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Tickle Your Grey Cells

Puzzle corner is a dedicated section for honing analytical, mathematical and reasoning skills. In this section every week you will find five Puzzles. Theses mind twisters have been carefully selected after a thorough research and provide right inputs for tickling your grey cells. Solving puzzles is considered very good exercise so as to remain mentally active. Puzzle solving enhances memory and processing speed.

Puzzle is one of the most popular category in competitive examinations. All the major Indian MBA entrance exams like CAT, MAT, XAT and SNAP have direct questions or questions based on similar logics in written test. Besides MBA exams, competitive exams like GRE, GMAT, Bank PO, SSC & other government exams include puzzle questions. Most of the companies while recruiting through campus includes Puzzles in the written tests or at interview stage. Hence those who are preparing for campus placement tests this section is a must.

Week of the Year 

Manisha prefers her date to be tall, dark and handsome. Of the preferred traits - tall, dark and handsome - no two of Anuj, Balbir, Chiman and Debjit have the same number.
Only Anuj or Debjit is tall and fair.
Only Balbir or Chiman is short and handsome.
Anuj and Chiman are either both tall or both short.
Balbir and Debjit are either both dark or both fair.
Who is Manisha's date?
As no two of them have the same number of preferred traits - from (1), exactly one of them has none of the preferred traits and exactly one of them has all the preferred traits.
From (4) and (5), there are only two possibilities:
* Anuj & Chiman both are tall and Balbir & Debjit both are fair.
* Anuj & Chiman both are short and Balbir & Debjit both are dark.
But from (2), second possibility is impossible. So the first one is the correct possibility i.e. Anuj & Chiman both are tall and Balbir & Debjit both are fair.
Then from (3), Balbir is short and handsome.
Also, from (1) and (2), Anuj is tall and fair. Also, Debjit is the person without any preferred traits. Chiman is Dark. Anuj and Chiman are handsome.
Thus, following are the individual preferred traits:
Chiman - Tall, Dark and Handsome
Anuj - Tall and Handsome
Balbir - Handsome
Debjit - None
Hence, Chiman is Manisha's date.

A girl found that she had a 56 cms strip of ribbon. She could cut a cm off every second. How long would it take for her to cut 56 pieces? She can not fold the strip and also, can not stack two or more strips and cut them together.
To get 56 pieces, the girl will have to put only 55 cuts. i.e. she can cut 56 pieces in 55 seconds. After getting 54 pieces, she will have a 2 cms long piece. She can cut it into two with just a one cut in 1 second. Hence, total of 55 seconds.

The cricket match between India and England was over.
Sehwag scored more runs than Saurabh.
Tendulkar scored more runs than Gautam but less than Rahul
Badani scored as much runs as Ajit but less than Rahul and more than Tendulkar.
Saurabh scored more runs than either Ajit or Rahul.
Each batsman scored 5 runs more than his immediate batsman. The lowest score was 20 runs.
How much did each one of them score?
Use the given facts and put down all the players in order. The order is as follow with Sehwag, the highest scorer and Gautam, the lowest scorer.
Sehwag - 45
Saurabh - 40
Rahul - 35
Badani, Ajit - 30
Tendulkar - 25
Gautam - 20

 A bag of Apricots was divided between Amitabh and Abhitabh. Abhitabh said, "It's not fair! You have 3 times as many Apricots I have." Amitabh said, "OK, I will give you one Apricot for each year of your age." Abhitab replied, "Still not fair. Now, you have twice as many Apricots as I have." "Dear, that's fair enough as I am twice older than you", said Amitabh. Amitabh went to Kitchen to drink juice. While he was in Kitchen, Abhitabh took apricots from Amitabh's pile equal to Amitabh's age. Who has more apricots now?
Let's assume that initially Abhitabh got N apricots and his age is T years. Hence, initially Amitabh got 3N apricots and his age is 2T years.
 

Operation

Amitabh's Apricots

Abhitabh's Apricots

Initially

3N

N

Amitabh gave T apricots to Abhitabh

(equals age of Abhitabh)

3N - T

N + T

Abhitabh took 2T apricots from Amitabh's pile (equals age of Amitabh)

3N - 3T

N + 3T

 
It is given that after Amitabh gave T apricots to Abhitabh, Amitabh had twice as many apricots as Abhitabh had.
3N - T = 2*(N + T)
3N - T = 2N + 2T
N = 3T
From the table, at the end Amitabh has (3N - 3T) apricots and Abhitabh has (N + 3T) apricots.
Substituting N = 3T, we get
Amitabh's apricots = 3N - 3T = 9T - 3T = 6T
Abhitabh's apricots = N + 3T = 3T + 3T = 6T
Thus, at the end Amitabh and Abhitabh, both have the same number of apricots.

Hansa ate a meal at Jugju hotel costing Rs.210. He gave the manager a Rs. 1000 note. He kept the change, came back a few minutes later and had some food packed for his girl friend 'Hansi'. He gave the accountant a Rs. 500 note and received Rs. 120 in change. Later the bank told the accountant that both the Rs. 1000 and the Rs. 500 notes were counterfeit.
How much money did the restaurant lose? Ignore the profit of the food restaurant.
Hotel lost Rs. 1500.
First time restaurant has given food worth Rs. 210 and Rs. 790 change. Similarly second time, food worth Rs. 380 and Rs. 120 change. Here, we are not considering food restaurant profits.

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