When 12 is divided by the positive integer k, the remainder is k − 3.

Question

When 12 is divided by the positive integer k, the remainder is k − 3. Which of the following could be the value of k ?

A. 3
B. 4
C. 6
D. 9
E. 10

Salsanousi · Answer

12/k = q + (k-3)/k

12 = qk + k-3

15 = qk + k

15 = k (q+1)

If q = 0 then k 15

If q = 2 then k = 5

If q = 4 then k = 3

Answer choice A.

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dave13 · Answer

hey Salsanousi

i dont get why are you dividing RHS by K \frac{12}{k} = \frac{q + (k-3)}{k} shouldnt it look like this \frac{12}{k} = q + (k-3) can you explain please

thanks!

KarishmaB · Answer

The options give you the value of k.

Say k = 3, when 12 is divided by 3, the remainder is 0 which is k - 3 = 3 - 3 = 0
k = 3 works. 
Other values don't work.

Answer (A)

Salsanousi · Answer

Hi  dave13

I'm happy to explain

The equation is  \frac{12}{k} = q + \frac{(k-3)}{k}

I'm basically multiplying by k to get rid of it so the equation becomes  12 = qk + k - 3

The form of the remainder equation is like this 
Let x be the integer (dividend)
d be divisor 
q be quotient
r be the remainder

so it becomes like this  \frac{x}{d} = q + \frac{r}{d}

x = qd + r

To make it simpler for you let's try 12/5 this becomes 12/5 = 2 + 2/5 = 10/5 + 2/5

In other words it is basically dividend = quotient * divisor + remainder

12 = q + (k-3)  << this is how it should like

I hope this helps let me know if there is anything that is not clear.

KSBGC · Answer

Remainder = k - 3.

you have to meet this condition .

Option A) 3. K=3.

12/3 = 4 + 0 .......remainder is 0.

Remainder = k -3 = 3 - 3 = 0

Remainder matches.

Option A is the correct answer.

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When 12 is divided by the positive integer k, the remainder is k − 3.

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When 12 is divided by the positive integer k, the remainder is k − 3.

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