Five Students

 

Five students – Ani, Chinu, Jigyasa, Mayank and Viru – appeared for an exam. There were total five questions – two multiple choice (a, b or c) and three true/false questions. They answered five questions each and answered as follow.

Also, no two students got the same number of correct answers.

1. Which are the correct answers?

2. What are their individual score?

 

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Arithmetic 

 

Three mathematics classes X,Y and Z take an geometry test. The average of class X is 64, The average of class Y is 80 and the average score of class Z is 76 . The average score of class X and Y is 70 while the average score of class X and Z is 68. What is the ratio of number of students in the class X,Y and Z?

(A) 6:10:3
(B) 5:3:1
(C) 10:6:5
(D) 3:10:1

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5 Fruits

 

In a contest, five fruits (an apple, a banana, an orange, a strawberry and a pear) have been placed in five closed boxes (one fruit per box). People may guess which fruit is in which box. 107 people participate in the contest. When the boxes are opened, it turns out that 40 people have guessed none of the fruits correctly, 30 people have guessed one fruit correctly, 20 people have guessed two fruits correctly and 10 people have guessed three fruit correctly. How many people have guessed four fruits correctly and how many people have guessed all the fruits correctly?

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100 Bulbs

There are 100 light bulbs lined up in a row in a long room. Each bulb has its own switch and is currently switched off. The room has an entry door and an exit door. There are 100 people lined up outside the entry door. Each bulb is numbered consecutively from 1 to 100. So is each person. Person No. 1 enters the room, switches on every bulb, and exits. Person No. 2 enters and flips the switch on every second bulb (turning off bulbs 2, 4, 6, …). Person No. 3 enters and flips the switch on every third bulb (changing the state on bulbs 3, 6, 9, …). This continues until all 100 people have passed through the room.
 

What is the final state of bulb No. 64?  And how many of the light bulbs are illuminated after the 100th person has passed through the room?
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Females

  • A is the father of two children – B and D who are of different sexes.
  • C is B’s spouse.
  • E is the same sex as D.
  • B and C have the two children – F who is the same sex as B and G who is the same sex as C.
  • E’s mother, H who is married to L, is the sister of D’s mother, M.
  • E and E’s spouse, I have two children – J and K who are the same sex as I.

Note that no persons have married more than once. Also, there are more number of females than males. How many females are there?

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