Step1. Lets say y = x
Step2. Multiply through by x xy = x2
Step3. Subtract y2 from each side xy - y2 = x2 - y2
Step4. Factor each side y(x-y) = (x+y)(x-y)
Step5. Divide both sides by (x-y) y = x+y
Step6. Divide both sides by y y/y = x/y + y/y
Step7. And so... 1 = x/y + 1
Step8. Since x=y, x/y = 1 1 = 1 + 1
Step9. And so... 1 = 2
Step 5 is invalid, because we are dividing by (x-y), and since x=y, we are thus dividing by 0. This is an invalid mathematical operation (division by 0), and so by not following basic mathematical rules
Set the first switches on for abt 10min, and then switch on the second switch and then enter the room.
Three cases are possible
1.Bulb is on => second switch is the ans
2.Bulb is off and on touching bulb , you will find bulb to be warm
=>1st switch is the ans.
3.Bulb is off and on touching second bulb , you will find bulb to be normal(not warm)
=>3rd bulb is the ans.
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.
You are given with two ropes with variable width. However if we start burning both the ropes, they will burn at exactly same time i.e. an hour. The ropes are non-homogeneous in nature. You are asked to measure 45 minutes by using these two ropes.
How can you do it?
Please note that you can’t break the rope in half as it is being clearly stated that the ropes are non-homogeneous in nature.
All you have to do is burn the first rope from both the ends and the second rope from one end only simultaneously. The first rope will burn in 30 minutes (half of an hour since we burned from both sides) while the other rope would have burnt half. At this moment, light the second rope from the other end as well. Where, the second rope would have taken half an hour more to burn completely, it will take just 15 minutes as we have lit it from the other end too.
Thus you have successfully calculated 30+15 = 45 minutes with the help of the two given ropes.
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.
There are two glasses in front of you. One of the glasses is full of coke and the other glass is full of lemonade. You take a spoonful of coke and mix it into the glass of lemonade. Now the lemonade glass has a mixture of coke and lemonade. You take a spoonful of that mixture and mix it inside the coke glass.
Now what do you think? - The glass with coke has more quantity of lemonade or the glass with lemonade have more quantity of coke mixed with it?
This problem can be solved with algebra as well as logical reasoning. We are going to tell you how it is logically possible.
Be it any quantity that was present in the beginning and any liquid as well. We know that we have taken a spoonful from one glass and put it into another. Then, we have taken a spoonful from the other glass and put it into the first glass. So, at the end of it, the quantity of liquid in either glass remains same as it was in the beginning.
Therefore, we can conclude the fact that any amount of coke that is missing in the glass with coke will be present in the lemonade glass. Also, the same quantity of lemonade will be missing from the lemonade glass and will be present in the coke glass.
The toothpicks in the picture have been arranged to form a donkey shaped figure. You have to move two matchsticks in a way that the entire shape is rotated / reflected while being intact. Also, you can't change the tail's direction it should be pointing up.
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.
f the last elf is taking some time to answer the question then it shall mean that the elf's before him are all wearing distinct coloured hats. However sufficient time shall be given to the last elf to give the answer.
If he views the similar coloured hats in front of him , he shall quickly tell the answer
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