Problem Solving

Vincen wrote: ↑

Tue Jun 30, 2020 6:26 am

When the integer \(x\) is divided by the integer \(y,\) the remainder is \(60.\) Which of the following is a possible value of the quotient \(\dfrac{x}{y}?\)

I. \(15.15\)
II. \(18.16\)
III. \(17.17\)

(A) I only
(B) II only
(C) III only
(D) I and II only
(E) I and III only

[spoiler]OA=D[/spoiler]

Solution:

Letting Q = the quotient, we can use the expression:

x/y = Q + 60/y

We see that 60/y is the remainder. We can set this to the decimal portion of each value in the Roman numerals and solve for y.

I. 15.15

60/y = 0.15

60 = 0.15y

y = 60/0.15 = 6000/15 = 400

We see that 15.15 could be a value of x/y since we have y as an integer.

II. 18.16

60/y = 0.16

60 = 0.16y

y = 60/0.16 = 6000/16 = 375

We see that 18.16 could be a value of x/y since we have y as an integer.

III. 17.17

60/y = 0.17

60 = 0.17y

y = 60/0.17 = 6000/17 = 352.94

We see that 17.17 could NOT be a value of x/y since we DON’T have y as an integer.

Answer: D