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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 ?

by vinni.k » Sun Apr 08, 2018 8:29 am

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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.

OA is E

Question is :- Is (x + y + z) / 6 = integer ?
S(1), Suppose x < y < z. So, out of x,y, and z, x is odd because it is the least integer.
x = 1 y = 2 z = 4
1 + 2 + 4 = 7 ==> Not divisible by 6
(here, i am under the impression that only one of them will be odd and that will be the least number)
So, s(1) is sufficient

S(2), same here 1 + 2 + 5 (Here again i think that one of them will be odd and that will be the greatest integer)
I think it is D but OA is E
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Source: — Data Sufficiency |
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by GMATGuruNY » Sun Apr 08, 2018 8:36 am

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vinni.k 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.
Statements combined:
Case 1: The 3 integers are 1, 6, and 11, with the result that the sum of the 3 integers = 1+6+11 = 18
Since 18 is divisible by 6, the answer to the question stem is YES.

Case 2: The 3 integers are 1, 5, and 11, with the result that the sum of the 3 integers = 1+5+11 = 17
Since 17 is NOT divisible by 6, the answer to the question stem is NO.

Since the answer is YES in Case 1 but NO in Case 2, the two statements combined are INSUFFICIENT.

The correct answer is E.
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by vinni.k » Sun Apr 08, 2018 9:29 am

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Mitch,

Thanks but i am not sure how you interpret S(1) and S(2).

S(1) clearly says that "the least of the 3 positive integers is odd". Doesn't it mean that only one of the 3 integers is odd ?
I know it doesn't talk about other two integers, but by the wording of the statements i think it should be only one integer and that is the least or the greatest integer as given in s(2)
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by GMATGuruNY » Sun Apr 08, 2018 9:38 am

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vinni.k wrote:Mitch,

Thanks but i am not sure how you interpret S(1) and S(2).

S(1) clearly says that "the least of the 3 positive integers is odd". Doesn't it mean that only one of the 3 integers is odd ?
The interpretation in red is incorrect.
Statement 1 states only that -- of the 3 positive integers -- the SMALLEST is odd.
Statement 2 states only that -- of the 3 positive integers -- the GREATEST is odd.
Neither statement indicates that ONLY ONE of the integers is odd.
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by vinni.k » Sun Apr 08, 2018 9:54 am

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GMATGuruNY wrote: The interpretation in red is incorrect.
Statement 1 states only that -- of the 3 positive integers -- the SMALLEST is odd.
Statement 2 states only that -- of the 3 positive integers -- the GREATEST is odd.
Neither statement indicates that ONLY ONE of the integers is odd.
So, how will you ask a question in which ONLY ONE of the integers is odd ?
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by GMATGuruNY » Sun Apr 08, 2018 10:16 am

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vinni.k wrote:So, how will you ask a question in which ONLY ONE of the integers is odd ?
Here are a few ways:

Only one of the three integers is odd.
Exactly one of the three integers is odd.
Exactly two of the three integers are even.
Only the least of the three integers is odd.
Of the three integers, only the greatest is odd.
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by vinni.k » Sun Apr 08, 2018 10:31 am

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GMATGuruNY wrote:
Here are a few ways:

Only one of the three integers is odd.
Exactly one of the three integers is odd.
Exactly two of the three integers are even.
Only the least of the three integers is odd.
Of the three integers, only the greatest is odd.
So, "only "was missing from S(1) and S(2).

Okay thanks. I appreciate it. You are a gem of a person.
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