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When 10 is divided by the positive integer n, the remainder is n

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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, 16:03
This topic is locked. If you want to discuss this question please re-post it in the respective forum.

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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28 Jan 2004, 16:33
rakesh1239 wrote:
C)7

Prove it
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28 Jan 2004, 16:46
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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28 Jan 2004, 18:03
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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29 Jan 2004, 10:44
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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20 Jun 2007, 14:02
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

Director
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20 Jun 2007, 14:12
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

r = n - 4 ..................................... 1

under certain circumstances:

10 = n + r .......................................2
10 = n + n -4
2n = 14
n = 7
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20 Jun 2007, 14:55
C it is. 10/7 gives remainder of 3 and 7-4 =3.
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20 Jun 2007, 14:58
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]

P.S. a really good question.
VP
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22 Jun 2007, 09:58
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

Current Student
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22 Jun 2007, 10:07
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
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22 Jun 2007, 10:18
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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02 Oct 2007, 15:43
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) + (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 ??
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Director
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02 Oct 2007, 22:03
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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02 Oct 2007, 22:16
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

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03 Oct 2007, 09:38
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)
Re: Quotient -   [#permalink] 03 Oct 2007, 09:38
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