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SLACIBangladesh

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  1. [1] In a certain algebra lecture class, Chris and Pat count the students and compare notes. "Hmm, 12/17 of my classmates in here are women," notes Pat. "Funny," recounts Chris, "5/7 of my classmates are women." They were both right. How many students, men and women, were in the class, and what were the genders of Chris and Pat? . .prob21 [2] Tenny and Tonny are two elephants. Every winter, Tenny gains ten percent of his body weight, and Tonny loses ten percent. Every summer, the opposite happens: Tenny loses ten percent and Tonny gains ten percent. This has gone on for ten years, and now they each weigh ten tons. How many tons did Tenny and Tonny weigh ten years ago? ...prob26 [3] A rectangular floor is composed of whole square tiles. A diagonal line is drawn and ruins some of the tiles. (on a 2 x5 floor, 6 tiles are ruined, on a 2 x4, only 4 are ruined.) a) How many tiles are ruined on a 4 by 6 floor? b) How about a 63 by 81 floor? c) Generalize to an m by n floor. ...prob27 [4] What is the maximum number of Friday-the-13ths that there can be in a single year? What is the minimum number? ....prob29 [5] Like the Fibonacci sequence 1, 1, 2, 3, 5, 8, . . . a certain turkey flock has as many turkeys on a given day as the sum of the number of turkeys on the previous two days. If there were 79 turkeys on November 7th, and 542 turkeys on November 11th, how many turkeys were there on November 18th? ..prob 30 [6] The student parking lot has 81 cars in it; all Acuras, Beetles, and Camrys. There are half as many Acuras as Beetles, and the number of Camrys is 80% of the number of Acuras and Beetles together. How many of each kind of car is in the parking lot ...prob12 [7] Two overlapping spherical soap bubbles, whose centers are 50 mm apart, have radii 40 mm and 30 mm. What is the diameter D of their circle of intersection? ....prob14 [8] A certain six-digit number is split into two parts; the first three digits and the last three digits are added (as 3-digit numbers), the resulting sum is squared, and the answer is the original 6-digit number! What was the number? ....prob 16 [9] At least a dozen ants are marching through my kitchen! If the ants walk in rows of 7, 11, or 13, there are 2 ants left over, while in rows of 10, there are 6 left over. What is the smallest number of ants there could be? .....prob17 [10] Two students were on a commuter train from New York to Boston. One said, "The trains coming from Boston pass us every five minutes. I wonder, how many Boston trains arrive in New York per hour, given equal speeds in both directions?" "Twelve, I figure," said the second, "sixty minutes divided by five." The first disagreed. Who was right? ....prob163 [11] Each day, Stevie is either happy or sad. If he is happy one day, then four times out of five he is happy the next day. If he is sad one day, then he is sad the next day one time out of three. In the long run, what are the chances that Stevie is happy on any given day? ....prob166 [12] Can You Digit? (A few puzzles about numbers with special digit properties) (back to top) a) Find two three-digit numbers, not containing zero, whose squares end in the same 3 digits (as the number, in the same order). (One-digit example: 5^2 = 25; both end in 5.) b) Find two pairs of consecutive three-digit numbers whose squares have the same digits (for each pair). (Two-digit example: 13^2 = 169, 14^2 = 196, same digits.) c) Find a set of six non-zero 1-digit numbers such that the sum of three of them equals the sum of the others, and the sum of the squares (of the same three) is the sum of the squares of the others. ....prob155 Hi dudes,See you soon. I am just taking break for couple of days. Goodluck stickler + hildog+shahed99 with these probs
  2. Great job dudes and so fast!!!!!! Wow. I haven't yet done these. I just collected from somewhere. Guessing you are too much free out there !!! So here are some new ones for you. [1] How many ways to make 6 as a sum of odd numbers? How many ways to make 6 as a sum of different numbers? [2] That 'Math Council Dinner' is in December, but I forgot which night, so I asked around. Alan said that the date was an odd number; Brenda claimed it was greater than 13. Carly declared it was not a perfect square, while Dara swore it was a perfect cube. Finally, Edward told me the date was less than one-fourth his age, which I know to be 68. Yesterday I learned that only one of them had told the truth! What is the date of the dinner? ....problem'98 [3] Eat Lots of Fruit! Cafe de la Peche offers three fruit bowls: Bowl A has 2 apples and one banana; Bowl B has 4 apples, 2 bananas, and 3 pears; Bowl C has 2 apples, 1 banana, and 3 pears. Your doctor tells you to eat exactly:16 apples, 8 bananas, and 6 pears per day. How many of each type of bowl can you buy so there's no fruit left over? ....problem'62 [4] Some primes can be expressed as the sum of two squares, as in 13 = 2^2 + 3^2; some can't: 7 =/= a^2 + b^2. Other primes can be c^2 + 2 e^2, like 11 = 3^2 + 2 * 1^2; still others are f^2 + 3 g^2 , like 31 = 2^2 + 3 * 3^2. How many primes less than 100 that can each be written in all three ways: p = a^2 + b^2 = c^2 + 2 e^2 = f^2 + 3 g^2? ...prob 63 [5] My friend jitu sometimes gets confused; 80% of the time he identifies a sheep as a sheep, and 80% of the time he calls a goat a goat. (Otherwise he thinks it's the other animal.) In his area, 85% of the animals are sheep and the rest are goats. Jitu sees a random animal and says it's a goat. What's the probability that he's right? ...prob 65
  3. Ok Guys Few problems: May be some of them are not related to this thread.Sorry. But hope you will have fun. [1] Fishing boat captains, when big storms form, behave as follows: 50% of the time they head for home, 30% of the time they choose to ride it out, and 20% of the time they head away from the storm. In a severe storm, the probability of being sunk is 97% if they head for home, 44% if they ride it out, and 17% if they head away. (i) What is the probability of being sunk? (ii) What is the probability that a boat was headed for home, given that it was sunk? [2] If a 1 is placed after this five-digit number, the result is triple the number you'd get by putting the 1 in front. What is the number? [3] It's the second-smallest odd number greater than 1 that's a perfect cube and also a perfect square.What is the number? [4] Every male bee has just a female parent, while every female bee has both a male and a female parent. How many ancestors does a male bee have, counting ten generations back? Don't count this male as a generation or include him in the 'final tally.' [5] Choosing four people at random, what is the probability that none of them have their birthdays on the same day of the week? [6] "Twin primes" are prime numbers that are 2 apart (such as 17 and 19). Consider the set of all pairs of twin primes, including (17, 19). a) If we pick a pair of twin primes, each less than 100, what is the probability that their sum is divisible by 12? b) If we pick a pair of twin primes between 10 and 1000, then what's the prob. their sum is div. by 12?
  4. Hi M_W_M, what is x is three times bigger than y x=4*y or x=3*y when x=4*y 1st digit 1 way 2nd digit 1 way 3rd digit 3 way 4th digit 4 way (0, 3, 6, 9) (5th,6th) digit (0,0), (1,4), (2,8) 3 ways ans= 36 is it? take care mwm
  5. Is the standard deviation needed for this problem?
  6. How this formula comes? Explanation needed. :rolleyes: :rolleyes: :rolleyes:
  7. Hi nishat, It's about prob. # 1. What is the domain ? if the squares must be integer then the ans. is 0. If the dopmain of squares is any real numbers then X^2 = 2310 + y^2 then there are infinity of X^2 , Y^2 pairs for which the equation will satisfy. Sothen the answer would be infinity Take care nishat
  8. stickler_nishat... i guess u r right.. not sure though.. waiting for others to response
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