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If the remainder is 1, when integer n(n>1) is divided by 3,
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30 Jul 2020, 15:20
30 Jul 2020, 15:20
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Question Stats:
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58% (02:01) wrong based on 31 sessions
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n is an integer greater than 1. If the remainder is 1, when n is divided by 3, then (n² + n - 2) must be divisible by which 2-digit number?
A. 12
B. 14
C. 16
D. 18
E. 20
A. 12
B. 14
C. 16
D. 18
E. 20
Re: If the remainder is 1, when integer n(n>1) is divided by 3,
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30 Jul 2020, 22:59
30 Jul 2020, 22:59
1
When n is divided by 3, the remainder is 1.
So lets say n is 7, when when divided by 3 gives remainder as 1.
Now, according to the equation, (n^2+n-2)
49 + 7 - 2 = 54
Only 18 can divide 54 completely. Thus, answer is D
So lets say n is 7, when when divided by 3 gives remainder as 1.
Now, according to the equation, (n^2+n-2)
49 + 7 - 2 = 54
Only 18 can divide 54 completely. Thus, answer is D
Re: If the remainder is 1, when integer n(n>1) is divided by 3,
[#permalink]
03 Aug 2020, 04:45
03 Aug 2020, 04:45
1
In general if we have integers x,y,m,and r such that
x/y=m+(r/y) then r is the remainder and m is the whole number part of the division
e.g. 4/3=1+1/3 here x=4, y=3, m=1, r=1
Let n and m be integers
n/3=m+(1/3)
m is the whole number part of the division and 1 in (1/3) represents the remainder.
multiple 3 on both sides
n=3m+1
therefore
n^2-n-2= (n+2)(n-1)= ((3m+1)+2)((3m+1)-1) =(3m+3)(3m) =3(m+1)3m= 9(m+1)(m)
Finally since m and m+1 are consecutive integers one of them must be even therefore we can factor out a 2 from it giving us
=9*2*((m+1)m)/2
=18*((m+1)(m))/2
Since 18 is a factor of n^2-n-2. Then n^2-n-2 is divisible by 18.
Final Answer: D
x/y=m+(r/y) then r is the remainder and m is the whole number part of the division
e.g. 4/3=1+1/3 here x=4, y=3, m=1, r=1
Let n and m be integers
n/3=m+(1/3)
m is the whole number part of the division and 1 in (1/3) represents the remainder.
multiple 3 on both sides
n=3m+1
therefore
n^2-n-2= (n+2)(n-1)= ((3m+1)+2)((3m+1)-1) =(3m+3)(3m) =3(m+1)3m= 9(m+1)(m)
Finally since m and m+1 are consecutive integers one of them must be even therefore we can factor out a 2 from it giving us
=9*2*((m+1)m)/2
=18*((m+1)(m))/2
Since 18 is a factor of n^2-n-2. Then n^2-n-2 is divisible by 18.
Final Answer: D
