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If n is an integer greater than 6, which of the following mu

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Re: If n is an integer greater than 6, which of the following mu [#permalink]

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dave13 wrote:
Bunuel wrote:
carcass wrote:
If n is an integer greater than 6, which of the following must be divisible by 3 ?

(A) n(n + 1)(n – 4)
(B) n(n + 2)(n – 1)
(C) n(n + 3)(n – 5)
(D) n(n + 4)(n – 2)
(E) n(n + 5)(n – 6)


Since 3 is a prime number then in order the product to be divisible by 3 either of the multiples must be divisible by 3. Now, to guarantee that at least one multiple is divisible by 3, these numbers must have different remainders upon division by 3, meaning that one of them should have the remainder of 1, another the reminder of 2 and the third one the remainder of 0, so be divisible by 3.

For option A: n and n+1 have different remainder upon division by 3. As for n-4, it will have the same remainder as (n-4)+3=n-1, so also different than the remainders of the previous two numbers.

Answer: A.

Similar question to practice: http://gmatclub.com/forum/if-x-is-an-in ... 26853.html

Hope it helps.


Bunuel good day! :) can you please explain this part "it will have the same remainder as (n-4)+3=n-1, so also different than the remainders of the previous two numbers" I dont understand the logic behind this (n-4)+3=n-1 :? have a great day :) thanks!



Hi dave,

it basically depends on the divisor..

here you are dividing a term by 3 to find the remainder that is why whatever remainder n-4 leaves, n-4+3 or n-4+6 will leave..

say n is 28, so n-4 = 28-4 = 24, remainder will be 0, when div by 3..
now if you add/subtract 3 or a multiple of 3 to 24, remainder will always be 0..
say n was 30, n-4 would be 26 and would leave a remainder of 2 when div by 3..
so 26-3 = 23 or 26-6=20 will also leave remainder of 2 when div by 3
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Absolute modulus :http://gmatclub.com/forum/absolute-modulus-a-better-understanding-210849.html#p1622372
Combination of similar and dissimilar things : http://gmatclub.com/forum/topic215915.html


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If n is an integer greater than 6, which of the following mu [#permalink]

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New post 15 Jan 2018, 16:59
VeritasPrepKarishma Bunuel niks18 chetan2u


Quote:
I know that talking about positive integers, in any set of 3 consecutive positive integers, one integer will be divisible by 3 and the other 2 will not be.

So I am looking for 3 consecutive positive integers e.g. (n-1)n(n+1)

Note that (n-4) is equivalent to (n-1) since if (n-4) is divisible by 3, so is (n-1). If (n-4) is not divisible by 3, neither is (n-1) (because the difference between these two integers is 3)
Hence (A) is equivalent to 3 consecutive integers.
Answer (A)


Excellent approach. :thumbup:

Just to make sure : there is no (n-1) terms in OA and since you knew sum / difference of three consecutive positive integers is
always divisible by 3, you looked for hint to equating characteristics of n-1 and n-4 and arriving that both are divisible by 3
as represented on number line.

Is my interpretation correct?
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Re: If n is an integer greater than 6, which of the following mu [#permalink]

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New post 15 Jan 2018, 20:44
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adkikani wrote:
VeritasPrepKarishma Bunuel niks18 chetan2u


Quote:
I know that talking about positive integers, in any set of 3 consecutive positive integers, one integer will be divisible by 3 and the other 2 will not be.

So I am looking for 3 consecutive positive integers e.g. (n-1)n(n+1)

Note that (n-4) is equivalent to (n-1) since if (n-4) is divisible by 3, so is (n-1). If (n-4) is not divisible by 3, neither is (n-1) (because the difference between these two integers is 3)
Hence (A) is equivalent to 3 consecutive integers.
Answer (A)


Excellent approach. :thumbup:

Just to make sure : there is no (n-1) terms in OA and since you knew sum / difference of three consecutive positive integers is
always divisible by 3, you looked for hint to equating characteristics of n-1 and n-4 and arriving that both are divisible by 3
as represented on number line.

Is my interpretation correct?


Yes, you are right.
Take a look here: https://www.veritasprep.com/blog/2011/0 ... h-part-ii/

If (n - 1) is a multiple of 3, so is (n - 4).
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Re: If n is an integer greater than 6, which of the following mu   [#permalink] 15 Jan 2018, 20:44

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