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Is the sum of 3 positive integers divisible by 6

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Is the sum of 3 positive integers divisible by 6 [#permalink] New post 26 Nov 2012, 00:21
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Is the sum of 3 positive integers divisible by 6 ?

(1) The least of the 3 positive integers is odd.
(2) The greatest of the 3 positive integers is odd.
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Re: Is the sum of 3 positive integers divisible by 6 [#permalink] New post 26 Nov 2012, 01:24
Bizarre question. My reaction after reading both (1) and (2) was "Ok...:|"

Divisibility by 6 needs divisibility by 2 AND 3. Also, the sum needs to be even.

(1) says nothing, really. If the least number is odd, we know of the other two numbers one is odd and one is even. However, this doesn't tell us anything about divisibility. Insufficient.
(2) also says nothing, amazingly. If the greatest number is odd, we know of the other two numbers one is odd and one is even. However, this doesn't tell us anything about divisibility. Insufficient.

(1) and (2) together are useless too. So E is correct.

There is NO information in either (1) and (2) any properties of the numbers which might imply divisibility. Generally, you need something to establish the property of the set like spacing, prime or not, correlation between numbers in a part of the set etc to say anything about divisibility. I hope you didn't miss typing out a key term like consecutive or evenly spaced etc.

I have no idea where you got this question from, but either:

(1) I am high on sleep deprivation and cant read basic text straight.
or
(2) You need to look at a better compendium of questions, no offense. :lol:
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Re: Is the sum of 3 positive integers divisible by 6 [#permalink] New post 26 Nov 2012, 02:52
ritumaheshwari02 wrote:
Is the sum of 3 positive integers divisible by 6 ?

(1) The least of the 3 positive integers is odd.
(2) The greatest of the 3 positive integers is odd.


The answer to this question is straight E. Consider that the integers are 1, 2 and 3 OR 1, 2, and 5.

Check below question to practice:

Is the sum of 3 consecutive integers divisible by 6 ?

(1) The least of the 3 consecutive integers is odd.
(2) The greatest of the 3 consecutive integers is odd.
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Re: Is the sum of 3 positive integers divisible by 6 [#permalink] New post 29 Nov 2012, 05:55
Bunuel wrote:
ritumaheshwari02 wrote:
Is the sum of 3 positive integers divisible by 6 ?

(1) The least of the 3 positive integers is odd.
(2) The greatest of the 3 positive integers is odd.


The answer to this question is straight E. Consider that the integers are 1, 2 and 3 OR 1, 2, and 5.

Check below question to practice:

Is the sum of 3 consecutive integers divisible by 6 ?

(1) The least of the 3 consecutive integers is odd.
(2) The greatest of the 3 consecutive integers is odd.



Answer to this question i think D.

I tried to look for a pattern: 123 div by 6, 234 not div by 6, 345 div by 6, 456 not div by 6 and so on, so whenever we have first and last integers odd in the sum of three consecutive integers then the sum will be divisible by 6.
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Re: Is the sum of 3 positive integers divisible by 6 [#permalink] New post 29 Nov 2012, 08:38
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ziko wrote:
Bunuel wrote:
ritumaheshwari02 wrote:
Is the sum of 3 positive integers divisible by 6 ?

(1) The least of the 3 positive integers is odd.
(2) The greatest of the 3 positive integers is odd.


The answer to this question is straight E. Consider that the integers are 1, 2 and 3 OR 1, 2, and 5.

Check below question to practice:

Is the sum of 3 consecutive integers divisible by 6 ?

(1) The least of the 3 consecutive integers is odd.
(2) The greatest of the 3 consecutive integers is odd.



Answer to this question i think D.

I tried to look for a pattern: 123 div by 6, 234 not div by 6, 345 div by 6, 456 not div by 6 and so on, so whenever we have first and last integers odd in the sum of three consecutive integers then the sum will be divisible by 6.


Yes, correct answer to the modified question is D.

Is the sum of 3 consecutive integers divisible by 6 ?

Say the 3 integers are x-1, x, and x+1, their sum is (x-1)+x+(x+1)=3x. Now, 3x is divisible by 6 if x is even.

(1) The least of the 3 consecutive integers is odd --> x-1=odd --> x=even. Sufficient.
(2) The greatest of the 3 consecutive integers is odd --> x+1=odd --> x=even. Sufficient.

Answer: D.
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Re: Is the sum of 3 positive integers divisible by 6 [#permalink] New post 29 Nov 2012, 09:01
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This is one of those questions that underlines the importance to read carefully, but really. 99.99 % of time the upfront work is the key: understand what's going on.

Nth kudos for the Mod :)
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Re: Is the sum of 3 positive integers divisible by 6   [#permalink] 29 Nov 2012, 09:01
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