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If x is a positive integer, which of the following is not necessarily

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If x is a positive integer, which of the following is not necessarily  [#permalink]

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New post 11 Jul 2019, 07:34
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A
B
C
D
E

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Question Stats:

70% (01:07) correct 30% (01:27) wrong based on 56 sessions

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Re: If x is a positive integer, which of the following is not necessarily  [#permalink]

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New post 11 Jul 2019, 07:47
I guess A since consecutive numbers do have divisor of those numbers.

Please correct me if I am wrong.

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If x is a positive integer, which of the following is not necessarily  [#permalink]

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New post 11 Jul 2019, 07:58
If x is a positive integer, which of the following is not necessarily a divisor of x(x+1)(x+2)?

A. x
As x is clearly a factor of (x)(x + 1)(x + 2), x has to be a divisor, and will, therefore, divide (x)(x + 1)(x + 2).

B. 2
If x is even, (x)(x + 1)(x + 2) will contain a factor 2, as either x or (x + 2) will have 2 as a factor. Therefore, 2 will divide (x)(x + 1)(x + 2).

C. 3
Every 3rd term in a series of consecutive numbers will contain a factor 3. As (x)(x + 1)(x + 2) contains 3 terms, 3 will be a factor, and therefore, divide (x)(x + 1)(x + 2).

D. 4
A series with at least four consecutive terms will be divisible by 4. (x)(x + 1)(x + 2) however, does not contain 4 terms. Therefore, (x)(x + 1)(x + 2) does not necessarily have to be divisible by 4.

E.6
If a number is divisible by 2 and 3, it will be divisible by 6. As (x)(x + 1)(x + 2) contains 3 terms, 2 and 3 will be factors. Therefore, 6 will divide (x)(x + 1)(x + 2).

I believe the answer is most likely D.
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Re: If x is a positive integer, which of the following is not necessarily  [#permalink]

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New post 11 Jul 2019, 10:06
Bunuel wrote:
If x is a positive integer, which of the following is not necessarily a divisor of x(x+1)(x+2)?

A. x
B. 2
C. 3
D. 4
E.6



3 consecutive is always divisible by 3!

Thus, 2, 3 , 6 , x are factors.

D is the best answer.
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Re: If x is a positive integer, which of the following is not necessarily  [#permalink]

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New post 11 Jul 2019, 10:52
Bunuel wrote:
If x is a positive integer, which of the following is not necessarily a divisor of x(x+1)(x+2)?

A. x
B. 2
C. 3
D. 4
E.6


x(x+1)(x+2)
x being +ve integer so value would always be of a consecutive series
in that case only divisor which wont be possible would be 4 ; as for a number to be divisible by 4 it has to be divisible twice by 2 which wont be possible when x=1
IMO D
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Re: If x is a positive integer, which of the following is not necessarily  [#permalink]

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New post 11 Jul 2019, 13:59
For this product of 3 consecutive Numbers,

1. x is a divisor since it is one of the numbers in the product
2. 2 is a divisor since one of the numbers has to be even
3. 3 is a divisor since one the numbers will definitely be a multiple of 3
4. 6 is a divisor combining points 2 and 3 above.
5. Only 4 is not a divisor. example 5X6X7

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Re: If x is a positive integer, which of the following is not necessarily  [#permalink]

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New post 11 Jul 2019, 14:19
for simplicity, suppose x=1

now X should be a factor for sure since the equation is factored by X

for x=1 the equation is equal 1(1+1)(1+2)= 1(2)(3)=6

6 is divisible by 6,3,2 and X which is equal to 1. the equation is not divisible by 4

so D) is the answer

Note:you can plug some other numbers and the equation will be divisible by 4 but dont get distracted, the stem says: which of the following is not necessarily a divisor of x(x+1)(x+2)? not necessarily here means that for some values of x the equation will be divisible by 4, however, the equation will be always divisible by 6,3,2 and X for any X
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Re: If x is a positive integer, which of the following is not necessarily  [#permalink]

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New post 12 Jul 2019, 18:59
Bunuel wrote:
If x is a positive integer, which of the following is not necessarily a divisor of x(x+1)(x+2)?

A. x
B. 2
C. 3
D. 4
E.6


First, we see that x is a divisor of x(x + 1)(x + 2). Now, notice that x, (x + 1), and (x + 2) are consecutive integers.When we are given the product of n consecutive integers, the product is divisible by n!. Since here we have the product of 3 consecutive integers, it’s divisible by 3! = 6, which means it’s also divisible by 2 and 3. So only 4 is not necessarily a divistor.

Alternate Solution:

Let’s let x = 1. Then, x(x + 1)(x + 2) = 1 * 2 * 3 = 6 is divisible by x (which is 1), 2, 3 and 6. As we can see, the product is not necessarily divisible by 4.

Answer: D
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Re: If x is a positive integer, which of the following is not necessarily   [#permalink] 12 Jul 2019, 18:59
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