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Director
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When 10 is divided by the positive integer n, the remainder is n [#permalink]
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28 Jan 2004, 17:03
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When 10 is divided by the positive integer n, the remainder is n4. Which of the following could be value of n?
(A) 3 (B) 4 (C) 7 (D) 8 (E) 12



Director
Joined: 03 Jul 2003
Posts: 652

rakesh1239 wrote: C)7
Prove it



Manager
Joined: 26 Dec 2003
Posts: 227
Location: India

When 10 is divided by 7, the remainder is 3 and it is given that n4 which is 74=3, all other choices r wrong, I went from the choices



Manager
Joined: 11 Oct 2003
Posts: 102
Location: USA

Here you go:
n*k+(n4) = 10, k any integer
k = (14/n)  1
Since k is an integer, 14 is divisible by n.
=> n = 7.



SVP
Joined: 30 Oct 2003
Posts: 1790
Location: NewJersey USA

10 = x*n + (n4)
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



Manager
Joined: 15 Sep 2006
Posts: 94

Remainder of division [#permalink]
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20 Jun 2007, 15:02
When 10 is divided by the positive integer n, the remainder is n4. Which of the following could be value of n?
a. 3
b. 4
c. 7
d. 8
e. 12
Please explain your answers.



Director
Joined: 26 Feb 2006
Posts: 899

Re: Remainder of division [#permalink]
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20 Jun 2007, 15:12
empanado wrote: When 10 is divided by the positive integer n, the remainder is n4. 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



Director
Joined: 08 Feb 2007
Posts: 610
Location: New Haven, CT

C it is. 10/7 gives remainder of 3 and 74 =3.



Director
Joined: 30 Nov 2006
Posts: 591
Location: Kuwait

10 = Qn + n4
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.



VP
Joined: 08 Jun 2005
Posts: 1145

n*x+(n4) = 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)



Current Student
Joined: 03 Oct 2006
Posts: 84

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.



VP
Joined: 08 Jun 2005
Posts: 1145

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.



Director
Joined: 10 Feb 2006
Posts: 657

Quotient  [#permalink]
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02 Oct 2007, 16:43
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) + (n4)
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!!!.



Director
Joined: 11 Jun 2007
Posts: 914

Re: Quotient  [#permalink]
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02 Oct 2007, 23:03
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) + (n4)
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.



VP
Joined: 08 Jun 2005
Posts: 1145

since:
10 = n*k+(n4)
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)



Manager
Joined: 22 May 2007
Posts: 110

Re: Quotient  [#permalink]
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03 Oct 2007, 10:38
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 (n4)










