3m+1
k+1 =3m+2

n=k(k+1)(k-1)
=3m(3m+1)(3m+2)

m=0 n=0 divisible by 6
m=1 n=3.4.5 divisible by 6
m=2 n=6.7.8 divisible by 6
m=3 n=9.10.11 divisible by 6
.....

so why (B) is CLEARLY insufficient by its own ?


so why the answer is (A) ?

[Vemuri]

I understand why stmt 1 is sufficient but do not understand how stmt 2 is NOT sufficient.

Probably I'm missing something so please help me out...

k-1 = 3m
k=3m+1
k+1 =3m+2

n=k(k+1)(k-1)
=3m(3m+1)(3m+2)

m=0 n=0 divisible by 6
m=1 n=3.4.5 divisible by 6
m=2 n=6.7.8 divisible by 6
m=3 n=9.10.11 divisible by 6
.....

so why (B) is CLEARLY insufficient by its own ?


so why the answer is (A) ?

You mixed the 1st statement with the 2nd. You should consider the 2nd statement seperately inorder to determine if it is sufficient or not. So, with that

k-1 = 3m
k=3m+1
k+1 =3m+2

is not enough to answer the question if n is divisible by 6 or not.

[Bidisha800]

I understand why stmt 1 is sufficient but do not understand how stmt 2 is NOT sufficient.

Probably I'm missing something so please help me out...

k-1 = 3m
k=3m+1
k+1 =3m+2

n=k(k+1)(k-1)
=3m(3m+1)(3m+2)

m=0 n=0 divisible by 6
m=1 n=3.4.5 divisible by 6
m=2 n=6.7.8 divisible by 6
m=3 n=9.10.11 divisible by 6
.....

so why (B) is CLEARLY insufficient by its own ?


so why the answer is (A) ?

You mixed the 1st statement with the 2nd. You should consider the 2nd statement seperately inorder to determine if it is sufficient or not. So, with that

k-1 = 3m
k=3m+1
k+1 =3m+2

is not enough to answer the question if n is divisible by 6 or not.

THANKS ....

STUPID ME ... IT IS 3:45 AM .... I'M SLEEPY