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Director
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When 10 is divided by the positive integer n, the remainder is n [#permalink]
 28 Jan 2004, 17:03
When 10 is divided by the positive integer n, the remainder is n-4. Which of the following could be value of n?
(A) 3
(B) 4
(C) 7
(D) 8
(E) 12
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Director
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rakesh1239 wrote: C)7
Prove it 
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Manager
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When 10 is divided by 7, the remainder is 3 and it is given that n-4 which is 7-4=3, all other choices r wrong, I went from the choices
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Manager
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Here you go:
n*k+(n-4) = 10, k any integer
k = (14/n) - 1
Since k is an integer, 14 is divisible by n.
=> n = 7.
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SVP
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10 = x*n + (n-4)
n(x+1) = 14 so n = 14/(x+1)
or (x+1) = 14/n
we know that n is integer and x+1 is also integer. Out of the given answers only n=7 yeilds us an integer
so n = 7
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Manager
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Remainder of division [#permalink]
20 Jun 2007, 15:02
When 10 is divided by the positive integer n, the remainder is n-4. Which of the following could be value of n?
a. 3
b. 4
c. 7
d. 8
e. 12
Please explain your answers.
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Director
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Re: Remainder of division [#permalink]
20 Jun 2007, 15:12
empanado wrote: When 10 is divided by the positive integer n, the remainder is n-4. Which of the following could be value of n?
a. 3
b. 4
c. 7
d. 8
e. 12
Please explain your answers.
r = n - 4 ..................................... 1
under certain circumstances:
10 = n + r .......................................2
10 = n + n -4
2n = 14
n = 7
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Director
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C it is. 10/7 gives remainder of 3 and 7-4 =3.
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Director
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10 = Qn + n-4
14 = n(Q+1) where Q is the qoutient and can be zero or any positive integer.
n can be any factor of 14 [ 14,1,7,2]
ANSWER: C
P.S. a really good question.
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VP
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n*x+(n-4) = 10
n*x+n = 14
n(x+1) = 14
from the choices only 7 will yield an integer, hence:
7*(x+1) = 14
x+1 = 2
x = 1
the answer is (C)
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Current Student
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Wait, this has to be a 500 level question at most...right? I just simply plugged in the numbers and got C. Was there some trick involved I didn't notice?
Thanks.
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VP
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hd54321 wrote: Wait, this has to be a 500 level question at most...right? I just simply plugged in the numbers and got C. Was there some trick involved I didn't notice?
Thanks.
no trick , thats an easy problem. Please note that plugging numbers can only take you so far.
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Director
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When 10 is divided by the positive integer n, the remainder is n - 4, which of the following could be the value of n ?
(A). 3
(B). 4
(C). 7
(D). 8
(E). 12
= > 10 = n(q) + (n-4)
Used the plug in .
= > 10 / = 7 + (7 - 4)
= > 10 = 7(1) + 3
Is this the best approach. i.e plugging in the number ??
_________________
GMAT the final frontie!!!.
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Director
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alimad wrote: When 10 is divided by the positive integer n, the remainder is n - 4, which of the following could be the value of n ?
(A). 3
(B). 4
(C). 7
(D). 8
(E). 12
= > 10 = n(q) + (n-4)
Used the plug in .
= > 10 / = 7 + (7 - 4)
= > 10 = 7(1) + 3
Is this the best approach. i.e plugging in the number ??
that's also how i approached the problem. seemed like the fastest and easiest method.
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VP
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since:
10 = n*k+(n-4)
14 = n*(k+1)
If we factor 14 we get 2,7
so n could be either 2 or 7.
since 2 is not an option then n=7
The answer is (C)
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Manager
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alimad wrote: When 10 is divided by the positive integer n, the remainder is n - 4, which of the following could be the value of n ?
(A). 3
(B). 4
(C). 7
(D). 8
(E). 12
Is this the best approach. i.e plugging in the number ??
yes it's the fastest
by the way: you don't have to test 3 because the remainder can't be negative (n-4)
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close
