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# If n is the product of 3 consecutive integers, which of the following

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Math Revolution GMAT Instructor
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If n is the product of 3 consecutive integers, which of the following  [#permalink]

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17 Nov 2016, 03:25
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) 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

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"Only $149 for 3 month Online Course" "Free Resources-30 day online access & Diagnostic Test" "Unlimited Access to over 120 free video lessons - try it yourself" CEO Joined: 11 Sep 2015 Posts: 3431 Location: Canada Re: If n is the product of 3 consecutive integers, which of the following [#permalink] ### Show Tags 17 Nov 2016, 05:39 2 Top Contributor 1 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 RELATED VIDEO _________________ Test confidently with gmatprepnow.com Board of Directors Status: QA & VA Forum Moderator Joined: 11 Jun 2011 Posts: 4383 Location: India GPA: 3.5 WE: Business Development (Commercial Banking) Re: If n is the product of 3 consecutive integers, which of the following [#permalink] ### Show Tags 17 Nov 2016, 07:51 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 There is a property which states - Quote: Product of three numbers is always divisible by 6 So, n will be a multiple of 2 and 3 Answer will be (D) _________________ Thanks and Regards Abhishek.... PLEASE FOLLOW THE RULES FOR POSTING IN QA AND VA FORUM AND USE SEARCH FUNCTION BEFORE POSTING NEW QUESTIONS How to use Search Function in GMAT Club | Rules for Posting in QA forum | Writing Mathematical Formulas |Rules for Posting in VA forum | Request Expert's Reply ( VA Forum Only ) Math Revolution GMAT Instructor Joined: 16 Aug 2015 Posts: 6955 GMAT 1: 760 Q51 V42 GPA: 3.82 Re: If n is the product of 3 consecutive integers, which of the following [#permalink] ### Show Tags 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. Answer: D _________________ MathRevolution: Finish GMAT Quant Section with 10 minutes to spare The one-and-only World’s First Variable Approach for DS and IVY Approach for PS with ease, speed and accuracy. "Only$149 for 3 month Online Course"
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If n is the product of 3 consecutive integers, which of the following  [#permalink]

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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.

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Re: If n is the product of 3 consecutive integers, which of the following  [#permalink]

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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.

Hence D.

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If n is the product of 3 consecutive integers, which of the following  [#permalink]

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22 Mar 2017, 01:52
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
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"Only $149 for 3 month Online Course" "Free Resources-30 day online access & Diagnostic Test" "Unlimited Access to over 120 free video lessons - try it yourself" Target Test Prep Representative Status: Head GMAT Instructor Affiliations: Target Test Prep Joined: 04 Mar 2011 Posts: 2827 Re: If n is the product of 3 consecutive integers, which of the following [#permalink] ### Show Tags 23 Mar 2017, 15:57 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 Since n is the product of 3 consecutive integers, n is divisible by 3! = 6. Since 2 and 3 are factors of 6, Roman numerals I and II must be true. Answer: D _________________ Jeffery Miller Head of GMAT Instruction GMAT Quant Self-Study Course 500+ lessons 3000+ practice problems 800+ HD solutions Intern Joined: 25 Jul 2016 Posts: 2 Re: If n is the product of 3 consecutive integers, which of the following [#permalink] ### Show Tags 23 Mar 2017, 18:43 can the integers be -1,0 and 1? in that case nothing holds true. I think it should have mentioned n not equal to 0. Math Revolution GMAT Instructor Joined: 16 Aug 2015 Posts: 6955 GMAT 1: 760 Q51 V42 GPA: 3.82 Re: If n is the product of 3 consecutive integers, which of the following [#permalink] ### Show Tags 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. The answer is D. Answer: D _________________ MathRevolution: Finish GMAT Quant Section with 10 minutes to spare The one-and-only World’s First Variable Approach for DS and IVY Approach for PS with ease, speed and accuracy. "Only$149 for 3 month Online Course"
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Re: If n is the product of 3 consecutive integers, which of the following  [#permalink]

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24 Mar 2017, 03:29
rai0512 wrote:
can the integers be -1,0 and 1? in that case nothing holds true. I think it should have mentioned n not equal to 0.

No, that's not right. You should know that 0 is divisible by every integer except 0 itself.
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Re: If n is the product of 3 consecutive integers, which of the following  [#permalink]

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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  [#permalink]

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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.
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Re: If n is the product of 3 consecutive integers, which of the following  [#permalink]

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