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What was the problem?
Let's first recall the given equation.
BASE +
BALL
---------
GAMES
----------
We are assuming repeating the numbers are not allowed.
Let's first take last 2 digits operation into consideration i.e. SE + LL = ES or 1ES (carry in 2 digit operation can't exceed 1). For a moment, let's assume no carry generated.
10S + E + 10L + L = 10E + S .....(1)
9 (E - S) = 11L
To satisfy this equation L must be 9 and (E - S) must be equal to 11. But difference between 2 digits can't exceed 9. Hence, SE + LL must have generated carry.So rewriting (1),
10S + E + 10L + L = 100 + 10E + S
9 (E - S) + 100 = 11L
Now if [9 (E - S)] exceeds 99 then L must be greater than 9. But L must be digit from 0 to 9. Hence, [9 (E - S)] must be negative bringing down LHS below 100. Only value of E - S to satisfy the given condition is -5 with L = 5. Or we can say, S - E = 5.
Now, possible pairs for SE are (9,4), (8,3), (7,2), (6,1), (5,0). Out of these only (8,3) is pair that makes equation SE + LL = SE + 55 = 1ES i.e. 83 + 55 = 138. Hence, S = 8 and E = 3.
Replacing letters with numbers that we have got so far.
1
---------
BA83 +
BA55
---------
GAM38
----------
Now, M = 2A + 1. Hence, M must be odd number that could be any one among 1,7,9 (since 3 and 5 already used for E and L respectively).
If M = 1, then A = 0 and B must be 5. But L = 5 hence M can't be 1
If M = 7, then A = 3 or A = 8. If A = 3 then B = 1.5 and that's not valid digit. And if A = 8 then it generates carry 1 and 2B + 1 = 8 again leaves B = 3.5 - not a perfect digit.
If M = 9, then A = 4 (A = 9 not possible as M = 9) and B must be 7 with carry G = 1.Hence for first 2 digits we have 74 + 74 + 1 = 149.
Finally, rewriting the entire equation with numbers replacing digits as -
1
---------
7483 +
7455
---------
14938
----------
So numbers for letters are S = 8, E = 3, L = 5, A = 4, B = 7, M = 9 and G = 1.
There are five men, let's say Tarun, Harish, Lavesh, Manoj and Manish.
All of them have a dot mark in their forehead. They can't see the dot on
their own forehead, but can see the ones on others. The owner of WHITE
dot is an honest person and will never lie, while the owner of BLACK dot
always tell the lie.
This are the statement from Tarun, Harish, Lavesh, and Manish:
Tarun: 'I see 3 whites and 1 black'
Harish: 'I see 4 black'
Lavesh: 'I see 3 black and 1 white'
Manish: 'I see 4 white'
What color is the dot on each Tarun, Harish, Lavesh, Manoj, Manish forehead?
Know color of dot on each forehead!
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Read this story first!
Let's take a look at who said what.
Tarun: 'I see 3 whites and 1 black'
Harish: 'I see 4 black'
Lavesh: 'I see 3 black and 1 white'
Manish: 'I see 4 white'
Harish and Manish made very contracting statements; so are statement of Tarun and Lavesh. That means, only one of them is telling the truth. Hence, only one of 4 have WHITE dot on his forehead. Till now we don't have idea of what Manoj had on his forehead. Even if he has WHITE dot then there can be maximum 2 WHITE dots among those 5.
Truth of Tarun and Manish:
Tarun and Manish must be lying as they are saying that they have seen 3 and 4 WHITE dots respectively. According to our first conclusion, there can be maximum 2 WHITE dots possible.
Truth of Harish:
Next if we assume Harish has WHITE dot and telling the truth then all other must be lying including Manoj and Lavesh. As per Lavesh, he had seen 3 BLACK and 1 WHITE dot. Now he must have seen BLACK dots on foreheads of Manoj, Tarun, Manish and WHITE dot on forehead of Harish as assumed. That mean he is telling truth though he has BLACK dot. But the man with BLACK is always lying, hence this case is also INVALID.
Truth of Lavesh:
So the only person left is Lavesh and must be telling the TRUTH with WHITE dot on his forehead. Hence, as his statement is suggesting, the Manoj must have WHITE dot and other three Tarun, Lavesh, Harish have BLACK dots (we already concluded these 3 are lying).
A car is crossing a 20km long bridge. The bridge can support at most
1500kg of weight over it. If somehow, the weight on the bridge becomes
more than that, it will break.
Now, the weight of the car is exactly 1500kg. At the midway, a bird
comes and sits on the roof of the car. This bird weighs exactly 200
gram.
Can you tell if the bridge breaks at this point or not?
Read what will happen next?
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What was the situation?
At first look, the first impression would be that the bridge will break certainly. But if you wait for a while before concluding anything you will get the right answer.
The bridge will not break in the case! It's 20 km long bridge & now it's in the middle of bridge after traveling 10 km. By now, it must have used half of the fuel that was in the tank initially at the start. This amount of fuel must be weighing more than 200 gm. Hence even a bird sits on the car there are hardly any chances the total weight on the bridge goes beyond 1500 kg! Hence, no chance of breaking of it.
Suppose we lay down two cups in front of you. One of the cups is filled
with tea and the other one with coffee. Now we ask you to take a
spoonful of tea and mix it with the coffee.
At this moment, the coffee
cup has a mixture of tea and coffee. You have to take that mixture
(spoonful) and add it back to the tea.
Can you now tell if the cup of coffee has more tea or the cup of tea has more coffee ?
Skip to the answer!
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How mixture made?
After adding 1 spoon of tea into coffee, the levels of liquids in both cups must be unequal. Whatever now tea cup is missing is now in cup of coffee & mixed with coffee. The content of tea in the cup of coffee is certainly more.
Now after taking spoonful of the mixture back to tea cup the levels of the liquid in both cups would be same. Hence, whatever the cup of tea is missing is replaced by coffee. That missing tea content is now in the cup of coffee where it has replaced some of coffee content!
Suppose there are 1000 molecules in each cup i.e. of tea & coffee. Let's assume 100 molecules of tea are mixed to coffee using spoon. Now, coffee cup will have 1100 molecules and tea will have 900 molecules. Obviously, right now the cup of coffee contains more tea (100 molecules) that coffee in cup of tea (0 molecules)!
Now while taking 100 molecules back from mixture having 1100 molecules, suppose 70 molecules of coffee & 30 of tea are taken. That means, exactly 100 - 30 = 70 molecules of tea left in mixture. That 70 + 30 molecules mixture is poured into cup of tea. That is exact 70 molecules of coffee mixed in tea.
What does it mean? 70 molecules of coffee have displaced 70 molecules of tea into cup of coffee maintaining level of both the liquids.
We can say other way as well. 30 molecules of tea displaced 30 molecules of coffee into cup of tea while maintaining levels of both the liquids same.
So the answer is both have same level of contents mixed.
One day, a class teacher was told that the school superintendent will be
visiting her class on the next day. The superintendent can ask
questions from anywhere and it can be easy as well as difficult. The
teacher will have the liberty to choose any pupil for answering the
question.
Now she is determined that the impression that is cast upon the
superintendent after the inspection should be great. How will she
instruct the students so that she maximizes the chances of receiving a
correct answer for each question? Also, she must create the best
impression. How will she do it?
This is what she should do!
What was the resolution of teacher?
Now what should teacher do here is to devise the 'sign' language to communicate with students. Also she needs to make sure that the superintendent won't have any doubt while questioning students.
She should ask all the students to raise hands for every question that is being asked by superintendent. However, those who know correct answers should raise right hand & rest of all should raise left hand. This way she would be able to know the students who knows the correct answer & choose any of them to answer the question.
All raised hands to each question would definitely leave great impression on the superintendent.
Note : We are assuming superintendent not smart enough to notice that students raising different hands for different questions.
A devotee visits 9 temples when he visits India. All these nine temples
have one thing in common - there are 100 steps in every temple. The
devotee puts Re.1 coin after climbing up every step. He does the same
while climbing down every step. At each temple, the devotee offers half
of his money from his pocket to god. In this way, his pocket becomes
empty after his visit to 9th temple.
Can you calculate the total amount he had initially ?
Click here to know exact amount!
Why to calculate those?
Using algebraic equations in the case can make things complicated unnecessarily. Hence, we would start from backward. Before putting 100 coins on steps while climbing down 9th temple devotee must had 100 coins. That means he had 200 coins when he climbed up the 9th temple half of which i.e. 100 he offered to that temple & 100 put on the 100 steps of 9th temple. Moreover, he must have placed 100 coins while climbing up 9th temple. So before visit to 9th temple he must had, (100 x 2) + 100 = 300 coins.
Same way, finding the amount he had before visit to each temple like below.
Before eight temple: (300+100)*2 + 100 = 900
Before seventh temple: (900+100)*2 + 100 = 2100
Before Sixth temple: (2100+100)*2 + 100 = 4300
Before fifth temple: (4300+100)*2 + 100 = 8900
Before fourth temple: (8900+100)*2 + 100 = 18100
Before third temple: (18100+100)*2 + 100 = 36,500
Before second temple: (36500+100)*2 + 100 = 73300
Before first temple: (73300+100)*2 + 100 = 146900
To conclude, he had Rs. 146900 initially.
A military car carrying an important
letter must cross a desert.
There is no petrol station on the
desert and the car has space only for petrol that lasts to the
middle of the desert.
There are also other cars that can
transfer their petrol into one another.
How can the letter be
delivered?
This is how letter can be delivered!
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What was the task?
We need 4 such cars to deliver the letter across the desert successfully.
Let's divide the entire route into 6 parts. That means the distance that car can travel (half the total path in desert) is divided into 3 parts. To travel each part car requires 1/3rd of it's petrol in the tank.
1. At first 1/6th of total path, all cars are 2/3rd full. Now 2/3rd of the petrol from 1 car can be used to fill 1/3rd of tanks in other 2 cars (1/3 + 1/3 = 2/3). This way, we would have 2 cars full while 1 car 2/3rd full. We are leaving behind the empty car, taking 3 cars forward.
|
Stage 1 |
2. At next 1/6th of the distance, 2 full cars will use 1/3rd of their petrol hence would be 2/3rd full. And the car that was 2/3rd at previous stage would be not 1/3rd full. At this stage, the petrol from car that is 1/3rd full can be used to fill tank of 1 car completely. So we are leaving behind one another empty car here & taking fully filled car & 2/3rd filled car for next stage.
|
Stage 2 |
3. For next 1/6th of the total distance, the car that was fully filled would have 2/3rd petrol. And the car which was 2/3rd at previous stage would be now 1/3rd filled. The petrol of this car can be used to fill the tank of the first car. Now we have 1 car fully filled while other one is empty. So we can leave behind the empty car & use fully filled car for the rest half of the journey. Remember, a car which tank is full can travel half the total path.
|
Stage 3 |
Alex, Betty, Carol, Dan, Earl, Fay, George and Harry are eight employees of an organization
They work in three departments: Personnel, Administration and Marketing with not more than three of them in any department.
Each of them has a different choice of sports from Football, Cricket,
Volleyball, Badminton, Lawn Tennis, Basketball, Hockey and Table Tennis
not necessarily in the same order.
1.Dan works in Administration and does not like either Football or Cricket.
2.Fay works in Personnel with only Alex who likes Table Tennis.
3.Earl and Harry do not work in the same department as Dan.
4.Carol likes Hockey and does not work in Marketing.
5.George does not work in Administration and does not like either Cricket or Badminton.
6.One of those who work in Administration likes Football.
7.The one who likes Volleyball works in Personnel.
8.None of those who work in Administration likes either Badminton or Lawn Tennis.
9.Harry does not like Cricket.
Who are the employees who work in the Administration Department?
In which Department does Earl work?
Who is the fan of each sports?
Click here for the complete picture.
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