If x, y, and z are consecutive positive integers, which of the

Question

If x, y, and z are consecutive positive integers, which of the following must be true?

I. xyz must be an even integer.
II. xyz is a multiple of 3.
III. xyz is a multiple of 4.

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

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bumbleBee3445 · Answer

For any 3 consecutive numbers, at least 1 will be a multiple of 3, and one will be even,(hence their product will always be even)
a number can be multiple of 4 but it is not always true.

eg. Consider nos as 1,2,3--> one is even, and one is multiple of 3.
1. xyz=1*2*3=6 i.e. even
2. xyz = 1*2*3 is multiple of 3
3. xyz = 1*2*3 is not multiple of 4

Hence answer is  (C) I and II only  must be true.

Whoisdmx15 · Answer

Given,
The numbers are x, x+1, x+2

Now by the very nature of consecutiveness, we can infer that
One of the three numbers is even (as we are spanning across 3 consecutive numbers, they can only be EOE,OEO.

Similarly one out of the three numbers has to be a multiple of 3 (One out of 3 consecutive numbers is a multiple of 3)

Hence,

I. xyz must be an even integer. : TRUE
II. xyz is a multiple of 3.: TRUE
III. xyz is a multiple of 4.: NOT NECESSARILY TRUE

Hence  IMO Ans C

S1mple3 · Answer

I think B, as must be true has been asked.

Krunaal · Answer

Answer is C, because x, y, and z are  consecutive  +'ve integers => there will always be one even integer, x, y and z will either be Even Odd Even or Odd Even Odd. When you multiply these integers, they will always give an even output since atleast one integer was even. Therefore, xyz  must  be even. Hope it helps.

S1mple3 · Answer

Yes, understood, I have thought of a 3 digit number.

If x, y, and z are consecutive positive integers, which of the

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GMAT Problem Solving (PS) Questions

If x, y, and z are consecutive positive integers, which of the

Prep Toolkit

615 to 715 in 15 Days (Ria's Strategies)

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