## Aptitude Test Questions and Answers

1. A man decides to buy a nice horse. He pays $60 for it, and he is very content with the strong animal. After a year, the value of the horse has increased to $70 and he decides to sell the horse. But already a few days later he regrets his decision to sell the beautiful horse, and he buys it again. Unfortunately he has to pay $80 to get it back, so he loses $10. After another year of owning the horse, he finally decides to sell the horse for $90. What is the overall profit the man makes?

2. A bus run at 100 km/hr top speed. It can carry a maximum of 6 persons. If speed of bus decreases in fixed proportion with increase in number of person, find speed when three person are traveling in bus.

3. A man wanted to enter an exclusive club but did not know the password that was required. He waited by the door and listened. A club member knocked on the door and the doorman said, “twelve.” The member replied, “six” and was let in. A second member came to the door and the doorman said, “six.” The member replied, “three” and was let in. The man thought he had heard enough and walked up to the door. The doorman said, “ten” and the man replied, “five”. But he was not let in. What should have he said?

4. There are 20 pieces of bread to divide among 20 people. A man eats 3 pieces, woman eats 2 pieces and a child eats half piece of bread. Tell the correct combination of men, women and children so that they are 20 people in total and everyone gets the bread. Note that a man cannot eat less than 3 or more than 3. A woman cannot eat less than 2 or more than 2 and the child cannot eat less than half or more than half piece of the bread. You have to tell there are how may are men, women and children in those 20 people.

5. A cube of side 4cm is painted with 3 colors red, blue and green in such a way that opposite sides are painted in the same color. This cube is now cut into 64 cubes of equal size.

- How many have at least two sides painted in different colors.
- How many cubes have only one side painted.
- How many cubes have no side painted.
- How many have exactly one side not painted.

6. How many squares are there on a normal chessboard?

7. Three people picked 65 apples altogether. At the first tree they each picked the same number of apples. At the second tree they each picked 3 times as many as they picked at the first tree. When they finished at the third tree, the group had 5 times as many apples as they had when they started at that tree. At the fourth tree the group picked just 5 apples. How many apples did each person pick at the first tree?

8. 4 criminals are caught and are to be punished. The Judge allows them to be freed if they can solve a puzzle. If they do not, they will be hung. They agreed. The 4 criminals are lined up on some steps (shown in picture). They are all facing in the same direction. A wall seperates the fourth man from the other three.

To Summarise

- Man 1 can see men 2 and 3.
- Man 2 can see man 3.
- Man 3 can see none of the others.
- Man 4 can see none of the others.

The criminals are wearing hats. They are told that there are two white hats and two black hats. The men initially don’t know what colour hat they are wearing. They are told to shout out the colour of the hat that they are wearing as soon as they know for certain what colour it is.

- They are not allowed to turn round or move.
- They are not allowed to talk to each other.
- They are not allowed to take their hats off.

Now the question is “Who is the first person to shout out and why?”

9. At a party, everyone shook hands with everybody else. There were 66 handshakes. How many people were at the party?

10. You have to measure exactly 4 liters of water, but you only have a 3-liter bottle and a 5-liter bottle. How do you do it?

11. If 5+3+2 = 151012, 9+2+4 = 183662, 8+6+3 = 482466, 5+4+5 = 202504 then what will be the answer of 7+2+5? Only 2% people are able to solve this aptitude question. Let’s see if you can do it.

12. The sum of ages of 5 children born at the intervals of 3 years each is 50 years. What is the age of the youngest child?

13. The difference between a two-digit number and the number obtained by interchanging the positions of its digits is 36. What is the difference between the two digits of that number?

14. Joyce has bought ten trees for her garden. She wants to plant these trees in five rows, with four trees in each row. How must Joyce plant the trees?

15. A light bulb is hanging in a room. Outside of the room there are three switches, of which only one is connected to the lamp. In the starting situation, all switches are off and the bulb is not lit. If it is allowed to check in the room only once to see if the bulb is lit or not (this is not visible from the outside), how can you determine with which of the three switches the light bulb can be switched on?

16. In the middle of a round pool lies a beautiful water-lily. The water-lily doubles in size every day. After exactly 20 days the complete pool will be covered by the lily. After how many days will half of the pool be covered by the water-lily?

17. A snail is at the bottom of a 20 meters deep pit. Every day the snail climbs 5 meters upwards, but at night it slides 4 meters back downwards. How many days does it take before the snail reaches the top of the pit?

### Answers of Aptitude Test Questions

1. Consider the trade-story as if it describes two separate trades, where: In the first trade, the man buys something for $60 and sells it again for $70, so he makes a profit of $10. In the second trade, the man buys something for $80 and sells it again for $90, so he makes again a profit of $10.

Conclusion: The man makes an overall profit of $10 + $10 = $20.

You can also look at the problem as follows:

The total expenses are $60 + $80 = $140 and the total earnings are $70 + $90 = $160. The overall profit is therefore $160 – $140 = $20.

2. 100 Km/hr because that is the top speed of the bus.

3. The man had to reply the number of characters in the word the Doorman was asking. He should have replied “Three” instead of “Five”.

4. There are 5 women, 1 man and 14 children.

5. Here are the answers.

- Cubes that have at least two sides painted in different colours are 24 + 8 = 32.
- Cubes that have only one side painted are 24.
- Cubes that have no side painted = 8.
- Cubes that have exactly one side not painted = 0.

6. There are actually 204 squares on a chessboard. Surprised! Here is the explanation. There are 64 (1×1) squares. There are 49 (2×2) squares. There are 36 (3×3) squares. There are 25 (4×4) squares. There are 16 (5×5) squares. There are 9 (6×6) squares. Then there are 4 (7×7) squares and 1 big 8×8 square. So, there are a total of 204 squares on a normal chessboard.

7. One Apple

8. Man 1 will shout first. If Man1 will not shout then Man 2 surely shouts.

Reason: Man 1 can see the other two criminals? hats. If the hats are same color then he told his hat is opposite color of remaining two hats. So he shouts first. If Man 1 does not shout, it means that the hats of Man 2 and Man 3 are of different color. So Man 2 sees the color of Man 3 hat and he tells that the color of his hat is opposite to the color of Man 3 Hat.

9. With two people, there is one handshake. With three people, there are three handshakes. With four people, there are six handshakes. In general, with n+1 people, the number of handshakes is the sum of the first n consecutive numbers: 1+2+3+…+n. Since this sum is n(n+1)/2, we need to solve the equation n(n+1)/2 = 66. This is the quadratic equation n^{2}+n-132 = 0. Solving for n, we obtain 11 as the answer and deduce that there were 12 people at the party.

10. Fill the 3-litre bottle and pour it into the empty 5-litre bottle. Fill the 3-litre bottle again, and pour enough to fill 5-litre bottle. This leaves exactly 1 litre in the 3-litre bottle. Empty the 5-litre bottle; pour the remaining 1 litre from the 3-litre bottle into the 5-litre bottle. Fill the 3-litre bottle and pour it into the 5-litre bottle. The 5-litre bottle now has exactly 4 litres.

11. 7 + 2 + 5 = 143542. Explanation: a + b + c leads to a 6-digit number.

- The first and second digits are the product of a and b.
- The third and fourth digits are the product of a and c.
- The fifth and sixth digits are b*(a+c) with the digits of the solution reversed.

12. 4 Years. Explanation: Let the ages of children be x, (x + 3), (x + 6), (x + 9) and (x + 12) years. Then, x + (x + 3) + (x + 6) + (x + 9) + (x + 12) = 50 i.e. 5x = 20 and x = 4. So, the age of the youngest child (x) is 4 years.

13. The difference between the two digits of that number is 4. Explanation: Let the ten’s digit be x and unit’s digit be y. Then, (10x+y)-(10y+x) = 36 i.e. 9(x-y) = 36 and that results to x-y = 4.

14. The trees must be planted on the edges of a five pointed star as shown in the figure below.

15. To find the correct switch (1, 2 or 3), turn switch 1 to ON and leave it like that for a few minutes. After that you turn switch 1 back to OFF, and turn switch 2 to ON. Now enter the room. If the light bulb is lit, then you know that switch 2 is connected to it. If the bulb is not lit, then it has to be switch 1 or 3. Now touching the light bulb will give you the answer. If the bulb is still hot, then switch 1 is connected to the bulb; if the bulb is cold, then it has to be switch 3.

16. 19 days. Since the water-lily doubles its size every day and the complete pool is covered after 20 days, half of the pool will be covered one day before that, so 19 days.

17. 16 days. Since the snail moves up 1 meter a day so it will reach 15 meters in 15 days. next day it will again climb 5 meters upward and reaches the top.

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