Problem Solving

BTGmoderatorDC wrote: ↑

Sun Apr 24, 2022 2:41 am

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

There's a nice rule that says, "If N divided by D equals Q with remainder R, then N = DQ + R"
For example, since 17 divided by 5 equals 3 with remainder 2, then we can write 17 = (5)(3) + 2
Likewise, since 53 divided by 10 equals 5 with remainder 3, then we can write 53 = (10)(5) + 3

When positive integer x is divided by positive integer y, the quotient is 17 and the remainder is 3
So, we can write x = 17y + 3

When x is divided by (y-3), the quotient is 24 and the remainder is 5.
So, we can write x = 24(y - 3) + 5

What is the value of x?
Since we now have two equations that equal to x, we can write: 17y + 3 = 24(y - 3) + 5
Expand and simplify the right side: 17y + 3 = 24y - 67
Add 67 to both sides of the equation: 17y + 70 = 24y
Subtract 17y from both sides of the equation: 70 = 7y
Solve: y = 10

Find the corresponding value of x, just plug y = 10 into one of our two equations.
We get: x = 17(10) + 3 = 170 + 3 = 173

Answer: B