## Problem Of The Week 24

**Let x,y be positive integers such that 19x+90+8y=1998. Let a be the max value of x and b the max of y.**

**Find a+b.**

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For All Your Quant Queries

**Let x,y be positive integers such that 19x+90+8y=1998. Let a be the max value of x and b the max of y.**

**Find a+b.**

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Written by Implex

September 23, 2008 at 12:49 am

Posted in Number Thoery, Problem of the week

Tagged with Number Theory, Problem of the week

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x = 100 y = 41

a+b=141

marijuanaSeptember 23, 2008 at 2:44 am

Sorry! The answer is :: 229 for x =100 and y = 229

i used the funda ::

ax+by = k

Get any value of (x,y) which satisfies the equation and then the next solution i.e x1,y1 is (x +- coeff of y ) (y+- coeff of x)

here x will decrease by 8 and y will increase by 19.

the last value which wud satisfy is x=4 and y = 229

Regards!

marijuanaSeptember 23, 2008 at 2:54 am

329

bOOnSeptember 23, 2008 at 7:33 am

yupp 329 is righlty done

100 is easy

229 is just a bit more 🙂

outtimedSeptember 23, 2008 at 11:24 am

Can somebody explain how the correct answer is 329 ?

riyaSeptember 23, 2008 at 7:00 pm

Riya its pretty simple

for x max can be easily found to be 100

as 1900+90+8=1998

now case 2

19x+90+8y=1998

as all terms are even so is x

we check for x=2 does not give integer y

we check for x=4 gives y=229

we are done here

outtimedSeptember 23, 2008 at 7:09 pm