When 10 is divided by the positive integer n,

plugging n with the options given...

II 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

Please illustrate your logic and working out.

Thanks,

divi

C.

Dividend = Quotient x Divisor + Remainder

any options less than 10 , quotient will be 1

so its
n*1+ n-4 =10
2n-4 =10
n =7

Hope that helps

Suyog wrote:plugging n with the options given...

Thanks ... and this is the approach I used ... was interested in learning about other alternative approaches.

Thanks.

sudhir3127 wrote:

II 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

Please illustrate your logic and working out.

Thanks,

divi

C.

Dividend = Quotient x Divisor + Remainder

any options less than 10 , quotient will be 1

so its
n*1+ n-4 =10
2n-4 =10
n =7

Hope that helps

any options less than 10 , quotient will be 1
But here option is 10, which is not less then 10 but quotient is 1. What is the explanation?

II 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

Please illustrate your logic and working out.

Thanks,

Numerator= Quotient* Denominator + remainder.

10 = Kn + n-4;
14 = (k+1)n;
14/k+1 = n;

now as n should be integer, therefore for k=6; n=7

here important thing to note is k can take any value.!!!!

II 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

Please illustrate your logic and working out.

Thanks,

Remember, Dividend = Divisor × Quotient + Remainder

Remainder in arithmetic is a non negative integer, and so are the Dividend and Quotient, hence n – 4 ≥ 0 or n ≥ 4.


We further have
10 = q × n + (n – 4) or n (q + 1) = 14.

Here is where we must play further logic; the product of two positive integers n and (q + 1) is 14, and n ≥ 4, which means that n can neither be 1 nor 2 as a possible factor of 14, and yes, n can either be 14 or 7 as a possible factor of 14. Since 14 is not among the choices, pick [spoiler]7



C[/spoiler]

And also note that the Remainder is always less than the Divisor, hence

n - 4 < 10 or n < 14

Note that when 10 is divided by 14, the remainder is 10, i.e. 4 less than 14. This explains the word could. Be careful not to confuse dividend with divisor

kevincanspain wrote:And also note that the Remainder is always less than the Divisor, hence

n - 4 < 10 or n < 14

Note that when 10 is divided by 14, the remainder is 10, i.e. 4 less than 14. This explains the word could. Be careful not to confuse dividend with divisor

Thanks kevincanspain, that was an error, now edited

II 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

Let’s test each answer choice:

A) n = 3

10/3 = remainder 1, which does not equal 3 - 4.

B) n = 4

10/4 = remainder 2, which does not equal 4 - 4.

C) n = 7

10/7 = remainder 3, which does equal 7 - 4.

Answer: C