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30 Jan 2025, 01:30
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C
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Difficulty:
15%
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Question Stats:
80% (01:03) correct
20%
(01:09)
wrong
based on 133
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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
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
30 Jan 2025, 03:56
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Bunuel
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
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)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
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.
30 Jan 2025, 06:41
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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
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
