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Given that x is a positive integer such that x ≥ 75, which of the foll
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26 Oct 2021, 04:30
26 Oct 2021, 04:30
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Question Stats:
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29%
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based on 136
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Q = x^3 − x
Given that x is a positive integer such that x ≥ 75, which of the following is the remainder when Q is divided by 6?
A. 0
B. 1
C. 3
D. 5
E. Cannot be determined by the information provided
Given that x is a positive integer such that x ≥ 75, which of the following is the remainder when Q is divided by 6?
A. 0
B. 1
C. 3
D. 5
E. Cannot be determined by the information provided
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Re: Given that x is a positive integer such that x ≥ 75, which of the foll
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26 Oct 2021, 04:43
26 Oct 2021, 04:43
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Q = x(x^2 - 1)
=> Q = x(x+1)(x-1)
We have three consecutive integers such that x >=75
Hence we can have the following possibilities
1. x = even , x+1 = odd and x-1 = odd
2. x = odd, x+1 = even and x-1 = even
Since these are consecutive numbers, we are bound to have a multiple of 3 among these numbers and also a multiple of 2 from the even number.
Hence the number would evenly divide Q.
Option A
=> Q = x(x+1)(x-1)
We have three consecutive integers such that x >=75
Hence we can have the following possibilities
1. x = even , x+1 = odd and x-1 = odd
2. x = odd, x+1 = even and x-1 = even
Since these are consecutive numbers, we are bound to have a multiple of 3 among these numbers and also a multiple of 2 from the even number.
Hence the number would evenly divide Q.
Option A
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Re: Given that x is a positive integer such that x ≥ 75, which of the foll
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26 Oct 2021, 06:01
26 Oct 2021, 06:01
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Expert Reply
Bunuel wrote:
Q = x^3 − x
Given that x is a positive integer such that x ≥ 75, which of the following is the remainder when Q is divided by 6?
A. 0
B. 1
C. 3
D. 5
E. Cannot be determined by the information provided
Given that x is a positive integer such that x ≥ 75, which of the following is the remainder when Q is divided by 6?
A. 0
B. 1
C. 3
D. 5
E. Cannot be determined by the information provided
\(Q = x^3 − x = x(x^2-1) = (x-1)*x*(x+1)\) i.e. Product of three consecutive positive Integers for given x ≥ 75
Product of three consecutive integers inclue
1) Atleast one multiple of 2
2) One multiple of 3
i.e. Product fo three consecutive integers is always divisible by (3*2=)6
i.e. Q = Multiple of 6
hence, remainder when Q is divided by 6 = 0
Answer: Option A
