BTGmoderatorDC wrote: ↑

Wed Aug 24, 2022 11:00 pm

When positive integer x is divided by positive integer y, the quotient is 17 and the remainder is 3. When x is divided by (y−3), the quotient is 24 and the remainder is 5. What is the value of x?

A. 169
B. 173
C. 180
D. 204
E. 211


OA B

Source: Veritas Prep

Solution:

We are given that when positive integer x is divided by positive integer y, the quotient is 17 and the remainder is 3. Thus:

x/y = 17 + 3/y

x = 17y + 3

We are also given that when x is divided by (y−3), the quotient is 24 and the remainder is 5. Thus:

x/(y-3) = 24 + 5/(y-3)

x = 24(y-3) + 5

x = 24y - 72 + 5

x = 24y - 67

We can equate our two equations and we have:

17y + 3 = 24y - 67

70 = 7y

y = 10

Thus, x = 17(10) + 3 = 173.

Answer: B