Problem Solving

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 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

The OA is D.

I don't have a clue how this will be solved. Can someone please help? Thanks!

AAPL wrote: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 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

When one positive integer is divided by another, we typically represent what's left over either as a REMAINDER or as a DECIMAL.
There is a relationship between the two representations:

Remainder/Divisor = Decimal.

When 5 is divided by 2:
Remainder representation: 5/2 = 2 R1.
Decimal representations: 5/2 = 2.5.
Remainder/Divisor = 1/2.
Decimal = 0.5.
Since the two values are equal:
Remainder/divisor = decimal.

It can be helpful to write the decimal representation AS A FRACTION IN ITS MOST REDUCED FORM.

In the problem above:
Remainder = 60.
Divisor = y.

Statement I:
Here, the decimal = 0.15 = 15/100 = 3/20.
Plugging the value in red and the blue values above into remainder/divisor = decimal, we get:
60/y = 3/20
3y = 20*60.
y = 20*20.
Since y is an integer value, Statement I is a valid option.
Eliminate B and C, which do not include Statement I.

Statement II:
Here, the decimal = 0.16 = 16/100 = 4/25.
Plugging the value in red and the blue values above into remainder/divisor = decimal, we get:
60/y = 4/25
4y = 25*60.
y = 25*15.
Since y is an integer value, Statement II is a valid option.
Eliminate A and E, which do not include Statement II.

The correct answer is D.

A similar problem in the OG:
https://www.beatthegmat.com/dealing-wit ... 69971.html