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Determine the value of z in the polynomials x^2-11x+z and x2-14x+2z such that these two polynomials have common factors.

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There is a box full of fruits,

all but two are grapes,

all but two are apples,

and all but two are oranges.

How many fruits are in the box ?

all but two are grapes,

all but two are apples,

and all but two are oranges.

How many fruits are in the box ?

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You had an infinite supply of water and a 5 ml and 3 ml gallons.

How would you measure exactly 4 ml in least number of steps ?

How would you measure exactly 4 ml in least number of steps ?

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There are 100 doors. 100 strangers have been gathered in the adjacent room. The first one goes and opens every door. The second one goes and shuts down all the even numbered doors – second, fourth, sixth... and so on. The third one goes and reverses the current position of every third door (third, sixth, ninth… and so on.) i.e. if the door is open, he shuts it and if the door is shut, he switches opens it. All the 100 strangers progresses in the similar fashion.

After the last person has done what he wanted, which doors will be left open and which ones will be shut at the end?
**category** :
LOGIC

After the last person has done what he wanted, which doors will be left open and which ones will be shut at the end?

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David and Albert are playing a game. There are digits from 1 to 9. The catch is that each one of them has to cut one digit and add it to his respective sum. The one who is able to obtain a sum of exact 15 will win the game?

You are a friend of David. Do you suggest him to play first or second?

You are a friend of David. Do you suggest him to play first or second?

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A wicked sorcerer felt enmity towards elf and thus he chooses four among the rest of the elf's and concealed them. The elves are concealed in the ground in a manner that apart from their head the rest of their body was underneath the ground. The elf's are unable to move their body and can only see in that direction that they are facing. All the elf's are concealed underground in such a way that they form a straight line and among those four elf's that are concealed underground one of the elf is detached form the other three elf's via wall. The entire elf's are in the same direction. The elf that is the furthest can only see the heads of its friends in front and a wall. The elf that is second last can only see one head of his friend and a wall. The second elf can only view the wall. The elf can see nothing.

The sorcerer understands the situation and tells the elf's that he has placed hats over their heads. Among the hats places two hat are blue and the other two are red. Among all the four elfs one of the elf has to guess that which colour hat is he wearing. If the elf answers correctly then he shall be set free or else he will have to dig beneath the ground till the very last.
**category** :
LOGIC

The sorcerer understands the situation and tells the elf's that he has placed hats over their heads. Among the hats places two hat are blue and the other two are red. Among all the four elfs one of the elf has to guess that which colour hat is he wearing. If the elf answers correctly then he shall be set free or else he will have to dig beneath the ground till the very last.

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A claustrophobic person boards a train that is just about to enter a tunnel.

Which place will be the best for him to sit?

Which place will be the best for him to sit?

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We all know that New Year occurs after a week from Christmas and thus it falls on the same day as of Christmas. But this will not happen in 2050. In 2050, Christmas will appear on Sunday while New Year will appear on Saturday.

How can this be possible ?

How can this be possible ?

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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?

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?

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In a closed jar, there are three strawberry candies, two mango candies and five pineapple candies. You can't see inside the jar. Now, how many toffees you must take out from the jar to make sure that you have one of each flavor?
**category** :
LOGIC

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Three college toppers are summoned by the inspecting faculty. To identify the best from them, the faculty takes them into a room and places one hat on each of their heads. Now all of them can see the hats on other’s heads but can’t see his own. There are two colored hats – green and red.

Now the faculty announces that he had made sure that the competition is extremely fair to all three of them. He also gives them a hint that at least one of them is wearing a red hat. Now the first one who is able to deduce his own hat color will be awarded the most intelligent student of all award. After a few minutes, one of them raises his hand and is able to deduce the color correctly.

How?
**category** :
LOGIC

Now the faculty announces that he had made sure that the competition is extremely fair to all three of them. He also gives them a hint that at least one of them is wearing a red hat. Now the first one who is able to deduce his own hat color will be awarded the most intelligent student of all award. After a few minutes, one of them raises his hand and is able to deduce the color correctly.

How?

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