The title of the problem tells you how to approach these four questions. (A). A bus leaves Moscow for Tula at noon. An hour later a cyclist leaves Tula for mosco, moving slower than the bus. When the bus and cyclist meet, which one of the two will be farther from Moscow? (B). Which is worth more: a pound of $10 gold peices or half a pound of $20 gold pieces? (C). At six o'clock the wall clock struck 6 times. Checking with my watch, I noticed the time between the first and last strokes was 30 seconds. How long will the clock take to strike 12 at midnight? (D). Three swallows fly outward from a point. When will they all be on the same plane in space? Now check the answers. Did you fall into any of the traps which lurk in these simple problems?
SEE ANSWER
(A). Neither
(B). A pound of metal is always more than half a pound of the same metal.
(C). Six strokes took 30 seconds, therefore 12 strokes will take 60 seconds. But when the clock struck six, there were only 5 intervals between strokes, and each interval was 30/5=6 seconds. Between the first and twelfth strokes there will be 11 intervals of 6 seconds each, therefore 12 strokes will take 66 seconds.
(D). There is always a plane that contains any 3 points
There are 100 light bulbs lined up in a row in a long room. Each bulb has its own switch and is currently switched off. The room has an entry door and an exit door. There are 100 people lined up outside the entry door. Each bulb is numbered consecutively from 1 to 100. So is each person. Person No. 1 enters the room, switches on every bulb, and exits. Person No. 2 enters and flips the switch on every second bulb (turning off bulbs 2, 4, 6, ...). Person No. 3 enters and flips the switch on every third bulb (changing the state on bulbs 3, 6, 9, ...). This continues until all 100 people have passed through the room. What is the final state of bulb No. 64? And how many of the light bulbs are illuminated after the 100th person has passed through the room?
Answer:- First think who will operate each bulb, obviously person #2 will do all the even numbers, and say person #10 will operate all the bulbs that end in a zero. So who would operate for example bulb 48: Persons numbered: 1 & 48, 2 & 24, 3 & 16, 4 & 12, 6 & 8 ........ That is all the factors (numbers by which 48 is divisible) will be in pairs. This means that for every person who switches a bulb on there will be someone to switch it off. This willl result in the bulb being back at it's original state. So why aren't all the bulbs off? Think of bulb 36:- The factors are: 1 & 36, 2 & 13, 6 & 6 Well in this case whilst all the factors are in pairs the number 6 is paired with it's self. Clearly the sixth person will only flick the bulb once and so the pairs don't cancel. This is true of all the square numbers. There are 10 square numbers between 1 and 100 (1, 4, 9, 16, 25, 36, 49, 64, 81 & 100) hence 10 bulbs remain on.
There are 30 cows in a field, and 28 chickens. How many didn't?
Answer:- 10. Listen closely: 30 cows, and twenty-eight chickens. Say EIGHT and ATE. They sound the same. Therefore, it means 20 ATE chickens. 30-20=10, so 10 cows didn't eat any chickens.
There are 50 horses and 50 kings riding along an old dirt road. They came to a peach tree with 50 peaches. Each took one, yet there were still 49 left. How is this possible?
Answer:- Each is the name of one of the kings and he's the only one that took one!
There are four brothers in this world that were all born together. The first runs and never wearies. The second eats and is never full. The third drinks and is always thirsty. The fourth sings a song that is never good. What are the four brothers?
Answer:- Water, Fire, Earth, and Wind.
There are ten birds sitting on a fence. You shoot one. How many are left?
Answer:- None are left. All the others are scared away because of the gunshot.
There are two numbers whose product added to the sum of their squares is 109, and the difference of whose squares is 24. What are the two numbers?
Answer:- 5 and 7.
(5)² = 25(7)² = 49(5x7)+25+49=10949-25=24
There is a barrel with no lid and some wine in it. "This barrel of wine is more than half full," said Curly. "No it's not," says Mo. "It's less than half full." Without any measuring implements and without removing any wine from the barrel, how can they easily determine who is correct?
Answer:- Tilt the barrel until the wine barely touches the lip of the barrel. If the bottom of the barrel is visible then it is less than half full. If the barrel bottom is still completely covered by the wine, then it is more than half full.
There is a bomb on top of a computer. Around the computer there is a phone, a hairbrush, keys and a cup. When the explosion comes which item is destroyed first?
Answer:- The bomb.
There is a bus full of people travelling over San Francisco and no one gets off the bus throughout the journey. But when it gets to the other side there is not a single person left. How is this possible?
Answer:- They are all married.
There is a certain club which is for men only. There are 600 men who belong to this club and 5% of these men wear one earring. Of the other 95% membership, half wear two earrings and the other half wear none. How many earrings are being worn in this club?
Answer:- Six hundred. We know that 5%, or 30 of the men are wearing one earring. Of the other 95%, or 570, we know that half are wearing two earrings and the other half none. This is the same as if they all wore one.
There is a frog, dead in the middle of an island. If he swims north, the distance to the mainland is 2 meters. If he swims south, the distance to the mainland is 3 meters. If he swims east or west, the distance is 4 meters. Which way does he swim?
Answer:- He doesn't swim at all, he is dead.
There is a man stood on top of a mountain frozen holding a peice of straw. How did he get there?
Answer:- He was with his friend in a hotair balloon when they were about to hit a mountin so they took of there clothes to make it lighter so they would go higher but it wasnt working so they drew straws and who ever had the shortest straw would have to jump out so he was the one who picked the shortest straw.