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If the sum of three integers is divisible by 2, is their product divis

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If the sum of three integers is divisible by 2, is their product divis  [#permalink]

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New post 27 Sep 2018, 04:51
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Question Stats:

66% (01:44) correct 34% (01:45) wrong based on 51 sessions

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If the sum of three integers is divisible by 2, is their product divisible by 4?

(1) The three integers are same.
(2) The product of the three integers is divisible by 2.

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Re: If the sum of three integers is divisible by 2, is their product divis  [#permalink]

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New post 27 Sep 2018, 06:34
1
Bunuel wrote:
If the sum of three integers is divisible by 2, is their product divisible by 4?

(1) The three integers are same.
(2) The product of the three integers is divisible by 2.


(1) If the three integers are same and are divisible by 2, the integer has to be even. Hence there will be at least three 2s in the product. So it should be divisible by 4. Sufficient.

(2) The product of the three integers is divisible by 2. If integers are 1,1, and 2, product is not divisible by 4. If integers are 2,4, and 6, product is divisible by 4. Not sufficient.

Hence A.

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If the sum of three integers is divisible by 2, is their product divis  [#permalink]

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New post 28 Sep 2018, 23:34

Solution



Given:
    • Sum of three integers is divisible by 2

To find:
    • Whether the product of the integers divisible by 4 or not

Analysing Statement 1
As per the information given in statement 1, the three integers are same.
We also know that their sum is divisible by 2.
    • As their sum is even, it is only possible when all of them are even.
    • And if we multiply 3 even numbers, then their product is always divisible by 4.

Hence, statement 1 is sufficient to answer the question.

Analysing Statement 2
As per the information given in statement 2, the product of the three integers is divisible by 2.
    • If the product of 3 numbers is divisible by 2, then at least one of them is a multiple of 2.
    • However, if only one multiple of 2 is present, then the product is not a multiple of 4.
    • In other cases, if two or three of them are multiples of 2, then the product is a multiple of 4.

Hence, statement 2 is not sufficient to answer the question.

Hence, the correct answer is option A.

Answer: A

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If the sum of three integers is divisible by 2, is their product divis   [#permalink] 28 Sep 2018, 23:34
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