"Save Your House From Me!"

Okay, I’ll ask three questions, and if you miss one I get your house. Fair enough? Here we go:

1.A clock strikes six in 5 seconds. How long does it take to strike twelve?

2.A bottle and its cork together cost $1.10. The bottle costs a dollar more than the cork. How much does the bottle cost?

3.A train leaves New York for Chicago at 90 mph. At the same time, a bus leaves Chicago for New York at 50 mph. Which is farther from New York when they meet?

You need little common sense in answering above!

Presence of Common Sense in Answers!

What where questions?

1. A clock strikes six in 5 seconds. How long does it take to strike twelve?

A: Not 10 seconds, it takes 11 seconds.

Here, interval between 2 strikes is 1 second i.e. if counter started at first strike, it will count 1 second after second strike, 2 seconds after third strike & so on. 

Hence, 11 seconds needed for strike 12.

2.A bottle and its cork together cost $1.10. The bottle costs a dollar more than the cork. How much does the bottle cost?

A: Not 1 dollar, it would cost $1.05.

If x is cost of cork,
x + (x +1) = 1.10
2x = 0.10
x = 0.05

Hence cost of bottle is $1.05 and cost of cork is $0.05



3.A train leaves New York for Chicago at 90 mph. At the same time, a bus leaves Chicago for New York at 50 mph. Which is farther from New York when they meet?

A: Obviously, when they meet at some point then that point must be at the some distance from New York. Hence, they are at the same distance from the city.

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.

How Accurate You are?

In a competitive exam, each correct answer could win you 10 points and each wrong answer could lose you 5 points. You sat in the exam and answered all the 20 questions, which were given in the exam.

When you checked the result, you had scored 125 marks in the test.
Can you calculate how many answers given by you were correct and wrong ?

These should be those numbers! 

Source 

  

Analysis Of Your Result

What was the test ?

Let C be the number of correct answers and W be the number of wrong answers.

Since there are 20 question in total,

C + W = 20    .....(1)

and the score 125 must be subtraction of marks obtained for correct answer and marks due to wrong answers.

10C - 5W = 125   .....(2)

Multiplying (1) by 5 and then adding it to (2),

5C + 5W + 10C - 5W = 100 + 125

15C = 225

C = 15.

From (1), W = 20 - C = 20 - 5 = 5.

Hence, your 15 answers are correct while 5 answers are wrong.