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.
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Ian Stewart
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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 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.
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Bidisha800
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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) ?
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) ?
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GMATPowerPrep Test1= 740
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Vemuri
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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 thatBidisha800 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) ?
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.
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Bidisha800
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THANKS ....Vemuri wrote: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 thatBidisha800 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) ?
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.
STUPID ME ... IT IS 3:45 AM .... I'M SLEEPY
Drill baby drill !
GMATPowerPrep Test1= 740
GMATPowerPrep Test2= 760
Kaplan Diagnostic Test= 700
Kaplan Test1=600
Kalplan Test2=670
Kalplan Test3=570
GMATPowerPrep Test1= 740
GMATPowerPrep Test2= 760
Kaplan Diagnostic Test= 700
Kaplan Test1=600
Kalplan Test2=670
Kalplan Test3=570
