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.

Mani_mba wrote: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.

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) ?

Bidisha800 wrote: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.

Vemuri wrote:Bidisha800 wrote: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

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