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Re: If n is the product of 3 consecutive integers, which of the following
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17 Nov 2016, 05:39

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MathRevolution wrote:

If n is the product of 3 consecutive integers, which of the following must be true about n?

I. n is a multiple of 2 II. n is a multiple of 3 III. n is a multiple of 4

A. I only B. II only C. III only D. I and II E. II and III

There's a nice rule says: The product of k consecutive integers is divisible by k, k-1, k-2,...,2, and 1 So, for example, the product of any 5 consecutive integers will be divisible by 5, 4, 3, 2 and 1 NOTE: the product may be divisible by other numbers as well, but these divisors are guaranteed.

In this question, n is the product of 3 consecutive integers. So, according to the rule, n must be divisible by 3, 2 and 1 So, we already know that statements I and II must be true.

Do we need to check statement III? No. Notice that NONE of the answer choices include all 3 statements. Since we've already concluded that statements I and II are true, the correct answer is D.

HOWEVER, if you want to check statement III, notice that the product of 1, 2 and 3 (3 consecutive integers) is 6, and 6 is not divisible by 4

Re: If n is the product of 3 consecutive integers, which of the following
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21 Nov 2016, 01:02

==> The product of 3 consecutive integers always become the multiple of 6, because the product always contains 3 and 2. Thus, in this question, it always becomes the multiple of 6 that contain 3 and 2, I and II are the answer. Therefore, the answer is D. III does not work because it becomes 1*2*3*=6, hence it cannot be the multiple of 4.

If n is the product of 3 consecutive integers, which of the following
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21 Nov 2016, 01:49

MathRevolution wrote:

) If n is the product of 3 consecutive integers, which of the following must be true?

I. a multiple of 2 II. a multiple of 3 III. a multiple of 4

A. I only B. II only C. III only D. I and II E. II and III

Among 3 consecutive integers, there is always at least one even integers, so n is divisible by 2. (I) is true

Among 3 consecutive integers, there is always only one integers divisible by 3, so n is divisible by 3. (II) is true.

3 consecutive integers could be even-odd-even or odd-even-odd. If they are even-odd-even, n is divisible by 4. If they are odd-even-odd, n is not divisible by 4. For example, \(n=1 \times 2 \times 3 =6\) is not divisible by 4. Hence, (III) is not true.

Re: If n is the product of 3 consecutive integers, which of the following
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15 Jan 2017, 23:42

Product of n consecutive integers is always divisible by n! So n will be of the form 6k for some integer k. Clearly it will always be divisible by 2 and 3 but may/may not be divisible by 4.

Re: If n is the product of 3 consecutive integers, which of the following
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24 Mar 2017, 02:56

==> If n is the product of 3 consecutive integers, it is always even and has 3, so it is always a multiple of 6. Thus, I and II is correct and for III, since n=1*2*3=6 is not a multiple of 4, hence it is incorrect.

Re: If n is the product of 3 consecutive integers, which of the following
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09 Apr 2017, 08:56

In three consecutive nos. one number (at least) will be 2 or a multiple of 2 thus making the product even. Thus divisible by 2.

The product of three consecutive nos. is always divisible by 3. For example, 4*5*6 (6 is a multiple of 3) 7*8*9 (9 is a multiple of 3)
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Re: If n is the product of 3 consecutive integers, which of the following
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11 Apr 2017, 18:40

Something you all need to know, an integer multiplied by the second and third consecutive will always be divisible by 2 and 3. For an example 1 x 2 x 3. There is no need to do any working out here. We all know that it is divisible by 2 and 3. Therefore, the answer is D

Re: If n is the product of 3 consecutive integers, which of the following
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03 Feb 2019, 21:13

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