Problem Solving

AAPL wrote:C/D = 9.75 when dividing positive integer C by positive integer D, the remaining is 3. Which of the following could be the value of C?

A. 39
B. 37
C. 36
D. 31
E. 30

IMPORTANT: There are infinitely many pairs of values of C and D that satisfy the condition that C/D = 9.75
For example, 975/100 = 9.75. In this case, C = 975 and D = 100
Likewise, 195/20 = 9.75. In this case, C = 195 and D = 20
Also, 390/40 = 9.75. In this case, C = 390 and D = 40
And 39/4 = 9.75. In this case, C = 39 and D = 4
etc.

In fact, ALL fractions that are equivalent to 975/100 will satisfy the condition that C/D = 9.75
Of course, we're also told that, when we divide C by D, the remainder is 3.
So, let's check some of our possible cases.

If C = 975 and D = 100, then the remainder is 75 when we divide C by D. NO GOOD
If C = 195 and D = 20, then the remainder is 15 when we divide C by D. NO GOOD
If C = 39 and D = 4, then the remainder is 3 when we divide C by D. BINGO!!!

Answer: A

Cheers,
Brent

AAPL wrote:C/D = 9.75 when dividing positive integer C by positive integer D, the remaining is 3. Which of the following could be the value of C?

A. 39
B. 37
C. 36
D. 31
E. 30

Simplifying the equation we have:

C/D = 9 + 0.75

C/D = 9 + 75/100

C/D = 9 + 3/4

We can also say that:

C/D = Q + 3/D

Since 3/4 = 3/D, we see that D = 4.

Thus, we see that C/4 = 9.75, so C = 4 x 9.75 = 39.

Answer: A