puzzles contest -22 With Answers

[HELP]

1. Can you name the square of a natural number that is twice the square of some other natural number?
2. 12 and 21 are numerical reversals of each other; so are the squares of these numbers; 144 and 441. How many more numbers can you think of which have this property?

3. Supposing the roots of a quadratic equation are: 8/5 and -7/3 What is the absolute value of the coefficient of the x term, if the equation is written in standard form (ax2 + bx + c = 0), and a = 1
4. Water Pipes A circular pipe with an inside diameter of six feet can carry a certain amount of water How many' circular pipes with an inside diameter of one inch will be needed to carry the same amout of water?
5. A boy was carrying a basket of eggs. He fell down and all the eggs broke. When he went back home without any eggs his mother asked how many he had been carrying altogether in the basket. He was unable to remember.
But he was able to recall that when they were counted two at a time one was left, when counted three at a time one was left, when counted four at a time one was left, when counted five at a time none were left.Can you tell how many eggs were broken




Answers


1. There is no such natural number.If A is a natural number, then 2A2 cannot be a square since A2 can be represented as the product of
pairs of prime factors. There is no 'extra' factor of two to 'pair up with' the factor of two in 2A2.



2. The next two numbers are: 13 and 31; 102, 201.Squares are 169 and 961; 10404 and 40401.




3. 11/5

Since (x –8/5) (x +7/3) = 0 x square + 11/5 x-56/15




4. 72 Square or 5784


5. There is only one way of finding a solution to this problem: NU111bers which leave a remainder of 1, when divided by 2: 3, 5, 7, 9, 11, 13, 15,17,19,21,23,25,27,29,31,33,35.
Numbers which leave a remainder of 1, when divided by 3: 4, 7, 10, 13, 16, 19, 22, 25, 28, 31,34, 37.....
Numbers which leave a remainder of 1, when nivided bv 4: 5,9,13,17,21,25,29,33,37.
Numbers which leave no remainder when divided by 5: 5, 10, IS, 20, 25, 30, 35. The only number fulfilling the four conditions is 25Edited by: HELP

[keerthi]

2. 12 and 21 are numerical reversals of each other; so are the squares of these numbers; 144 and 441. How many more numbers can you think of which have this property?

Next no's are 13 and 31
square of the numbers = 169 and 961
Think we can get some more if we try

[keerthi]

3. Supposing the roots of a quadratic equation are: 8/5 and -7/3 What is the absolute value of the coefficient of the x term, if the equation is written in standard form (ax2 + bx + c = 0), and a = 1


Ans)11/15


the equation can be written as x2 + (b/a)x +( c/a )= 0


this is obtained by dividing by 'a' on both sides.


now sum of the roots of this equation is -b/a = -(8/5-7/3) = -11/15


and product of the roots is c/a


b/a = 11/15


since a = 1 then coefficient of 'x' term is b = 11/15

[keerthi]

5. A boy was carrying a basket of eggs. He fell [/i]down and all [/i]the eggs broke. When he went back home without any eggs his mother asked how many he had been carrying altogether in the basket. He was unable to remember.
But he was able to recall that when they were counted two at a time one was left, when counted three at a time one was left, when counted four at a time one was left, when counted five at a time none were left.[/i]Can you tell [/i]how many eggs were broken.
Ans)25
clearly the no should give a reminder one when divided with 2 or 3 or 4
and leave a reminder zero when divided by 5
jot down all the no's which have such charecteristics and find the one which follows all the 4 conditions
the no's which give reminder 1 when divided by 2 are
3,5,7,9,11,13,15,17,19,21,23,25,27................
the no's which give a reminder 1 when divided by 3 are
4,7,10,13,16,19,22,25,28,31...................
the no's which give remainder 1 when divided by 4 are
5,9,13,17,21,25,29,..................................
the no's which give a reminder zero when divided by 5 are
5,10,15,20,25,30,35,40...........................
so the least possible such number which follows the 4 conditions is 25

[faraz]

4.1296 pipes(maybe)