## 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.**

Advertisements

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.**

Advertisements

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

Subscribe to comments with RSS.

- Para Jumbles 19.08.09
- Fill In the blanks 08.08.09
- Fill In The Blanks 05.08.09
- Para Jumbles 05.08.09
- Para Jumbles 04.08.09

- Algebra
- Announcements
- Arithmetic
- CAT 2008
- CAT 2009
- Combinatorics
- concepts
- Conundrum
- Coordinate Geometry
- Data Sufficiency
- Functions
- General
- Geometry
- IIM Interview Experiences
- Inequalities
- Mock Cat
- Mock Quant
- Number Thoery
- Online CAT
- Power Play
- Prime Numbers
- Probability
- Problem of the week
- Problems
- Tips

- Problem of the day 26.08.09
- Problem of The day 06.08.09
- Problem of the Day 30.07.09
- Bonus QUestion 28.07.09
- Problem of the day 28.07.09

- Art of Problem Solving
- CAT Material (free)
- Math Lessons
- Pagal Guy
- Pagalbille
- Test Funda
- Verbal Logic

- Concept 1 Perfect Squares
- Concept 5 Pigeon- Hole Principle
- Problem of the day 27.07.09
- CAT 2008 Key and Solutions
- Problems 8.07.09

sujeet3035 on Problem of the day 17.07.… | |

vinit on Bonus Question 26.07.09 | |

harsh bansal on The Funny Side of Mathema… | |

KT on IIM A Interview Experienc… | |

tushar on Concept 3 Circle and Triangles… |

- 126,221 hits

- RT @dd85518: @free_thinker @padhalikha Go for it sir. Tell the world that your father never cheated on your mom for Rana bibi. Expose your… 1 hour ago
- RT @MukulAgarwal66: cc @myogiadityanath Please take action twitter.com/ShivAroor/stat… 2 hours ago
- RT @coolfunnytshirt: This is the end product you get when you turn on the mixer to mix a comedian with a political analyst and a twitter ac… 2 hours ago
- RT @bhak_sala: Not long back, Swati Chaturvedi revealed my personal details on twitter and organized mass attacks on me. Now Pratik is reve… 4 hours ago
- RT @AFixedPoint_: Scary stuff. The opposition is now openly talking about Narendra Modi’s assassination. Hope Modi does not do any more roa… 4 hours ago

%d bloggers like this:

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