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For The Mathematically Inclined

Submitted by Aadhaarshila (ATFS) - The Math and Science Institute
11/03/2003

FOR CHILDREN

PROBLEM # 1

The mean weight of a class of 34 students is 46.5 kg. If the weight of the teacher be included , the mean rises by 500g. Find the weight of the teacher.

PROBLEM # 2

The diameter of a roller 120 cm long is 84 cm. If it takes 500 complete revolutions to level a playground, determine the cost of leveling it at the rate of 30 cents per sq meter.

FOR GROWNUPS

PROBLEM # 3

1
11
21
1211
111221
312211

What are the next 2 lines?

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Please send your solutions to both problems to anil@lokvani.com.

Use "Problem Solutions M-110603" as the subject line. Please include your full name in the text of the main message. The first one to submit the right answer will be profiled in the next issue of Lokvani.

Please do not post your solution in "Post Comments". No credit will be give 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 10/23/03

PROBLEM # 1

What rate of return is needed to earn $960 on an investment of $6840?

SOLUTION

14.04%

PROBLEM # 2

A collection of quarters and dimes amounts to $4.35. If there are 33 coins coins in all, find the number of each coin.

SOLUTION

7 quarters, 26 dimes. .

PROBLEM # 3

We have selected a secret four-digit number. Your task is to determine this number. Column One contains guesses for the four-digit number. A "D" in Column Two indicates that the guess has one digit in common with the secret number. A "P" indicates that the guess has one digit in common with the secret number and it is in the correct place. For example, if Column One Column was 1546 and Column Two showed D D, then two of the digits are correct but they are not in the correct place. If Column Two showed D P P, then three of the digits would be correct with two of them in the correct place.

Col. One Col. Two

3 9 2 0 . . D D D

8 7 4 5 . . P

9 0 7 5 . . D D

8 3 9 7 . . D D D

What is the secret number?

SOLUTION

2 7 3 9

MATH SMART Starting the previous issue of Lokvani, ATFS introduced a Math Smart section for our readers. This section provides a smart trick for faster calculations.

MATH SMART TIP of the issue:
For Multiplication of single digit numbers above 5 use the rule VERTICALLY AND CROSSWISE. See how far the numbers are below 10 , subtract one number's deficiency from the other number, and multiply the deficiencies together.

For example 8 x 7 = 56
The diagram below shows how to apply the rule.

7 ! - 3
6 ! - 4
------------
3 12 = 42
Subtract crosswise 7-4 or 6-3 to get 3 , the first figure of the answer.
Multiply vertically 3 x 4 to get 2 , the last figure of the answer. But here there is a carry: the 1 in the 12 goes over to make 3 into 4.
Try some yourself:
1) 8 x 8 2) 9 x 7 3) 8 x 9 4) 7 x 7 5) 9 x 9
6) 6 x 6 7) 8 x 7 8) 6 x 9 9) 7 x 6 10) 8 x 6

Congratulations to Bharath Venkataraman, Nidhi Shah, Rajesh Saluja, Rekha R., Sumanth Shankar and Sushama Dasari , who were all winners of the last puzzle. In this issue we bring you yet another challenge, one for children and one for adults.



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