Ten seniors who share a house, decide to exchange graduation presents. Each of them put their name into a hat, mix the name cards thoroughly & draws a card out at random. What is the probability that none of the 10 people draws his or her own name ?
Ans: (9!/10!)
If a hen and a half lays an egg and a half in a day and a half how many eggs can a hen lay in three days.
How many rectangles are on an 8 by 8 chessboard if the squares count as rectangles?
Ans:1296
A company gets 16 cans of paint each month. The problem is that one of the 16 cans is always contaminated with lead. Fortunately, the company has the capacity to test for lead. However, due to time and money constraints, the results of the tests cannot be made known until after all of the tests have been performed. What is the fewest number of cans that must be tested in order to know for certain which of the 16 cans is contaminated.
Answer: It can be done in a maximum of 4 tests by mixing samples from half of the cans and then testing that mixture. If positive, the other half of the cans are dismissed and ifnegative that set of cans is dismissed. Repeat three times for the remaining cans.
Can you think of two numbers which does not contain zeros at the end but whose product results in 1000000. How many such possible numbers are there?
Ans:15625 and 64 is the only solution
Is there a number which can be expressed as cubes of two numbers in two different ways? i.e. If A^3+B^3=C^3+D^3=X and A,B,C,D are four different numbers.Find X if present.
Ans:(12n)^3+(n)^3=(10n)^3+(9n)^3=1729n^3 for all n>=1
A man decides to buy a nice horse. He pays Rs600 for it, and he is very content with the strong animal. After a year, the value of the horse has increased to Rs700 and he decides to sell the horse. But already a few days later he regrets his decision to sell the beautiful horse, and he buys it again. Unfortunately he has to pay Rs800 to get it back, so he loses Rs100. After another year of owning the horse, he finally decides to sell the horse for Rs900. What is the overall profit the man makes?
Ans:Rs200
In the middle of a round pool lies a beautiful water lily.The water lily doubles in size every day.After exactly 20 days the complete pool will be covered by the lily.After how many days will half of the pool be covered by the water lily?
A problem has been proposed in class. At the end of the lesson it turned out that the number of boys, who had solved the problem, was the same as the number of girls, who had not solved it. Were there more girls in the class than students who had solved the problem?
Ans: The number of all the girls in the class equals to the number of students who solved the problem. Indeed, by the condition, the number of students who solved the problem equals to the sum of the number of girls who solved it and the number of boys, who solved it. But the number of boys who solved the problem is the same as the number of girls who did not solve the problem. So, the number of all the girls in the class equals to the number of students who solved the problem.
Chaitu and Dileep decided to make some jam. So they started to weigh the fruits. It turned out that 1 peach and 6 plums weighted as much as 1 pear. And, 3 peaches and a pear weighed as much as 10 plums. Chaitu started to think: how many plums would weigh as much as 1 pear? Dileep found the answer very quickly. How about you?
Ans:7 plums
1. The first question with B as the correct answer is:
A. 1
B. 4
C. 3
D. 2
2. The answer to Question 4 is:
A. D
B. A
C. B
D. C
3. The answer to Question 1 is:
A. D
B. C
C. B
D. A
4. The number of questions which have D as the correct answer is:
A. 3
B. 2
C. 1
D. 0
5. The number of questions which have B as the correct answer is:
A. 0
B. 2
C. 3
D. 1
What are the answers of the above 5 questions?
Ans:
1. C
2. D
3. B
4. C
5. B
Mary's Father has 4 daughters 1.AABZ 2.AEBY 3.AIBX . . . .
Find out the name of fourth girl. . . . .?
Ans:Mary
There are three Federation Officers assigned to take three hostile aliens to "Peace Talks" on another planet. However, they must follow the following rules:
They have only one small space ship.
Only two individuals can ride in the space ship each time.
All Federation Officers can pilot the space ship, but only one alien can pilot the ship.
If at any time there are both Federation Officers and aliens on a planet, then there must always be more (or the same number of) Federation Officers than aliens on that planet. This is because if there are more aliens than Federation Officers, then the aliens will kill the Federation Officers. Count any individual in the space ship when it is on one planet as being on that planet.
The one space ship is the only means of transportation. There is no other way to get to the "Peace Talks". No one can exit the space ship while it is in flight.
To start off, all the Federation Officers and aliens are on the same planet.
Can all Federation Officers and aliens get to the other planet alive, and if so: how
Solution::
Yes, all individuals can reach the other planet! Consider the following abbreviations for the individuals:
F = Federation Officer
A = alien that can fly the space ship
a = alien that cannot fly the space ship
Then the flight schedule to reach the other planet will be:
planet 1 flight planet 2
F F F A a a
-- A a -->
F F F a A a
<-- A ----
F F F A a A a
-- A a -->
F F F A a a
<-- A ----
F F F A a a
-- F F -->
F A F F a a
<-- F a --
F F A a F a
-- F A -->
F a F F A a
<-- F a --
F F a a F A
-- F F -->
a a F F F A
<-- A ----
A a a F F F
-- A a -->
a F F F A a
<-- A ----
A a F F F a
-- A a -->
F F F A a a
We want to cut the chess-board paper into pieces (over the lines!) such that each piece has twice as much squares of one color than of the other color (i.e. twice as much black squares as white squares or twice as much white squares as black squares). Is this possible?
Ans:No, it is not possible to cut the chess-board paper into pieces such that each piece has twice as much squares of one color than of the other color.
If it would be possible, then every piece would have a number of squares divisible by 3 (because if a piece has n squares of one color and 2×n squares of the other color, it has 3×n squares in total). The total number of squares of all pieces would then also be divisible by 3. This is, however, impossible since the total number of squares on the chess-board is 64, which is not divisible by 3.
A prisoner was given a chance to be blindfolded and pick one ball from two bowls that would contain a total of 50 white and 50 black balls. Choosing white meant freedom, black meant death. He asked if he could divide the balls between the bowls before he was blindfolded and his request was granted. What is the best way to divide the balls between the bowls?
Solution::He asked that all the balls be put in one bowl except one white ball in the other. There was a 1/2 chance of getting the bowl with the white ball, and 100% chance of getting a white ball in that case. Even if he got the other one, he still had a 49/99 chance of life, which is nearly 1/2. Thus the total odds are about 1/2 (if right bowl) + 1/4 (half the time if wrong bowl) = 3/4.
An explorer wishes to cross a barren desert that requires 6 days to cross, but one man can only carry enough food for 4 days. What is the fewest number of other men required to help carry enough food for him to cross?
Solution::
Two other men are required to help the explorer.
The first helper only goes on day into the desert. He feeds the other two men during the first day, so that at the beginning of the second day, he only has one day rations left. So he goes back to camp. On the second day, the second helper feeds himself and the explorer. On the beginning of the third day the helper now has two days rations left so he heads back. The explorer is two days into the journey and still has all four days of his food left, so he continues on alone.
A man needed to pay his rent and was out of money, but found that his rent was worth about one gold link on his chain per day. What is the fewest number of cuts he can make in his 23-link chain to pay the rent daily for up to 23 days?
Ans:It requires only two links to be cut. Cut link number 4 and link number 11 counting from the same beginning link. He then has 2 pieces of length 1 (the cut links), and one of 3, 6, and 12. He can then pay the rent as follows. One each of the first two days he can give a cut link. On the third day he gives the chain of 3 and gets his two cut links back. He uses them on days 4 and 5, and then trades all given so far and gives the 6-link chain on day 6. He then again repeats the first steps for days 7-11. On day 12 he gets all those links back and gives the 12-link chain. The then repeats the actions of the first 11 days to go all the way though day 23
While a red mark was placed on the forehead of each of three blindfolded women seated facing each other in a circle, they were told that the mark might be either red or white. Upon removal of the blindfolds, each was to raise her hand if she saw at least one red mark, and then to take it down if she could logically deduce the color of her own mark. All three hands were quickly raised, but then one of them lowered her hand. How did she know?
Solution::This is a variation of the above problem, but very hard for some people to solve. Everyone can see that each woman could be thinking that her own forehead might be red or white because the other two women could be raising their hands because of each other. Again, this is the point where most people stop, and indeed, where the women stopped while all three hands were up. The trick to solving this problem is to REALLY put yourself into the smart woman's shoes. If you REALLY were she, you'd say, either I have a white spot or a red. Suppose you had a white spot. Then the other two women would be looking at one white spot and one red. They would each quickly figure out that that only reason the others hand was up was because of their own red spot. The fact that neither of them figured it out was the tip off to the first that she must also have a red spot. Most people put themselves in the place of the first person, but to solve this one, you must then also put yourself in the place of a second woman.
Potatoes are made up of 99% water and 1% "potato matter." Chaitu bought 100 pounds of potatoes and left them outside in the sun for a while. When he returned, he discovered that the potatoes had dehydrated and were now only made up of 98% water. How much did the potatoes now weigh?
Ans:If 100 pounds of potatoes is 1% potato matter, then that means there is one pound of potato matter. After the potatoes dehydrated somewhat, this one pound accounted for 2% of the total mass (with the remaining 98% being water). One pound is 2% of 50 pounds, so the total mass of the potatoes after sitting out in the sun is 50 pounds.
Two boys sell apples. Each sells thirty apples a day. The first boy sells his apples at two for five rupees (and therefore earns Rs 75 per day). The second boy sells his apples at three for five rupees (and therefore earns Rs 50 per day). The total received by both boys each day is therefore Rs 125.
One day, the first boy is sick, and the second boy takes over his apple selling duties. To accommodate the differing rates, the boy sells the sixty apples at five for Rs 10. But selling sixty apples at five for Rs 10 yields only Rs 120 earnings at the end of the day. What happened to the other 5 rupees?
Ans: After ten sales of five apples, all the three-for-Rs 5 apples are sold; the remainder is still sold at five for Rs 10 when they should be sold at two for Rs 5.
If a boy and a half can eat a hot dog and a half in a minute and a half, how many hot dogs can six boys eat in six minutes?
Ans:24
We know that a boy and a half can eat a hot dog and a half in a minute and a half. So how many hot dogs could six boys eat in a minute and a half? We have the same amount of time, but four times as many boys, so the answer is four times as many hot dogs -- six, to be precise.
But now let's consider what six boys could eat in six minutes. We now have four times as much time, so the answer is four times as many hot dogs -- specifically, 24.
You're a cook in a restaurant in a quaint country where clocks are outlawed. You have a four minute hourglass, a seven minute hourglass, and a pot of boiling water. A regular customer orders a nine-minute egg, and you know this person to be extremely picky and will not like it if you overcook or under cook the egg, even by a few seconds. What is the least amount of time it will take to prepare the egg, and how will you do it?
Ans:It should only take nine minutes to cook the egg. If you want to try to figure out how it is done in this short amount of time before seeing the answer, stop reading now. To start, flip both hourglasses over and put the egg in the water. When the four minute hourglass runs out, flip it back over immediately. When the seven minute hourglass runs out, flip that back over immediately too. One minute later, the four minute hourglass will run out again. At this point, flip the seven minute hourglass back over. The seven minute hourglass had only been running for a minute, so when it is flipped over again it will only run for a minute more before running out. When it does, exactly nine minutes will have passed, and the egg is done.
A box contains two rupee coins. One is a double-headed coin, and the other is an ordinary coin, heads on one side, and tails on the other. You draw one of the coins from a box and look at one of the sides. Assuming it is heads, what is the probability that the other side shows heads also?
Ans:
When the coin is drawn, there are four possibilities, each of which is equally likely:
| Coin Drawn | Side Shown | Other Side |
| Double-Headed Coin | Heads | Heads |
| Double-Headed Coin | Heads (the other heads) | Heads |
| Ordinary Coin | Heads | Tails |
| Ordinary Coin | Tails | Heads |
The problem tells us that the last possibility did not occur. Therefore, there are three remaining possibilities, each of which is equally likely. Of the three, two of the possibilities will show heads on the other side; only one will show tails on the other side. So the probability that the other side of the coin is heads is two thirds.
Rama and
Ans:The speed of the train turned out to be four times that of the bike's speed. The bike's speed turned out to be two times faster than walking speed. Who got to the hotel first?
If the biking is twice as fast as walking, the time it takes to bike the whole way is equal to the time it takes to walk half the way. So if the train's speed is anything shy of infinite, biking will still be faster.
