When 10 is divided by the positive integer n, the remainder is (n - 4). What could be the value of n?

10/n

Remainder = n - 4

Is the equation set up (10/n) = n - 4?

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- Nov 28th 2018, 06:40 AM #1

- Nov 28th 2018, 08:27 AM #2

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## Re: Value of n

No, the dividend divided by a divisor equals a quotient, plus any remainder.

Or, put another way, the divisor multiplied by the quotient, plus the remainder, equal the dividend.

Here, 10 is the dividend, n is the divisor, the remainder is (n - 4), but the quotient is not explicitly given.

I'll call the quotient Q.

n*Q + (n - 4) = 10

n*Q + n = 14

n(Q + 1) = 14

$\displaystyle n \ = \ \dfrac{14}{Q + 1}$

This should help you determine the value(s) for n.

- Nov 28th 2018, 06:02 PM #3

- Nov 29th 2018, 01:09 PM #4

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## Re: Value of n

Suppose you start out with the interval $\displaystyle \ 1 \le n \le 10 $.

For usual division, the remainder is non-negative, so $\displaystyle \ (n - 4) \ge 0$.

Or, $\displaystyle \ \ n \ge 4$.

If 10 is divided by an n in this interval, the quotient would be in this interval: $\displaystyle \ 1 \le Q \le 10 $.

(Q + 1) must be positive and divide 14. So, candidates for Q are 1 and 6. But, a Q-value of 6 makes an n-value of 2,

and we already stated that $\displaystyle \ \ n \ge 4$.

Check out what happens if Q = 1.

- Nov 29th 2018, 05:33 PM #5

- Nov 29th 2018, 06:26 PM #6

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- Nov 29th 2018, 07:06 PM #7

- Nov 29th 2018, 11:23 PM #8

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- Nov 30th 2018, 07:09 AM #9

- Nov 30th 2018, 04:42 PM #10
## Re: Value of n

- Dec 1st 2018, 07:51 AM #11

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- Dec 2nd 2018, 07:04 PM #12