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Math Expert V
Joined: 02 Sep 2009
Posts: 58445

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Difficulty:   35% (medium)

Question Stats: 56% (00:47) correct 44% (01:05) wrong based on 18 sessions

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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

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Math Expert V
Joined: 02 Sep 2009
Posts: 58445

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Official Solution:

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

We’ll go for ALTERNATIVE since we’re asked about an expression with variables.

When looking at the answers, $$x$$ is definitely a divisor, since it is a multiplier in the expression itself. But what about the rest of the answers? Since this is an expression with only letters, we can pick a number: $$x = 1$$ gives us $$1 × 2 × 3 = 6$$. So 2, 3, and 6 are all divisors of 6, but 4 isn’t.

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Intern  B
Joined: 03 Sep 2018
Posts: 2

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I don't understand this question. If we are allowed to "pick a number" and I choose x=4 then the solution is divisible by all the answer choices. I must try another number that isn't divisible by all the answers?
x=1
1(1+1)(1+2)
(1)(2)(3)= 6 (which is not divisible by 4

but what if I choose x=4

4(4+1)(4+2)
4(5)(6)= 120 (divisible by 3,6,and 4.

Do I have to chose a number that is not a possible answer?
Intern  Joined: 10 Sep 2018
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Correct. Keep in mind, the question reads: "which of the following is not NECESSARILY a divisor of x(x+1)(x+2)x(x+1)(x+2)?" That means there will be some answer choices where they all work. But you need to find the one where one of them doesn't work. Even though 4 is divisible when X=4, it is not divisible when X=1. The other answer choices will be divisible regardless of what X is equal to. So if you try X=4 and can't determine the correct answer, try incrementing your X value by one until you find the correct answer.
Intern  B
Joined: 22 Jun 2018
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Poor question
Intern  Joined: 19 Nov 2018
Posts: 1

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It will definitely be divisible by 2 because any 3 consecutive numbers would contain an even number (thus the product would be even); and any 3 consecutive numbers would contain a multiple of 3 (thus divisible by 3). Since it is an even number that can be divided by 3, it would definitely be divisible by 6. But 4 is not a definite divisor of the product of any 3 consecutive numbers. Re: M70-01   [#permalink] 28 Nov 2018, 09:27
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