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If x is the product of three consecutive positive integers, which of the following must be true?

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If x is the product of three consecutive positive integers, which of the following must be true?

by BTGModeratorVI » Sat Apr 18, 2020 9:14 am

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If x is the product of three consecutive positive integers, which of the following must be true?

I. x is an integer multiple of 3.
II. x is an integer multiple of 4.
III. x is an integer multiple of 6.

(A) I only
(B) II only
(C) I and II only
(D) I and III only
(E) I, II, and III

Answer: D
Source: Official guide
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Re: If x is the product of three consecutive positive integers, which of the following must be true?

by Jay@ManhattanReview » Mon Apr 20, 2020 12:10 am
BTGModeratorVI wrote: ↑
Sat Apr 18, 2020 9:14 am
 If x is the product of three consecutive positive integers, which of the following must be true?

I. x is an integer multiple of 3.
II. x is an integer multiple of 4.
III. x is an integer multiple of 6.

(A) I only
(B) II only
(C) I and II only
(D) I and III only
(E) I, II, and III

Answer: D
Source: Official guide
Note that the product of any three consecutive positive integers is always divisible by 6. This, only Statements I and III are correct.

Statement II is incorrect. Let's take the three consecutive integers as 1, 2, and 3. We see that the product 1*2*3 = 6 is not divisible by 4.

The correct answer: D

Hope this helps!

-Jay
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Re: If x is the product of three consecutive positive integers, which of the following must be true?

by Brent@GMATPrepNow » Mon Apr 20, 2020 5:41 am
BTGModeratorVI wrote: ↑
Sat Apr 18, 2020 9:14 am
 If x is the product of three consecutive positive integers, which of the following must be true?

I. x is an integer multiple of 3.
II. x is an integer multiple of 4.
III. x is an integer multiple of 6.

(A) I only
(B) II only
(C) I and II only
(D) I and III only
(E) I, II, and III

Answer: D
Source: Official guide
----ASIDE---------------------
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
Likewise, the product of any 11 consecutive integers will be divisible by 11, 10, 9, . . . 3, 2 and 1

NOTE: the product may be divisible by other numbers as well, but the divisors (noted above) are guaranteed.
------------------------------

Since x = the product of three consecutive integers, the above rule tells us that x is definitely divisible by 3 and 2.
So statement I is true

Also, if x is divisible by 3 and 2, then x is also divisible by 6.
So statement III is true

What about statement II? Is x necessarily divisible by 4?
No. All we knows for certain is that x must be divisible by 2

For example it COULD beat the case that x = (1)(2)(3) = 6
Since 6 is NOT divisible by 4, we can see that statement II is not necessarily true

Answer: D

Cheers,
Brent
Brent Hanneson - Creator of GMATPrepNow.com
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