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Show exactly one of the number n, n 2,n 4 is divisible by 3?
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Show exactly one of the number n, n 2,n 4 is divisible by 3?
We know that any positive integer is of the form 3q,3q+1,3q+2 for some integer q
CASE 1
When n =3q , is divisible by 3
n+2= 3q+2 , is not divisible by 3 as it leaves a remainder 2
n+4 = 3q+4, 3q + 3 +1, 3(q+1)+1, not divisible by 3 as it leaves a remainder 1
Therefore n is divisible by 3 and n+2 and n+4 are not divisible by 3.
CASE 2
n= 3q +1 noy divisible by 3 because it leaves a remainder 1
n+2= 3q+1+2, 3q+3, 3(q+1) , divisible by 3
n + 4 = 3q+1+4 , 3q+5 , 3q +3+2,3(q+1)+2 ,not divisible by 3 because it leavesa remainder 2
Therefore n +2 is divisible by 3 and n and n+4 are not divisible by 3
CASE 3
n=3q+2 ,not divisible by 3 because it leaves a remainder 2
n+2= 3q+2+2 , 3q+4 , 3q + 3+1, 3 (q+1)+1 ,not divisible by 3 as it leaves a remainder 1
n+4=3q+2+4, 3q+6 ,3(q+2),divisible by 3
Therefore n+4 is divisible by 3 but n and n +2 are not divisible by 3
Therefor only one out of n , n+2, n+4 is divisible by 3
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Show exactly one of the number n, n 2,n 4 is divisible by 3?
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Show exactly one of the number n, n 2,n 4 is divisible by 3? for Class 10 2024 is part of Class 10 preparation. The Question and answers have been prepared according to the Class 10 exam syllabus. Information about Show exactly one of the number n, n 2,n 4 is divisible by 3? covers all topics & solutions for Class 10 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Show exactly one of the number n, n 2,n 4 is divisible by 3?.
Show exactly one of the number n, n 2,n 4 is divisible by 3? for Class 10 2024 is part of Class 10 preparation. The Question and answers have been prepared according to the Class 10 exam syllabus. Information about Show exactly one of the number n, n 2,n 4 is divisible by 3? covers all topics & solutions for Class 10 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Show exactly one of the number n, n 2,n 4 is divisible by 3?.
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