Two trains under a controlled experiment begin at a speed of 100 mph in the opposite direction in a tunnel. A supersonic bee is left in the tunnel which can fly at a speed of 1000 mph. The tunnel is 200 miles long. When the trains start running on a constant speed of 100 mph, the supersonic bee starts flying from one train towards the other. As soon as the bee reaches the second train, it starts flying back towards the first train.
If the bee keeps flying to and fro in the tunnel till the trains collide, how much distance will it have covered in total?
A typical way will be to start thinking about summing up the distance that the bee will travel but that will be quite a tedious task. How about we offer you a much easy solution?
The tunnel is 200 miles long and the trains are running at as peed of 100 mph which means that they will collide exactly at the center of the tunnel and seeking their speed, they will collide after an hour.
Now consider the bee which is flying at a speed of 1000 mph and will keep flying till the train collides. As calculated, it will keep flying for an hour which means the distance that it will cover is 1000 miles.
I bought three toys for my triplet boys (one for each). I placed the toys in the dark store. One by one each boy went to the store and pick the toy. What is the probability that no boy will choose his own toy?
Since marbles can only be taken out in pairs and you started off with an odd number of yellows there is always going to be one yellow left over that you'll keep putting back in the box until it's left on it's own.
There are a hundred statements.
1st person says: At least one of the statements is incorrect.
2nd person says: At least two of the statements is incorrect.
3rd person says: At least three of the statements are incorrect.
4th person says: At least four of the statements are incorrect.
100th person says: At least a hundred of the statements are incorrect.
Now analyze all the statements and find out how many of them are incorrect and how many are true?
The 100th statement for sure is incorrect because it says that at least 100 of the statements are incorrect.
Suppose if that is correct, then 100 statements cannot be true.
This suggests that the 100th statement is incorrect and that the first statement is true.
Similarly 99 statements cannot be true because if they were true, then two statements would become correct i.e. the 1st and the 99th.
But the 99th statement says that at least 99 are incorrect.
This suggests that the 99th statement is incorrect and that 2ndone is true.
If we keep analyzing is the same way till the end, we will find out that only the first fifty statements are true and all the remaining ones are incorrect.
In a guess game , five friends had to guess the exact numbers of balls in a box.
Friends guessed as 31 , 35, 39 , 49 , 37, but none of guess was right.The guesses were off by 1, 9, 5, 3, and 9 (in a random order).
Can you determine the number of balls in a box ?
Two friends , Torres and Lampard, meet after a long time.
Torres: Hey, how are you man?
Lampard: Not bad, got married and I have three kids now.
Torres: That's awesome. How old are they?
Lampard: The product of their ages is 72 and the sum of their ages is the same as your birth date.
Torres: Cool..But I still don't know.
Lampard: My eldest kid just started taking piano lessons.
Torres: Oh now I get it.
The sum of their ages is the same as your birth date. That could be anything from 1 to 31 but the fact that Torres was unable to find out the ages, it means there are two or more combinations with the same sum. From the choices above, only two of them are possible now.
Jonathan has three boxes containing milk chocolates and dark chocolates. The problem is that all of them have been labeled incorrectly as follows.
Box1: Dark Chocolates
Box2: Milk Chocolates
Box3: Dark Chocolates and Milk Chocolates
How will he label all the boxes correctly by just opening one box?
It has been clearly mentioned that all the boxes are labeled incorrectly. If he opens the Box3, then he will get either Dark Chocolates or Milk Chocolates as it is labeled incorrectly. Let us suppose he finds Dark Chocolates in there. Now since all are labeled incorrectly, Box B A must contain Milk Chocolates and Box B must contain Milk Chocolates and Dark Chocolates.
A couple had to take shelter in a hotel for they could not proceed their journey in the rain. Having nothing to do at all, they started playing cards. Suddenly there was a short circuit and the lights went off. The husband inverted the position of 15 cards in the deck (52 cards normal deck) and shuffled the deck.
Now he asked his wife to divide the deck into two different piles which may not be equal but both of them should have equal number of cards facing up. There was no source of light in the room and the wife was unable to see the cards.
For a certain amount of time, she thought and then divided the cards in two piles. To the husband’s astonishment, both of the piles had equal number of cards facing up.
The answer is very simple. All she had to do is take the fifteen cards from the top and reverse them. This would make another pile out of that and there will be two piles - one of 15 cards and one of 37 cards. Also both of them will have the same number of inverted cards.
Just think about it and if the mathematical explanation will help you understand better, here it is.
Assume that there were p inverted cards initially in the top 15 cards. Then the remaining 37 cards will hold 15-p inverted cards.
Now when she reverses the 15 cards on the top, the number of inverted cards will become 15-p and thus the number of inverted cards in both of the piles will become same.
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