1.Three friends divided some bullets equally. After all of them shot 4 bullets the total number of bullets remaining is equal to the bullets each had after division. Find the original number divided.
18
-------------------------------------------------------------------------- 2.Find sum of digits of D. Let A= 19991999
B = sum of digits of A, C = sum of digits of B, D = sum of digits of C. (HINT: A = B = C = D (mod 9))
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3.There is a 50m long army platoon marching ahead. The last person in the platoon wants to give a letter to the first person leading the platoon. So while the platoon is marching he runs ahead, reaches the first person and hands over the letter to him and without stopping he runs and comes back to his original position.
In the mean time the whole platoon has moved ahead by 50m.
The question is how much distance did the last person cover in that time. Assuming that he ran the whole distance with uniform speed.
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4.If you take a marker & start from a corner on a cube, what is the maximum number of edges you can trace across if you never trace across the same edge twice, never remove the marker from the cube, & never trace anywhere on the cube, except for the corners & edges? 9
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5.One of Mr. Bajaj, his wife, their son and Mr. Bajaj's mother is an Engineer and another is a Doctor.
If the Doctor is a male, then the Engineer is a male.
If the Engineer is younger than the Doctor, then the Engineer and the Doctor are not blood relatives.
If the Engineer is a female, then she and the Doctor are blood relatives. Can you tell who is the Doctor and the Engineer?
Doc is
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6.Three men - Sam, Cam and Laurie - are married to Carrie, Billy and Tina, but not necessarily in the same order.
Sam's wife and Billy's Husband play Carrie and Tina's husband at bridge. No wife partners her husband and Cam does not play bridge.
Who is married to Cam?
Cam carrie
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7.There are 3 persons X, Y and Z. On some day, X lent tractors to Y and Z as many as they had. After a month Y gave as many tractors to X and Z as many as they have. After a month Z did the same thing. At the end of this transaction each one of them had 24.
Find the tractors each originally had?
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8.A certain street has 1000 buildings. A sign-maker is contracted to number the houses from 1 to 1000. How many zeroes will he need?
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9.There are 9 coins. Out of which one is odd one i.e weight is less or more. How many iterations of weighing are required to find odd coin?
10.In a sports contest there were m medals awarded on n successive days (n > 1). On the first day 1 medal and 1/7 of the remaining m - 1 medals were awarded.
On the second day 2 medals and 1/7 of the now remaining medals was awarded; and so on.
On the nth and last day, the remaining n medals were awarded.
How many days did the contest last, and how many medals were awarded altogether? -------------------------------------------------------------------------- 11.A number of 9 digits has the following properties:
The number comprising the leftmost two digits is divisible by 2, that comprising the leftmost three digits is divisible by 3, the leftmost four by 4, the leftmost five by 5, and so on for the nine digits of the number i.e. the number formed from the first n digits is divisible by n, 2<=n<=9.
Each digit in the number is different i.e. no digits are repeated.
The digit 0 does not occur in the number i.e. it is comprised only of the digits 1-9 in some order.
Find the number.
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12. 1/3 rd of the contents of a container evaporated on the 1st day. 3/4th of the remaining contents of the container evaporated on the second day.
What part of the contents of the container is left at the end of the second day?
(x-1/3x)-((x-1/3x)3/4)=2/3x-1/2x= 1/6x
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13.Vipul was studying for his examinations and the lights went off. It was around 1:00 AM. He lighted two uniform candles of equal length but one thicker than the other. The thick candle is supposed to last six hours and the thin one two hours less. When he finally went to sleep, the thick candle was twice as long as the thin one.
For how long did Vipul study in candle light? 3 hrs
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14.If you started a business in which you earned Rs.1 on the first day, Rs.3 on the second day, Rs.5 on the third day, Rs.7 on the fourth day, & so on.
How much would you have earned with this business after 50 years (assuming there are exactly 365 days in every year)?
Math gurus may use series formula to solve it.(series: 1,3,5,7,9,11.....upto 18250 terms)
------------------------------------------------------------------------------------------------------ 15.A worker earns a 5% raise. A year later, the worker receives a 2.5% cut in pay, & now his salary is Rs. 22702.68
What was his salary to begin with?
------------------------------------------------------------------------------------------------------ 16.At 6'o a clock ticks 6 times. The time between first and last ticks is 30 seconds. How long does it tick at 12'o.
------------------------------------------------------------------------------------------------------ 17. 500 men are arranged in an array of 10 rows and 50 columns according to their heights. Tallest among each row of all are asked to come out. And the shortest among them is A. Similarly after resuming them to their original positions, the shortest among each column are asked to come out. And the tallest among them is B.
Now who is taller A or B? a&b same person
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18.In Mr. Mehta's family, there are one grandfather, one grandmother, two fathers, two mothers, one father-in-law, one mother-in-law, four children, three grandchildren, one brother, two sisters, two sons, two daughters and one daughter-in-law. How many members are there in Mr. Mehta's family? Give minimal possible answer. 7
------------------------------------------------------------------------------------------------------ 19.When Alexander the Great attacked the forces of Porus, an Indian soldier was captured by the Greeks. He had displayed such bravery in battle, however, that the enemy offered to let him choose how he wanted to be killed. They told him, "If you tell a lie, you will put to the sword, and if you tell the truth you will be hanged."
The soldier could make only one statement. He made that statement and went free. What did he say?
20.A person wanted to withdraw X rupees and Y paise from the bank. But cashier made a mistake and gave him Y rupees and X paise. Neither the person nor the cashier noticed that.
After spending 20 paise, the person counts the money. And to his surprise, he has double the amount he wanted to withdraw.
Find X and Y. (1 Rupee = 100 Paise)
21.The game of Tic-Tac-Toe is being played between two players. Only the last mark to be placed in the game as shown.
Who will win the game, O or X? Can you tell which was the sixth mark and at which position? Do explain your answer.
Assume that both the players are intelligent enough.
22At the Party:
There were 9 men and children.
There were 2 more women than children.
The number of different man-woman couples possible was 24. Note that if there were 7 men and 5 women, then there would have been 35 man-woman couples possible.
Also, of the three groups - men, women and children - at the party:
There were 4 of one group.
There were 6 of one group.
There were 8 of one group.
Exactly one of the above 6 statements is false.
Can you tell which one is false? Also, how many men, women and children are there at the party
23There is a shortage of tube lights , bulbs and fans in a village - Kharghar. It is found that All houses do not have either tubelight or bulb or fan. exactly 19% of houses do not have just one of these.
atleast 67% of houses do not have tubelights. atleast 83% of houses do not have bulbs. atleast 73% of houses do not have fans.
What percentage of houses do not have tubelight, bulb and fan?
23.Mr. Subramaniam rents a private car for Andheri-Colaba-Andheri trip. It costs him Rs.
300 everyday.
One day the car driver informed Mr. Subramaniam that there were two students from Bandra who wished to go from Bandra to Colaba and back to Bandra. Bandra is halfway between Andheri and Colaba. Mr. Subramaniam asked the driver to let the students travel with him.
On the first day when they came, Mr. Subramaniam said, "If you tell me the mathematically correct price you should pay individually for your portion of the trip, I will let you travel for free."
How much should the individual student pay for their journey?
24.Substitute digits for the letters to make the following Division true
O U T
-------------
S T E M | D E M I S E
| D M O C
-------------
T U I S
S T E M
----------
Z Z Z E
Z U M M
--------
I S T
Note that the leftmost letter can't be zero in any word. Also, there must be a one-to-one mapping between digits and letters. e.g. if you substitute 3 for the letter M, no other letter can be 3 and all other M in the puzzle must be
Answer
C=0, U=1, S=2, T=3, O=4, M=5, I=6, Z=7, E=8, D=9
It is obvious that U=1 (as U*STEM=STEM) and C=0 (as I-C=I).
S*O is a single digit and also S*T is a single digit. Hence, their values (O, S, T) must be 2, 3 or 4 (as they can not be 0 or 1 or greater than 4).
Consider, STEM*O=DMOC, where C=0. It means that M must be 5. Now, its simple. O=4, S=2, T=3, E=8, Z=7, I=6 and D=9.
O U T 4 1 3
------------- -------------
S T E M | D E M I S E 2 3 8 5 | 9 8 5 6 2 8
| D M O C | 9 5 4 0
------------- -------------
T U I S 3 1 6 2
S T E M 2 3 8 5
---------- ----------
Z Z Z E 7 7 7 8
Z U M M 7 1 5 5
-------- --------
I S T 6 2 3
Also, when arranged from 0 to 9, it spells CUSTOMIZED.
25.At what time after 4.00 p.m. is the minutes hand of a clock exactly aligned with the hour hand?
Answer
4:21:49.5
Assume that X minutes after 4.00 PM minute hand exactly aligns with and hour hand.
For every minute, minute hand travels 6 degrees.
Hence, for X minutes it will travel 6 * X degrees.
For every minute, hour hand travels 1/2 degrees.
Hence, for X minutes it will travel X/2 degrees.
At 4.00 PM, the angle between minute hand and hour hand is 120 degrees. Also, after X minutes, minute hand and hour hand are exactly aligned. So the angle with respect to 12 i.e. Vertical Plane will be same. Therefore,
6 * X = 120 + X/2
12 * X = 240 + X
11 * X = 240
X = 21.8182
X = 21 minutes 49.5 seconds
Hence, at 4:21:49.5 minute hand is exactly aligned with the hour hand.
25.A soldier looses his way in a thick jungle. At random he walks from his camp but mathematically in an interesting fashion.
First he walks one mile East then half mile to North. Then 1/4 mile to West, then 1/8 mile to South and so on making a loop.
Finally how far he is from his camp and in which direction?
Answer
The soldier is 0.8944 miles away from his camp towards East-North.
It is obvious that he is in East-North direction.
Distance travelled in North and South directions
= 1/2 - 1/8 + 1/32 - 1/128 + 1/512 - 1/2048 + and so on... (a geometric series with r = (-1/4) )
(1/2) * ( 1 - (-1/4)n )
= --------------------------- ( 1 - (-1/4) )
= 1 / ( 2 * ( 1 - (-1/4) ) )
= 2/5
Similarly in East and West directions
= 1 - 1/4 + 1/16 - 1/64 + 1/256 - and so on... (a geometric series with r = (-1/4) )
(1) * ( 1 - (-1/4)n )
= --------------------------- ( 1 - (-1/4) )
= 1 / ( ( 1- (-1/4) )
= 4/5
So the soldier is 4/5 miles away towards East and 2/5 miles away towards North. So using right angled triangle, soldier is 0.8944 miles away from his camp.
26.Raj has a jewel chest containing Rings, Pins and Ear-rings. The chest contains 26 pieces. Raj has 2 1/2 times as many rings as pins, and the number of pairs of earrings is 4 less than the number of rings.
How many earrings does Raj have?
Answer
12 earrings
Assume that there are R rings, P pins and E pair of ear-rings.
It is given that, he has 2 1/2 times as many rings as pins.
R = (5/2) * P or P = (2*R)/5
And, the number of pairs of earrings is 4 less than the number of rings.
E = R - 4 or R = E + 4
Also, there are total 26 pieces.
R + P + 2*E = 26
R + (2*R)/5 + 2*E = 26
5*R + 2*R + 10*E = 130
7*R + 10*E = 130
7*(E + 4) + 10*E = 130
7*E + 28 + 10*E = 130
17*E = 102
E = 6
Hence, there are 6 pairs of Ear-rings i.e. total 12 Ear-rings
27.How many ways are there of arranging the sixteen black or white pieces of a standard international chess set on the first two rows of the board?
Given that each pawn is identical and each rook, knight and bishop is identical to its pair. Submitted
Answer
6,48,64,800 ways
There are total 16 pieces which can be arranged on 16 places in 16P16 = 16! ways.
(16! = 16 * 15 * 14 * 13 * 12 * ..... * 3 * 2 * 1)
But, there are some duplicate combinations because of identical pieces.
There are 8 identical pawn, which can be arranged in 8P8 = 8! ways.
Similarly there are 2 identical rooks, 2 identical knights and 2 identical bishops. Each can be arranged in 2P2= 2! ways.
Hence, the require answer is
= (16!) / (8! * 2! * 2! * 2!)
= 6,48,64,800
28.A person with some money spends 1/3 for cloths, 1/5 of the remaining for food and 1/4 of the remaining for travel. He is left with Rs 100/-
How much did he have with him in the begining?
Answer
Rs. 250/-
Assume that initially he had Rs. X
He spent 1/3 for cloths =. (1/3) * X
Remaining money = (2/3) * X
He spent 1/5 of remaining money for food = (1/5) * (2/3) * X = (2/15) * X
Remaining money = (2/3) * X - (2/15) * X = (8/15) * X
Again, he spent 1/4 of remaining maoney for travel = (1/4) * (8/15) * X = (2/15) * X Remaining money = (8/15) * X - (2/15) * X = (6/15) * X
But after spending for travel he is left with Rs. 100/- So
(6/15) * X = 100
X = 250
29.Grass in lawn grows equally thick and in a uniform rate. It takes 24 days for 70 cows and 60 days for 30 cows to eat the whole of the grass.
How many cows are needed to eat the grass in 96 days?
Answer
20 cows
g - grass at the beginning r - rate at which grass grows, per day y - rate at which one cow eats grass, per day
n - no of cows to eat the grass in 96 days
From given data,
g + 24*r = 70 * 24 * y ---------- A g + 60*r = 30 * 60 * y ---------- B
g + 96*r = n * 96 * y ---------- C
Solving for (B-A),
(60 * r) - (24 * r) = (30 * 60 * y) - (70 * 24 * y)
36 * r = 120 * y ---------- D
Solving for (C-B),
(96 * r) - (60 * r) = (n * 96 * y) - (30 * 60 * y)
36 * r = (n * 96 - 30 * 60) * y
120 * y = (n * 96 - 30 * 60) * y [From D]
120 = (n * 96 - 1800) n = 20
Hence, 20 cows are needed to eat the grass in 96 days.
30.There is a safe with a 5 digit number as the key. The 4th digit is 4 greater than the second digit, while the 3rd digit is 3 less than the 2nd digit. The 1st digit is thrice the last digit. There are 3 pairs whose sum is 11.
Find the number.
Answer
65292
As per given conditions, there are three possible combinations for 2nd, 3rd and 4th digits.
They are (3, 0, 7) or (4, 1, 8) or (5, 2, 9)
It is given that there are 3 pairs whose sum is 11. All possible pairs are (2, 9), (3, 8), (4, 7), (5, 6). Now required number is 5 digit number and it contains 3 pairs of 11. So it must not be having 0 and 1 in it. Hence, the only possible combination for 2nd, 3rd and 4th digits is (5, 2, 9)
Also, 1st digit is thrice the last digit. The possible combinations are (3, 1), (6, 2) and (9, 3), out of which only (6, 2) with (5, 2, 9) gives 3 pairs of 11. Hence, the answer is 65292.
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