About Us Contact Us Help


Archives

Contribute

 

For The Mathematically Inclined


10/09/2009

PROBLEM # 1
Suppose f(x+3) = 3x2 + 7x + 4 and f(x) = ax2 + bx + c. What is a+b+c?

PROBLEM #2
Let a + ax + ax2 + ax3 +...  and a + ay + ay2 + ay3 +... be two different infinite geometric series of positive numbers with the same first term. The sum of the first series is x, and the sum of the second series is y. What is x + y?

----------------------------------------------------------------------------------------------------------

Please send your solutions to anil@lokvani.com.

Use Problem Solutions M-101509 as the subject line. Please include your full name in the text of the main message. Everyone with the right answer will be acknowledged in the next issue of Lokvani.

Please do not post your solution in Post Comments. No credit will be given for solutions not sent to anil@lokvani.com.

If you need clarification on any problem, please contact anil@lokvani.com.

-------------------------------------------------------------------------------------------------------------

Problems from 10/01/09

PROBLEM # 1

The first three terms of an arithmetic sequence are 2x-3, 5x-11, and 3x+1, respectively. The nth term of the sequence is 2009. What is n?

SOLUTION

502.

PROBLEM #2

Convex quadrilateral ABCD has AB = 9 and CD = 12. Diagonals AC and BD intersect at E, AC =14 and triangles AED and  BEC have equal areas. What is AE?

SOLUTION
6.

Congratulations to Sitaram Chandawarkar, Dattatraya Joshi, Prabhakar Nadkarni and Bharath Venkataraman, who were the winner of the last set of puzzles.



Bookmark and Share |

You may also access this article through our web-site http://www.lokvani.com/




Home | About Us | Contact Us | Copyrights Help