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11 Jun 2021, 08:15
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E
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
5%
(low)
Question Stats:
88% (00:58) correct
12%
(00:55)
wrong
based on 249
sessions
History
Date
Time
Result
Not Attempted Yet
If n is the smallest of three consecutive positive integers, which of the following must be true?
(A) n is divisible by 3
(B) n is even
(C) n is odd
(D) (n)(n + 2) is even
(E) n(n + 1)(n + 2) is divisible by 3
(A) n is divisible by 3
(B) n is even
(C) n is odd
(D) (n)(n + 2) is even
(E) n(n + 1)(n + 2) is divisible by 3
11 Jun 2021, 08:27
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Bunuel
Method1: Product of n consecutive integers is divisible by n!, Hence(E)
Method2:
A) Numbers = {4, 5, 6} - Not true!
B) Numbers = {3, 4, 5} - Not true!
C) Numbers = {8, 9, 10} - Not true!
D) Numbers = {7, 8, 9} - Not true!
E) Only option left - True!
Either ways, IMO,(E)!
11 Jun 2021, 09:39
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Solution:
If \(n\) the smallest of three consecutive positive integers then rest 2 integers will be \(n+1\) and \(n+2\).
Option A: n is divisible by 3
This is not sure to be true.
If n = 6 (for example) then n is divisible by 3.
But if n = 5(for example) then n is not divisible by 3.
Option B: n is even
This is not sure to be true.
If n = 6 (for example) then n is even.
But if n = 5(for example) then n is not even.
Option C: n is odd
This is not sure to be true.
If n = 6 (for example) then n is not odd.
But if n = 5(for example) then n is odd.
Option D: n(n + 2) is even
This is not sure to be true.
If n = 6 (for example) then n(n+2) is even.
But if n = 5(for example) then n(n+2) is not even.
Option E: n(n + 1)(n + 2) is divisible by 3
This is always true.
No matter what positive integer you assume as n, the product of 3 consecutive positive integer n(n + 1)(n + 2) is always gonna be divisible by 3.
Hence the right answer is Option E.
If \(n\) the smallest of three consecutive positive integers then rest 2 integers will be \(n+1\) and \(n+2\).
Option A: n is divisible by 3
This is not sure to be true.
If n = 6 (for example) then n is divisible by 3.
But if n = 5(for example) then n is not divisible by 3.
Option B: n is even
This is not sure to be true.
If n = 6 (for example) then n is even.
But if n = 5(for example) then n is not even.
Option C: n is odd
This is not sure to be true.
If n = 6 (for example) then n is not odd.
But if n = 5(for example) then n is odd.
Option D: n(n + 2) is even
This is not sure to be true.
If n = 6 (for example) then n(n+2) is even.
But if n = 5(for example) then n(n+2) is not even.
Option E: n(n + 1)(n + 2) is divisible by 3
This is always true.
No matter what positive integer you assume as n, the product of 3 consecutive positive integer n(n + 1)(n + 2) is always gonna be divisible by 3.
Hence the right answer is Option E.
