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#### Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here. # If the remainder is 1, when integer n(n>1) is divided by 3,  Question banks Downloads My Bookmarks Reviews Important topics
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Intern Joined: 30 Jul 2020
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If the remainder is 1, when integer n(n>1) is divided by 3, [#permalink] 00:00

Question Stats: 87% (01:00) correct 12% (01:16) wrong based on 8 sessions
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 double-digit number?

A. 12
B. 14
C. 16
D. 18
E. 20
Manager Joined: 09 Mar 2020
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Re: If the remainder is 1, when integer n(n>1) is divided by 3, [#permalink]
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 Manager Joined: 22 Jan 2020
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Re: If the remainder is 1, when integer n(n>1) is divided by 3, [#permalink]
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.

Intern Joined: 25 Jul 2020
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Re: If the remainder is 1, when integer n(n>1) is divided by 3, [#permalink]
Saraforgre wrote:
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 double-digit number?

A. 12
B. 14
C. 16
D. 18
E. 20

If n/3 yields a remainder of 1, then n must be one greater than a multiple of 3. Since the problem specifies that the given equation MUST be divisible by one of the answers choices, we know that we can choose any value that satisfies the criteria.

Let n = 4. (4)^2 + 4 - 2 = 18, so D is clearly the correct answer. Re: If the remainder is 1, when integer n(n>1) is divided by 3,   [#permalink] 04 Aug 2020, 12:23
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