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# If t is a positive integer, can (t+2)(t-3) be evenly divided by 6?

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If t is a positive integer, can (t+2)(t-3) be evenly divided by 6? [#permalink]

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12 Aug 2017, 03:33
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Difficulty:

65% (hard)

Question Stats:

39% (01:49) correct 61% (01:56) wrong based on 33 sessions

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If t is a positive integer, can (t+2)(t-3) be evenly divided by 6?

(1) 5(t^3 +1) is not divisible by 2.

(2) t is a 3-digit number, whose digits are consecutive integers.

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[Reveal] Spoiler: OA

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If t is a positive integer, can (t+2)(t-3) be evenly divided by 6? [#permalink]

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12 Aug 2017, 04:48
fitzpratik wrote:
If t is a positive integer, can (t+2)(t-3) be evenly divided by 6?

t > 0
Question is if (t+2)(t-3) are divisible by both 2 and 3?

Quote:
(1) 5(t^3 +1) is not divisible by 2.
(2) t is a 3-digit number, whose digits are consecutive integers.

1) 5($$t^3$$ + 1) ≠ 2n
=> t is even.
If t = 2, (t+2)(t-3) is not divisible by 6
If t = 4, (t+2)(t-3) is divisible by 6
Insufficient.

2) t = abc
where a, b, c are 3 consecutive integers
=> t = 123, 234, 345, 456,...
=> (t+2)(t-3) will always be divisible by 2 and 3, so it's divisible by 6.
=> (t-3) will always be a multiple of 3, as t is a multiple of 3.
=> and for all even integer values of t, (t+2) will be divisible by 2

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Re: If t is a positive integer, can (t+2)(t-3) be evenly divided by 6? [#permalink]

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12 Aug 2017, 06:59
fitzpratik wrote:
If t is a positive integer, can (t+2)(t-3) be evenly divided by 6?

(1) 5(t^3 +1) is not divisible by 2.

(2) t is a 3-digit number, whose digits are consecutive integers.

Hi..

Let's analyze the main statement...
1) For div by 6, it should be div by both 2 and 3..
2) if t+2 is even T+2-2-2=t-2 should also be even.
3) But t-2 & t-3 should be consecutive integers.. so their product should be even
4) Now we know the product is MULTIPLE of 2
5) We have to check for div by 3!!!

Now let's see the statements..
1) $$5(t^3+1)$$ is NOT div by 2.
So $$t^3 +1$$ is ODD. Hence the is EVEN.
But we are looking for div by 3
Insufficient

2)T is a 3 digit number with consecutive numbers..
3 CONSECUTIVE numbers when added are always div by 3
So t is div by 3 and hence t-3 will also be div by 3.
Now we know product (t-2)(t-3) is div by 3
So SUFFICIENT

B

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Re: If t is a positive integer, can (t+2)(t-3) be evenly divided by 6?   [#permalink] 12 Aug 2017, 06:59
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