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Pythagorean triplets with Consecutive natural numbers
For readers interested in Pythagorean triplets with Consecutive natural numbers, take any odd number -- say 11 -- and square It. 11 squared = 121 = 2(60)+ 1. Add 60 squared to both sides to get 11 squared + 60 squared = 60 squared + 2(60) + 1 = (60 + 1) squared = 61 squared. What do we get? (11, 60, 61). Works every time. Prove it For a general case.
stockball
- May 24th, 2011
This is an overly simple algebra question. The first form of the equation is x^2 = 2y + 1. The second form of the equation is x^2 + y^2 = (y+1) ^2, which is just y^2 + 2y + 1. Subtract the y^2 from both sides of the equation and you again have x^2 = 2y + 1.
C. Sivasankaran
- May 16th, 2006
There are some other ways also1. Multiples of the Odd number triplets, say for example 3, 4, 5 Its multiples also triplets i.e. 6,8,10 ; 9, 12, 15 ;&nbs...
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There was a robbery happened at a bank and 3 suspects taken into custody. Their statementsA: I am innocentB: I am innocentC: B did it.I didn\'t remember names, In these three one is lying and we have to find the culprit
stockball
- May 24th, 2011
The question is invalid. If only one is lying, then if A & B told the truth and C lied, C is the culprit. But if C told the truth, then A also told the truth and B is the one lying, so B would be the culprit. Bad question.
arun4p
- Sep 2nd, 2006
Suppose c is the culprit and liar.then both a and b are talking the truth,and c who is the culprit is telling the lie.
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can u find the numbers such that sum of every 2 and sum of all 4 may be perfect squares.
praveenscience
- Mar 12th, 2011
The four numbers are:
A. 10430
B. 3970
C. 2114
D. 386
Explanation:
A+B = 14400 = 1202
A+C = 12544 = 1122
A+D = 10816 = 1042
B+C = 6084 = 782
B+D = 4356 = 662
C+D = 2500 = 502
A+B+C+D = 16900 = 1302
Hope this is correct! :)
Bharath Shetty
- Sep 25th, 2006
Hi SoorajCould you please share the logic used for the same?i.e. sum of every 2 nos and sum of eevery 4 nos is a squareAppreciate ur helpregardsBharath
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A jail has 100 cells, numbered 1 to 100. The king Declares some sort of amnesty and orders the following. step 1: make sure all Cells are closed step2: reverse (if open, close; if close, open) those Cells whose numbers are divisible by 1 (in this step, all cells will be Opened); step 3: reverse those that are divisible by 2 (in this step, All even numbered cells will be closed); step 4: reverse those that are Divisible by 3; step 5: reverse those divisible by 4; step 6 to step 101: and so on . . . step 102: release the prisoners in those cells which are finally Open. How many prisoners will be released, and from which cells?
vamsi_krishna475
- Dec 26th, 2010
A small modification for the first ans is that, 1 is also opened along with all those perfect squares.
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Quadrants
Can there be a line passing through all the four quadrants? If so, how?
bsrikanthreddy007
- Sep 7th, 2010
Yes,A thick straight (say a pipe) line inserted into the axis perpendicularly from the top view.
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A says if 75 chickens are sold from what we have now the feed will last for extra 20 days. But B says if we buy additional 100 chickens then feed will get over 15 days earlier. Find the No. of chickens both are having now?
gaurav4067
- Dec 7th, 2010
The answer for this question is, there are 300 chickens and 60 days. by
solving the eqs
xy = (x-75)*(y+20).....................(1)
xy = (x+!00)*(y-15).....................(2)
Let x be the no. of chickens and the days be y
gaurav4067
- Dec 7th, 2010
he ans for this q is there are 300 chickens and 60 days. by solving the eqs xy (x-75)*(y+20)xy (x+!00)*(y-15)let x be the no of chickens and the days be y
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the combined ages of reena ,seena are 44 yrs and reena is twic as old as seena was when reena was half the as old seena will be when seena is three times as old as reena was when reena was 3 times as old as seena. How old is reena??? (SakDev – 127)
gaurav4067
- Dec 5th, 2010
Reena and Seena's age ratio will be 5:3Because sum of their ages equals 44 so their ages will be 27.5 & 16.5
dichu
- Jun 3rd, 2006
i personally feel the quetion is ambiguous , slightly the language is incorrect
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Hawkeye Foodlemyer is firing a rifle at a paper target 500m away. The target is 10cm square, and each bullet hole is circular, 1cm in diameter. The bullet holes are uniformly distributed in the target area, and none extend beyond the boundary. (A) How many bullets must be fired before there is a 50% chance that 2 bullet holes overlap? (B) How many bullets must be fired before there is a 50% chance that the next bullet hole will overlap an existing hole?
gaurav4067
- Dec 5th, 2010
Target 500m away not used in soln. (I guess given unnecessarily) we make holes on the target area , we get 10*10 = 100 holes on the sheet now we take one shot, and let say it hits any one hole. No...
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Grass in lawn grows equally thickand in auniform rate. It takes 24 days for 70 cows and 60 for30 cows . How many cows can eat away the same in 96days.?
gaurav4067
- Dec 5th, 2010
g - grass at the beginning r - rate at which grass grows, per day y - rate at which one cow eats grass, per day n - no of cows to eat the grass in 96 days From given data, g + 24*r = 70 * 24...
Jaichandran.R
- Feb 13th, 2007
Answer is 10.When the days increases from 24 to 60, no. of cows decreases from 70 to 30,hence the reduction in cows for 36 days increment is obtained by half of the previous days cows ,that is 70/2= 3...
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A girl visits to her cousin's house for a vacation. They both played a game for all the days she stayed there for every win they need to give a chocolate to the other. At the day when she left she had given 12 chocolates but had won 8 games. Find how many days she stayed there ?Ans:32please tell the approach
Venugopal668
- Nov 27th, 2010
8+8+12= 28 days she stayedfirstly she won 8 games she must loose all 8 so it will take 16 days then she lost 12 games to loose 12 chocolates
Debarghya
- Sep 19th, 2006
First of all the right question is:Last Year my cousin came to my place and we played a game where the loosing one has to give one chocolate to the person who won the game .At the end of the vacation,...
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We have a brick of regular size. It weights 4 kilogrammes. How much do u think a similar brick, 4 times smaller, but made of the same material weigh?
Venugopal668
- Nov 27th, 2010
Actual brick is 4000gm 1 time smaller (1/2 of the brick)2000gm2 times smaller(1/2 of the 1 time smaller) 1000gm3 times smaller (1/2 of the 2 time smaller)500gm 4 times smaller(1/2 time of the 3 time smaller) 250 gm
digvijay87
- Jun 20th, 2008
The question should have been the dimensions of the brick are 4 times smaller than the original dimensions....then the explanation given that it weighs 1/16th is valid
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50min's ago if it was 4 times as many min's past 3 o'clock, how many min's is it to 6o'clock
26 min's , please send me mail how to get this answer
Venugopal668
- Nov 27th, 2010
3hr 3 min 20 sec 50 mins before it will be 46 min 40 sec back so it might be 2 hr 13min 20 sec 3.20*4=12.80 =13.20 sec so at 6.29 minutes diffrent will becaluculate time taken to reach 6.29 from 2.13.20sec
soumia george
- Dec 17th, 2006
4x+50=180-x4 times a time which is 50 mins ago=(3 hrs)-x5x=130x=26
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Net Pesticide Expense
A pesticide available in the market reduces the number of plants dying within 4 weeks of plantation by 25%. If each bottle of pesticide costs Rs.770 and lasts for seven days and the nursery starts using it only on the plants planted after the 50th week, the net income (in Rs.'000s) from the project (net of pesticide expenses) is:1) 1592.5 2) 1725.5 3) 2106.5 4) None of these.
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A cow is standing 5 feet from the middle of the bridge .A train is at a distance of 2 times length of the bridge from direction in which cow is nearer to end of the bridgeis coming at a speed of 90 miles/hour.If cow moves towards train it will be saved by 1 foot.If cow moves away from train it will be hit by three inches of cow(i)Find length of bridge(ii)Find cows speed
ayyub abdul
- Oct 31st, 2010
Therefore Velocity of cow is 2 feet/ second and. Length of the bridge is X=460 feets. ...
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Price of Cow
A man sold two cows for Rs. 210 at a total profit of 5 %. He sold one cow at a loss of 10% and another at a profit of 10%. What is the price of each cow?
khushbu.kathiriya
- Oct 27th, 2010
Total 5% profit on Rs.210 i.e. Original Price=200Rs.Suppose one cow is of X Rs.i.e. another is of 200-X Rs.now loss of 10% on X =10x/100& profit of 10% on (200-x) =(200-x)10/100i.e.x-[...
S.P.K.A.
- Sep 28th, 2010
The cost of 2 cows is 200.Overall Profit is 10 Rs..The cost of 1st cow (sold for 10% loss) is 50 Rs. i.e. loss=5 RsThe cost of 2nd cow (sold for 10% profit) is 150Rs. i.e. profit=15 Rs.
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A person observes that his minute’s hand hours hand coincide every 65 min. Does the watch gain or lose time? If so, how much?
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Finding Original Number Divided
Three friends divided some bullets equally. After all of them shot 4 bullets the total no.of remaining bullets is equal to that of one has after division. Find the original number divided?
Pradeep Narra
- Sep 3rd, 2010
Let x be the total number of bullets,x/3 will be each share...after each shooting 4 bullets..x/3 -4 will be there with each one..so suming them.....x-12 = x/3x = 18;
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A rich man wanted to distribute his collection of gold coins among his ten children comprising of 5 sons and 5 daughters. He also wanted to give some coins to his car driver. He proceeds on the following basis. The first coin went to the car driver and then 1/5th of the remaining coins to his first son. He then gave another coin to the car driver and distributed 1/5th of the remaining coins to his second son. This procedure went on till all the five sons received their share. Once all the sons received their shares, he distributed the remaining coins equally among his daughters. Can u find how many gold coins the rich man had? Ans i think is 881
premaa
- Jul 21st, 2010
Total Coins = 3121. 3121 = (3121-1), (3120 * 1/5), (2496-1), (2495 * 1/5), (1996-1), (1995 * 1/5), (1596-1), (1595 * 1/5), (1276-1), (1275 * 1/5), 1020Now divide in girls equaly = 1020 / 5 = 204 coins to each
Himanshu
- Dec 8th, 2005
i think the question z incomplete but equation that i am getting islet 5th son receives 'y' coins then4th son's share=1+5y3rd=6+25y"1st=155+625ythen the old man has 156+625y(this is boys s...
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Time Puzzle
2 and a half artist with 2 and a half canvases and two in two and a half hours can paint 2 and a half drawings. How many artist are needed for 24 canvases and 24 drawings in 24 hours?
aries.mishra
- Jun 25th, 2010
Answer is 2 and a half artists. This question usually asked similarly as that one cloth takes one hour to be dry then how much time will 10 cloths take to be dry?Mostly people confuse and say 10hrs. this is same question.Ans is 2.5 artists
prateek katta
- Feb 19th, 2010
2 artists are needed.
(2 artists in 2.5 hours can make 2.5 paintings.
In 22.5 (2.5*9) hours they will make 22.5 paintings.
In next one and a half hour they will make 1.5 paintings(this can be found by chain rule).
So in 24 hrs 2 artists will make 24 paintings) -
1.a cube whose surface is painted red is sliced six times such that it is divided into 27 smaller cubes. how many of smaller cubes have: a. no red sides b. 2 red sides c. 3 red sides d. 1 red side2.2 men r playing tossing a coin. if one of them wins he gets 1$ frm the loser. at the end of a no. of games one of them had 3$ and the other won 3 times. how many games did they play?3.Q) their 20 balls each of color red,blue,green n yellow. wat's is the minimum no. of ball u hav to take out so that all r of different color. ??4.If XYZ are there number then (1>=Y>X) and if the XY=Z than find out which is the condition that must be true? A)Z=0 B)XZ D)Y
antonyshaji15
- May 4th, 2010
1) If a big cube is divided into 27 small cubes, then each side is 3 units. so total cubes is 3^3-->27 small units.Now, total corners with 3 sides coloured is "8"2 sides coloured is ...
