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
When positive integer x is divided by positive integer y, the quotient is 17 and the remainder is 3. When x is divided
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Solution:BTGmoderatorDC wrote: ↑Wed Aug 24, 2022 11:00 pmWhen 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
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
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