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11 Jul 2019, 07:34
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D
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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
A. x
B. 2
C. 3
D. 4
E.6
11 Jul 2019, 07:47
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I guess A since consecutive numbers do have divisor of those numbers.
Please correct me if I am wrong.
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Please correct me if I am wrong.
Posted from my mobile device
11 Jul 2019, 07:58
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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.
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.
