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A Medium question, pls help me to explain

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A Medium question, pls help me to explain [#permalink] New post 24 Jul 2011, 02:31
00:00
A
B
C
D
E

Difficulty:

  5% (low)

Question Stats:

67% (01:42) correct 33% (00:48) wrong based on 9 sessions
If x is the product of three consecutive positive integers, which of the following must be true?

I. x is an integer multiple of 3.

II. x is an integer multiple of 4

III. x is an integer multiple of 6

a) I only
b) II only
c) I and II only
d) I and III only
e) I,II and III

pls tell the process of calculation.
[Reveal] Spoiler: OA
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Re: A Medium question, pls help me to explain [#permalink] New post 24 Jul 2011, 04:13
tracyyahoo wrote:
If x is the product of three consecutive positive integers, which of the following must be true?

I. x is an integer multiple of 3.

II. x is an integer multiple of 4

III. x is an integer multiple of 6

a) I only
b) II only
c) I and II only
d) I and III only
e) I,II and III

pls tell the process of calculation.


The answer should be D i.e. X will be an integer and multiple of 3 and 6.

Let us take example n, n+1, n+2 as 3 three consecutive positive integers.
In a sequence of consecutive integers a number is multiple of 3 after every interval of 2 numbers i.e 3,4,5,6 Or 8,9,10,11,12
Hence in a product of 3 consecutive integers, the product is always divisible by 3.
Now, in a consecutive sequence every alternate is an even number, and when an even number is multiplied by 3 we will have 6 as one of the multiple also.

Now for a number to be a multiple of 4 we need at least 2 2's. this is only possible if the first number of three consecutive positive integers is an even number so that 3 is also even and we have 2 2's. But incase the sequence starts with odd we will have one 2 hence, the divisibility by 4 depends on the first number to be even
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Re: A Medium question, pls help me to explain [#permalink] New post 24 Jul 2011, 20:45
suppose we have 4 plus 5 plus 6. The sum of these three integer is not multipled by 6. Could explain me why II is correct as well. Thank u.


Sudhanshuacharya wrote:
tracyyahoo wrote:
If x is the product of three consecutive positive integers, which of the following must be true?

I. x is an integer multiple of 3.

II. x is an integer multiple of 4

III. x is an integer multiple of 6

a) I only
b) II only
c) I and II only
d) I and III only
e) I,II and III

pls tell the process of calculation.


The answer should be D i.e. X will be an integer and multiple of 3 and 6.

Let us take example n, n+1, n+2 as 3 three consecutive positive integers.
In a sequence of consecutive integers a number is multiple of 3 after every interval of 2 numbers i.e 3,4,5,6 Or 8,9,10,11,12
Hence in a product of 3 consecutive integers, the product is always divisible by 3.
Now, in a consecutive sequence every alternate is an even number, and when an even number is multiplied by 3 we will have 6 as one of the multiple also.

Now for a number to be a multiple of 4 we need at least 2 2's. this is only possible if the first number of three consecutive positive integers is an even number so that 3 is also even and we have 2 2's. But incase the sequence starts with odd we will have one 2 hence, the divisibility by 4 depends on the first number to be even


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Re: A Medium question, pls help me to explain [#permalink] New post 24 Jul 2011, 20:49
tracyyahoo wrote:
suppose we have 4 plus 5 plus 6. The sum of these three integer is not multipled by 6. Could explain me why II is correct as well. Thank u.


The question says Product, not sum.
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Re: A Medium question, pls help me to explain [#permalink] New post 25 Jul 2011, 00:53
tracyyahoo wrote:
suppose we have 4 plus 5 plus 6. The sum of these three integer is not multipled by 6. Could explain me why II is correct as well. Thank u.


Sudhanshuacharya wrote:
tracyyahoo wrote:
If x is the product of three consecutive positive integers, which of the following must be true?

I. x is an integer multiple of 3.

II. x is an integer multiple of 4

III. x is an integer multiple of 6

a) I only
b) II only
c) I and II only
d) I and III only
e) I,II and III

pls tell the process of calculation.


The answer should be D i.e. X will be an integer and multiple of 3 and 6.

Let us take example n, n+1, n+2 as 3 three consecutive positive integers.
In a sequence of consecutive integers a number is multiple of 3 after every interval of 2 numbers i.e 3,4,5,6 Or 8,9,10,11,12
Hence in a product of 3 consecutive integers, the product is always divisible by 3.
Now, in a consecutive sequence every alternate is an even number, and when an even number is multiplied by 3 we will have 6 as one of the multiple also.

Now for a number to be a multiple of 4 we need at least 2 2's. this is only possible if the first number of three consecutive positive integers is an even number so that 3 is also even and we have 2 2's. But incase the sequence starts with odd we will have one 2 hence, the divisibility by 4 depends on the first number to be even


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Tracy: I guess the question is asking for product of 3 numbers and not addition.
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Re: A Medium question, pls help me to explain [#permalink] New post 27 Jul 2011, 03:29
Product of three consecutive integers
a) it will always be a multiple of 3 as every third number is a multiple of 3
b) it is not necessary a multiple of 4 e.g. 5,6,7. The product of these numbers is not a multiple of 4
c) the product of 3 consecutive numbers is a multiple of 6(3 and 2) as, it will be a multiple of 3 and every 2nd number is a multiple of 2. So the product will be a multiple of 6

Hence, the answer is D
Re: A Medium question, pls help me to explain   [#permalink] 27 Jul 2011, 03:29
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A Medium question, pls help me to explain

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