We know that the number 7 is the prime followed by a cube. Which next number is also a prime followed by a cube ?
There is no number other than 7 that is a prime followed by a cube.
To prove, let us assume that n3-1 is a prime for n.
N2-1 = (n^1)(n2+n+1)
Now, n-1 divides n3-1.
If n-1>1, then we are done as it is a contradiction to n3-1 being a prime.
Alpha, Beta and Gamma are in a desert. Alpha doesn't like Gamma and hence decides to murder him. He poisons the water supply of Gamma. Since it is the desert area, Gamma must drink or he will die of thirst.
Beta does not know of the actions of Alpha and also decides to murder Gamma. To succeed in his ill motives, he removes the water supply of Gamma so he dies of thirst.
Gamma dies due to thirst. Who murdered Gamma?
The answer to this question might sound more of a philosophical one.
It is Beta whose action led to Gamma's death directly. It was the scarcity of water that led to his death ultimately. It may be the circumstances prevailing his demise and not a specific person who killed him.
It comprises of roots which nobody sees,
Much taller than those trees,
Up and up it goes,
Still it never grows?
Mountain
A dead body is found at the bottom of a multistory building. Seeing the position of the body it is evident that the person jumped off from one of the floor for attempting suicide.
A homicide detective is called to look after the case. He goes to the first floor and walks in the room facing the direction in which the body was found. He opens the window in that direction and flips a coin towards the floor.
The he goes to the second floor and repeats the process. He keeps on doing it till the last floor. Then, when he climbs down, he tells the team that it is a murder not suicide.
How did he come to know that it was a murder?
At each floor, he did the same task of opening the window and flipping the coin. If it was a suicide, then at least the window at any of the floor must have been left open by the person who jumped off. The present situation only suggests that someone pushed him off and then closed the window again.
In the figure given with this question, place the numbers from 1 to 19 in the circles in a manner that each side of the triangle sums up to 17.
There are a hundred statements.
First person says: At least one of the statements is false.
Second person says: At least two of the statements is false.
Third person says: At least three of the statements are false.
Fourth person says: At least four of the statements are false.
..
..
..
Hundredth person says: At least a hundred of the statements are false.
Analyzing it, how many statements do you think are false and how many are right?
The hundredth statement is surely false as it says that at least a hundred of the statements are false.
But in a situation if that is correct, then hundred statements cannot be right.
This implies that the hundredth statement is wrong and that the first statement is true.
Similarly ninety nine statements can’t be true as if they were correct, then two statements would become correct i.e. the first and the ninety ninth.
But the ninety ninth statement says that at least ninety nine are wrong.
This implies that the ninety ninth statement is false and that second is correct.
If we go on calculating in the similar fashion, we will come to the conclusion that:
The first fifty statements are right and the remaining fifty statements are false.
An innocent person is accused of a murder in a village. The head of the village knows that the man is innocent but he also knows that the truth may be uncovered one day that his own son is the murderer. Just to hinder the attention of people, he offers a chance to the man. In a jar, he places two chits of paper – one reads innocent and the other reads guilty. Among all the other villagers, he asks the accused person to pick up a chit. He says that their almighty god is watching them and the person will meet his fate truthfully with the chit.
Of course, the village head is cheating. He has put both chits with Guilty written on them. The accused person somehow suspects the same. But no one will believe him if he tries to expose the head. Also, he knows no one will look at the other chit once his fate is decided by his selected chit.
What should he do to prove that he is innocent?
When asked to draw a chit, the person will pick any and then without looking at it, he will swallow the chit. In this manner, to decide his fate, they will have to look at the other chit which reads Guilty. Thus people will understand that the chit which he ate had innocent written over it.
Find the logic in the figure given and find out the missing one.
Every single symbol is associated with each another's position. If you look closely, you will find out that the upside-down spade symbol is always used on the left of a right-side-up heart.
You have to put a letter on the following to make it a meaningful word. The only challenge is that you can't use 'E'.
S E Q U E N C _
It's simple. Just put the letter 'F' over the line and it will become E to form the word SEQUENCE.
You have three bowls with you of capacity 8, 5 and 3 liters. The 8 liters bowl is filled completely. Using these three bowls you have to divide the 8 liters in (4 + 4) liters. How can you do it in minimum number of transfers?
Fill the 5 liters bowl from the 8 liters bowl.
Take the 5 liters bowl and fill the 3 liters bowl.
Take this 3 liters bowl and empty it inside 8 liters bowl.
Pour the remaining 2 liters from the 5 liters bowl to the 3 liters bowl.
Take the 8 liters bowl and pour it in the 5 liters bowl.
Pour the missing 1 liter from the 5 liter bowl to the 3 liters bowl.
Now there is 4 liters left in the 5 liters bowl.
Now pour 3 liters back from the 3 liters bowl to the 8 liters bowl.
That's it, we now have 4 liters in the 8 liters bowl and 5 liters bowl.