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

Question

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

sashiim20 · Answer

Required number is in form 
 x = 17y + 3  ----------- (i)
 x = 24(y-3) + 5  -------- (ii)

Equating (i) and (ii), we get;
 17y + 3 = 24 (y - 3) + 5 
 17y + 3 = 24y - 72 + 5 
 24y - 17y = 72 + 3 - 5 
 7y = 70 
 y = 10

x = 17 (10) + 3 = 170+3 =173 . Answer B...

ScottTargetTestPrep · Answer

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

nkme2007 · Answer

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

BrentGMATPrepNow · Answer

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

IanStewart · Answer

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

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

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