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vcbabu
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If n is an integer, what is the remainder when n is divided Updated on: 12 Oct 2013, 09:19
Originally posted by vcbabu on 31 May 2009, 10:07.
Last edited by Bunuel on 12 Oct 2013, 09:19, edited 1 time in total.
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If n is an integer, what is the remainder when n is divided by 7?

(1) n+1 is divisible by 7
(2) n+8 is divisible by 7

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D
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If n is an integer, what is the remainder when n is divided 31 May 2009, 18:02
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If n is an integer, what is the remainder when n is divided by 7?

1) n+1 is divisible by 7
2) n+8 is divisible by 7
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D. Reminder(s) can never be negative but is(are) always: 0 <= r =< 7.
Lets say n = ax + r, where a = 7, x is quotient, and r is reminder.
Or, n = 7x + r
Then in each case above, r = 6.

1) If n = 7x + r, n+1 = (7x+r) + 1. If so, r must be 6. Suff............

If "n= 7x + r" is -ve, x has to be -ve. Then
n +1 = (7x + r) + 1
If suppose x = -1, n+1 = 7(-1) + r + 1 = -6+r.
What has to be r to have (n+1) divisible by 7? r = +6. Somebody might say -1 but remember r can never be -ve. So what is the minimum r can be 6 because r must be >0 but smaller than 7.


2) If n = 7x + r, n+8 = (7x+r) + 8.
Or, n+8 = 7(x+1) + r +1
Now the equation is similar to the eq. in 1. Therefore r = 6 again. Suff................

So d.
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If n is an integer, what is the remainder when n is divided 31 May 2009, 21:32
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D

Question: (N/7 remainder)?

(1) (N+1)/7 = X, where X is any integer
N+1=7X
N = 7X-1 = 7(X-1)+7-1 = 7(X-1) + 6

Remainder of 6.

(2) Same thing as 2,

(N+8)/7 = X, where X is any integer
N+8=7X
N = 7X-8 = 7X - 7 - 1 = 7(X-1) - 1 = 7X - 1 (same as A)

Final Answer, \(D\).
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If n is an integer, what is the remainder when n is divided 31 May 2009, 21:36
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Although there is a better method, my Finding The Pattern method-- when in doubt, FTP!!!!!!!!
Because there is always a pattern.

Question: (N/7 remainder?)

(1)N+1 is divisible by 7

N=6,13,20,27,34,...
Question=6,6,6,6,6,......

Sufficient

(2)N+8 is divisible by 7

N=6,13,20,27,34,...
Question=6,6,6,6,6...

Sufficient

General rule of thumb generate the possible values and check the remainder really fast... if it changes insufficient, otherwise sufficient.
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If n is an integer, what is the remainder when n is divided 03 Jun 2009, 05:28
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Wikipedia has an interesting article on remainder. https://en.wikipedia.org/wiki/Remainder
It says Remainder can have negative values as well, unless specified by the condition x < r ≤ x+|d| (or x ≤ r < x+|d|), where x is a constant, d is the divisor, and r is the remainder.
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If n is an integer, what is the remainder when n is divided 21 Jun 2009, 10:40
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Wikipedia has an interesting article on remainder. https://en.wikipedia.org/wiki/Remainder
It says Remainder can have negative values as well, unless specified by the condition x < r ≤ x+|d| (or x ≤ r < x+|d|), where x is a constant, d is the divisor, and r is the remainder.
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Several points here:

-First, as that wikipedia article makes clear, mathematicians do not allow remainders to be negative (see where they say "as is usual for mathematicians", when giving the positive solution). ;

-So, when you divide an integer by 7, there are only seven possible remainders: 0, 1, 2, 3, 4, 5 and 6. Remainders can't be negative, they can't be decimals, and they can't be greater than or equal to what you're dividing by;

-I have never seen a real GMAT question that asks about remainders when dividing by a negative number. Nor have I seen questions which ask for the remainder when dividing a negative by a positive number;

-Still, we can see how to find the remainder when dividing, say, -15 by 7. First, we find the remainder when dividing, for example, 20 by 7 as follows:

--we find the nearest multiple of 7 which is *smaller* than 20. That's 14;
--we subtract: 20 - 14 = 6. That is, 20 is 6 larger than the nearest smaller multiple of 7, so the remainder is 6 when we divide 20 by 7;

-Doing the same for -15:

--the nearest multiple of 7 which is *smaller* than -15 is -21;
--now, -15 - (-21) = 6. That is, -15 is 6 greater than the nearest multiple of 7 which is smaller than -15, and the remainder is 6 when -15 is divided by 7.

So, going back to the original question in this post, the remainder is the same regardless of whether n is positive or negative, and the answer is D.

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