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# When positive integer x is divided by positive integer y, the quotient

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Re: When positive integer x is divided by positive integer y, the quotient [#permalink]
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Bunuel wrote:
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

The question stem forms two equations as below

x = 17y+3
x=24(y-3)+5

Solving the above 2 equations

x=173

OA: B
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Re: When positive integer x is divided by positive integer y, the quotient [#permalink]
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Bunuel wrote:
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

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

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Re: When positive integer x is divided by positive integer y, the quotient [#permalink]
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When we divide x by y, the quotient is 17 and the remainder is 3, so when we divide x by 17, the quotient is y and the remainder is 3 (that's what the equation x = 17y + 3 means -- x is 3 greater than a multiple of 17, so the remainder is 3 when we divide x by 17). Only answer B gives us a remainder of 3 when we divide it by 17, so it has to be right, and we don't need to use the rest of the information in the question.
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Re: When positive integer x is divided by positive integer y, the quotient [#permalink]
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Re: When positive integer x is divided by positive integer y, the quotient [#permalink]
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