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For The Mathematically Inclined

Anil Saigal
02/05/2006

FOR CHILDREN

PROBLEM # 1

Ram is 20% older than Shyam, and Shyam is 40% younger than Bhim. The sum of their ages is 23.2 years. How old will Ram be on his next birthday?

FOR GROWNUPS

PROBLEM # 2
The expression
(x+y+z)^2006 + (x-y-z)^2006
is simplified by expanding it and combining like terms. How many terms are in the simplified expression?

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Please send your solutions to anil@lokvani.com.

Use Problem Solutions M-020906 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.

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SOLUTIONS TO PROBLEMS ON 01/26/06

FOR CHILDREN

PROBLEM # 1
Ann purchased a house for $ 160,312. She wants to sell it for a profit of exactly 12%. However, she does not want to sell it herself. She wants a Real Estate Agent to sell it for her. The Agent must make a commission of exactly 5.5% (in addition to Ann's 12% profit). How much must the Agent sell the house for? Give your answer to the nearest dollar.

SOLUTION
$189,999.

FOR GROWNUPS

PROBLEM # 2
What is the limit of the function
f(x) = (4 - x^2) / (3 - sqrt(x^2 + 5))
as x tends to 2.

SOLUTION
6.


Congratulations to Nando Bansal, Sandeep Bansal, Aseem Chandawarkar, Shailesh Goregaokar, Nikita Jain, Pankaj Jain, Madhavi Muralidharan, Pooja Nagda, Sarthak Pani, Bipin Parekh, Ameek Ponda, Suryateja Rao, Ramya Tamisetty and Niharika Yerneni, who were winners of the last set of puzzles.



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