"Your Surname Tells My Shirt's Color!"

Mr. Yellow, Mr. Black and Mr. Brown, three best friends since kindergarten meet in a function after 5 years. The three of them are wearing either a Yellow, Black or Brown shirt.
After giving each other a friendly hug, Mr. Black says, "Hey, did you notice that we are wearing a different colored shirt than our names!"
The man wearing a Brown shirt said, "Wow I certainly did not notice that but you are right Mr. Black."
Based on this conversation, can you find our who was wearing which colored shirt? 

 
Know color of each person's shirt here! 
  

Surnames And Shuffling of Shirts

Read this conversation first!

One thing is sure that Mr.Black is not wearing the BLACK shirt. He is also not wearing BROWN as well as we found the other person wearing the BROWN colored shirt is agreed with the statement made by Mr.BLACK in a conversation. So only color left is the YELLOW & Mr. Black must be wearing that.

Now, the colors left are BROWN and BLACK and persons left are Mr. Yellow and Mr.Brown. Since, each of them wearing different color than his surname, Mr. Brown must be wearing the BLACK shirt. And hence, Mr. Yellow is wearing the BROWN shirt! 

To conclude, Mr.Black is wearing YELLOW shirt, Mr. Brown is wearing BLACK shirt & Mr. Yellow must be wearing BROWN shirt.

 

Test of an Examiner

Five students - Adam, Cabe, Justin, Michael and Vince appeared for a competitive exam. There were total five questions asked from them from which were two multiple choice questions (a, b or c) and three were true/false questions. Their answers are given as follows:

Name I II III IV V

Cabe c b True True False

Adam c c True True True

Justin a c False True True

Michael b a True True False

Vince b c True False True

Also, no two students got the same number of correct answers. Can you tell the correct answer? Also, what are their individual score?

Know correct answers and scores here!

Source 

Responding To Test of an Examiner

What was the test?

There are 2 possibilities of scores & that are either 0,1,2,3,4 or 1,2,3,4,5. First of all, let's arrange students' responses in order like below.

Table 1

What we notice here is that, there are few responses to same question by different student matching.

For the Question III, only Justin given different answers than other.

Case 1 : If we assume Justin's answer is correct then rest of all are wrong in response to Question III. That means either maximum score in test is 4 or Justin himself has scored 1 to 5.

Let's test that apart from Justin who can have score of 4. If any body other scores 4 then he must share at least 3 similar answers with other (excluding Answer III; refer image below). Only Adam has exact 3 matching responses with Justin.

Table 2

If Adam's score is 4 (Answers to I, II, IV, V are correct) then, Justin too would score 4 (Answers to II, III, IV,V are correct) since Adam & Justin have same responses to Questions II, IV,V).
  
If nobody scoring as 4 then Justin can have score of 4 or 5.

Case 1.1 : If his score is 4 then there has to be somebody has to be there scoring 0. Now Vince and Adam has at least 2 responses matching with the Justin. That means they can't score 0 since even 1 answer is wrong as Justin the other must be correct as Justin. Michael or Cabe can have 0 score in the case. If anybody of them has score 0 then answer as a TRUE to the Question IV is incorrect i.e. correct Answer IV is FALSE. So Justin is WRONG in Answer IV only. In short, a, c, FALSE, FALSE, TRUE is correct combination of answers. But thing is here in the case both Michael and Cabe would have score 0! Hence Justin's score can't be 4 too.

Case 1.2 : If Justin's score is 5, then a, c, FALSE, TRUE, TRUE are the right answers. No one would score 4 in that case with 3 as second highest by Adam.

An Experimental Professor

An eccentric professor used a unique way to measure time for a test lasting 15 minutes.
He used just two hourglasses. One measured 7 minutes and the other 11 minutes.
During the whole time he turned the hourglasses only few times. 

How did he measure the 15 minutes?

Couple of methods to count 15 minutes. 

Source 

15 Minutes Countdown

What was the challenge?

There were 2 ways for professor to count 15 minutes using 11 & 7 minutes hourglasses.

Method 1 :

1. He started both 7 & 11 minutes hourglasses but didn't begin test.

2. After 7 minutes hourglass ran out, he started the test. Still 11 one yet to count 4 minutes.

3. After conducting test for 4 minutes, 11 hourglass ran out.

4. Now he turns around 11 hourglass & continues. So 11 + 4 = 15 minutes counted.

Method 2 :

1. He started both the hourglasses & started to conduct the test as well.

2. When 7 minutes ran out he turned around it & kept 11 minutes counting.

3. After 4 minutes, 11 minutes hourglass ran out. Meanwhile 7 minutes hourglass also counted 4 minutes. So far 11 minutes counted.

4. Then he again turned around 7 minutes hourglass which had counted 4 minutes. That's how 7 minutes counted 4 minutes again.

5. In this way, 11 + 4 = 15 minutes counted.

A Check Post At Each Mile

A poor villager grows mango in his land and sells them in the town. The town is 1000 miles away from the village. He has rented a truck for transporting the mangoes to the town. The truck can carry 1000 mangoes at one time and this season, he was able to yield 3000 mangoes.

There is a problem. At each mile till the town, there is a check post at which he must give one mango each while traveling towards the town. However, if he is traveling from the town towards his village, he won’t have to give anything.

Transportation Truck

Tell a way in which the villager can take highest possible number of mangoes to the town.

Know here that highest possible number!

Source