Sunday, January 30, 2011

Munchausen Number

Munchausen Number


Munchausen Number

Posted: 30 Jan 2011 06:44 AM PST

Munchausen Number is a number that is equal to the sum of its digits each raised to a power equal to the digit.

Munchausen number is also called perfect digit-to-digit invariant (PDDI) because of the above feature.

The only Munchausen numbers are 1 and 3435.

Specialty of  3435 -

33 + 44 + 33 + 55 = 27 + 256 + 27 + 3125 = 3435

though, 00 is undefined but if we consider it as 0, then there is one more Munchausen number founded till date -  that number is 438579088

44 + 33 + 88 + 55 + 77 + 99 + 00 + 88 + 88

= 256 + 27 + 16777216 + 3125 + 823543 + 387420489 + 0 + 16777216 + 16777216 = 438579088

Now you know about properties of Munchausen number. Both the above shown examples are in decimal system. So friends use your grey cells and come up with more such numbers in any base other than decimal.

I know it's little difficult but since so many intelligent people are regular visitors to QuickerMaths.com, I am assured that we will get some answers.

Vineet Patawari

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Saturday, January 29, 2011

Verbal Ability Questions

Verbal Ability Questions


Verbal Ability Questions

Posted: 29 Jan 2011 12:47 AM PST

Directions for next 4 Verbal Ability Questions: Each verbal ability question below contains six statements followed by four sets of combinations of three; Choose the set in which the statement are logically related.

1. A. No school boy studies hard.
B. All school boys go to school.
C. Some school boys are good at games.
D. All school girls study hard.
E. No school girl is a school boy.
F. All school girls are children.
a. ABC
b. BCD
c. ADE
d. DEF
e. CFB

2. A. Some businessmen have good planning skills.
B. Some professionals have good planning skills.
C. Some businessmen have good implementation skills.
D. Some businessmen have good planning skills.
E. Good planning skills lead to good implementation.
F. Some businessmen implement well.
a. ACD
b. ADB
c. DEF
d. ABC
e. CFA

3. A. Some humans are non-vegetarians.
B. All Indian are humans.
C. All humans need food to live.
D. All Indians are non-vegetarian.
E. Indians need food to live.
F. Some humans are Indians.
a. ADF
b. ABC
c. AEF
d. BCE
e. None of these

4. A. All lions are brave.
B. All lions are regal.
C. All animals are lions.
D. All lions need food.
E. All animals need food.
F. All animals need rest.
a. CDE
b. ABC
c. BCD
d. CEF

e. None of these

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Thursday, January 27, 2011

Solving more problems by Lateral thinking

Solving more problems by Lateral thinking


Solving more problems by Lateral thinking

Posted: 27 Jan 2011 03:52 AM PST

Lateral Thinking is a powerful method to use the unused potential of brain. This is originally propounded by Edward De Bono.  In this post various simple methods which can bring about lateral thinking capabilities in a reader are described.

To know more about Lateral Thinking

In this post I am presenting my favorite collection of more than 50 Lateral Thinking puzzles/riddles/questions/statements. Some of them are really tricky. Hope you will like it


Lateral Thinking Questions and Answers

1. What can you hold in your right hand, but not in your left?

Your left hand, forearm or elbow.

2. How many animals of each species did Moses take into the Ark?

None. NOAH built the Ark

3. A man built a rectangular house, each side having a southern view. He spotted a bear. What color was the bear?

White, because it’s a polar bear. Only at the North Pole can all four walls be facing south.

4. Two fathers took their sons fishing. Each man and son caught one fish, but when they returned to camp there were only 3 fish. How could this be? (None of the fish were eaten, lost, or thrown back.)

There were only three people. The son, his father, and his grandfather.

5. If you were alone in a deserted house at night, and there was an oil lantern, a candle, a lamp and a matchbox with only one match stick, which would you, light first?

The match stick!

6. A graduate applying for pilot training with a major airline was asked what would be his reaction, if after a long-haul flight to Sidney, he saw the captain wearing a Saree and applying lipstick and mascara?

His reaction should be indifferent. The captain was a woman. Many airlines are now hot on equal opportunities and a candidate who has difficulty envisaging that an airline captain might be female will not go very far!

7. Which side of a cat contains the most hair?

The outside

8. The 1st and 4th CEO of a MNC had the same mother and father, but were not brothers. How can this be possible?

The 1st and 4th CEO is the same person

9. A Black man is wearing Black shoes, socks, trousers, coat, gloves and ski mask. He is walking down a back street with all the street lamps off. A black car is coming towards him with its light off but somehow manages to stop in time. How did the driver see the man?

It was day time

10. How many birthdays does a typical woman have?

One

11. A peasant is convicted and gets the death penalty. The judge allows him to say a last sentence in order to determine the way the penalty will be carried out. If what the peasant says is false, he will be hanged, if he speaks the truth he will be beheaded. The peasant speaks a last sentence and to everybody surprises some minutes later he is set free because the judge cannot determine his penalty.

What did the peasant said?

The peasant said: “I shall be hanged!”

If what the peasant said was false, he would be hanged. But that’s what the peasant was saying. So he speaks the truth. But if he speaks the truth, he would be beheaded, so then he was not speaking the truth. So it is impossible for the judge to determine whether the peasant speaks the truth or not. So therefore the judge cannot determine the penalty and sets the peasant free.

12. Why it is illicit to bury a man in Bihar, if he is living in kolkata.

Because he is still alive.

13. To the nearest cubic centimeter, how much soil is there in a 5m x 3m x 2m hole?

None – it’s a hole!

14. If you drove a coach leaving Esplanade with 35 passengers, dropped off 6 and picked up 2 at Central, picked up 9 more at M.G.Road, dropped off 3 at Maniktala,and then drove on to arrive in Kankurgachi 1 hr 40 minutes later, what is the name of the driver ?

YOU are the driver!

15. A woman lives on the tenth floor of a block of flats. Every morning she takes the lift down to the ground floor and goes to work. In the evening, she gets into the lift, and, if there is someone else in the lift she goes back to her floor directly. Otherwise, she goes to the eighth floor and walks up two flights of stairs to her flat. How do you explain this?

The woman is of small stature and couldn’t reach the upper lift buttons

16. The band of stars across the night sky is called the “…… Way”

Milky Way

17. If a red house is made of red bricks, and a blue house is made of blue bricks, what is a green house made of?
Glass
18. A murderer is condemned to death. He has to choose between three rooms. The first is full of raging fires, the second is full of assassins with loaded guns, and the third is full of lions that haven’t eaten in 3 years. Which room is safest for him?
3rd one. As the lions haven’t eaten in 3 years are dead.

19. Ram, a party magician, is carrying three gold balls each weighing one kilogram. On the way to a session he comes to a bridge which has a sign posted saying the bridge could hold only a maximum of 80 kilograms. Steve weighs 78 kilograms and the three gold balls weigh total three kilograms. He reads the sign and still safely crossed the bridge with all three gold balls. How did he manage this?

Steve is a juggler. When he came to the bridge he juggled the gold, always keeping one piece in the air

20. If a plane crashes on the India/Pakistan border, where do you bury the survivors? [You can't use no man's land]

You don’t bury survivors!

21. This is an unusual paragraph. I’m curious how quickly you can find out what is so unusual about it. It looks so plain you would think nothing was wrong with it. In fact, nothing is wrong with it! It is unusual though. Study it, and think about it, but you still may not find anything odd. But if you work at it a bit, you might find out.

The letter “e,” which is the most common letter in the English language, does not appear once in the long paragraph…

22. Ram’s mother has 3 children, one is named April, one is named May. What is the third one named?
Ram

23. You can imagine an arrow in flight, toward a target. For the arrow to reach the target, the arrow must first travel half of the overall distance from the starting point to the target. Next, the arrow must travel half of the remaining distance.

For example, if the starting distance was 10m, the arrow first travels 5m, then 2.5m.
If you extend this concept further, you can imagine the remaining distances getting smaller and smaller but Would never become 0. But in reality the arrow does reach the target. Why ?

This is because the sum of an infinite series can be a finite number. Let the initial distance be 1 . so remaining distances will be 1/2 , 1/4 , 1/8 …

Now, 1/2 + 1/4 + 1/8 + …
=1/2 / ( 1- 1/2)
= 1
and the arrow hits the target.

24. Four switches can be turned on or off. One of them (you don’t know which) is the right switch for the bulb next room, which is initially off. The other three switches do nothing. From the room with the switches in it, you can’t see whether the light in the next room is turned on or off. You may flip the switches as often and as many times as you like, but once you enter the next room to check on the light, you must be able to say which switch controls the light without flipping the switches any further. (And you can’t open the door without entering, either!) How can you determine which switch controls the light?
Turn on switches 3 and 4 and wait fifteen minutes or so. Then turn switch 3 off, turn switch 2 on, and enter the room. If the bulb is dark and cool, switch 1 controls it. If the bulb is bright and cool, switch 2 controls it. If the bulb is dark and warm, switch 3 controls it. If the bulb is bright and warm, switch 4 controls it.

25. A cowboy rode into town on “Monday”, spent one night there, and left on “Monday”. How can this be possible?
His horse was named “Friday”

26. If Costa Rica goes with Thailand, Cuba goes with Puerto Rico, and the Netherlands go with Yugoslavia, what country would the Ivory Coast go with?

Ireland .If you look at the flags of these countries, the countries that go with each other have the same design and the same colors, however the colors are swapped around. All of these flags contain white, the white stays as it is.

27. How man degrees are there between clock hands at 3.15 pm?
Not zero degrees as you might at first think. The minute hand will be at 15 minutes (90 degrees clockwise from vertical) but the hour hand will have progressed to one quarter of the distance between 3 pm and 4 pm. Each hour represents 30 degrees (360 / 12), so one quarter of an hour equals 7.5 degrees, so the minute hand will be at 97.5 degrees: a 7.5 degree difference between the hands.

28. You’ve been sentenced to death in an obscure foreign country which has a strange law. Before the sentence is carried out, two papers — one with “Alive” written on it and one with “DEAD” written on it — are folded up and placed in a hat. You are permitted to pick out one of the papers (without looking), and if you choose the one with “ALIVE” written on it, you are exonerated. Otherwise, the death sentence is carried out. On this occasion, One of your enemies, has substituted the paper with “ALIVE” written on it with another one with “DEAD” written on it. This person gleefully informs you of what he has done and that you are doomed to die. You are not permitted to speak to anyone about this misdeed, nor will you have a chance to switch the papers or the hat yourself in time. How will you avoid certain death?

After you draw one of the papers, swallow it. The jailer will be forced to check the remaining paper to determine what the one you drew said. The jailer will of course see a paper with “DEAD” written on it, assume you drew the one with “ALIVE” written on it, and set you free.

29. Can you name three consecutive days without using the words Monday, Tuesday, Wednesday, Thursday, Friday, Saturday, or Sunday? (or day names in any other language)
yesterday , today , tomorrow.

30. You can take away the whole and still have some left. You can take away some and still have the whole left. What is it?
‘Wholesome’

31. Acting on an anonymous phone call, the police raid a house to arrest a suspected murderer. They don’t know what he looks like but they know his name is Daud and that he is inside the house. The police bust in and saw a doctor, a lawyer, a pilot and a fireman all playing poker. Without hesitation or communication of any kind, they immediately arrest the fireman. How do they know they’ve got their man?[Policemen got no hints from their dresses or accessories]
The fireman is the only man in the room. The rest of the poker players are women

32. There are six balls in the basket. Six boys each take one of the balls. How can it be that one ball is left in the basket?
The last person took the basket with the last ball still inside.

33. You want to send a valuable object to a friend securely. You have a box which can be fitted with multiple locks, and you have several locks and their corresponding keys. However, your friend does not have any keys to your locks, and if you send a key in an unlocked box, the key could be copied en route. How can you send the object securely?
Put the valuable object into the box, secure it with one of your locks, and send the box to your friend. Your friend should then attach one of his own locks and return it. When you receive it again, remove your lock and send it back. Now your friend can unlock his own lock and retrieve the object.

34. A woman had two sons who were born on the same hour of the same day of the same year. But they were not twins. How could this be so?
They were two of a set of triplets (or quadruplets, etc.).
Or , they were adopted. It’s a coincidence they were born on the same exact day

35. Why is it better to have round manhole covers than square ones?
Length of the diagonal of a square is always greater than the length of it’s side. So if it’s mistakenly placed across the diagonal dropped or fall down a manhole but round covers cannot be dropped or fall down a manhole.

36. Bay of Bengal is in which state?

Liquid state

37. A man went to a party and drank some beer. He was not feeling well so left early, leaving some beer in the mug. Everyone else at the party who drank that beer subsequently died of poisoning. Why did the man not die? [ 1st man's resistance power is same as all other men , and effect of the poison was same to every one ]

Because he was the one who put the poison in the beer.

38. A man buys Wheat at $1 a KG. from American growers and sells them at $0.05 a KG. in Africa. As a result of this he becomes a millionaire. How come?
The man is a philanthropist who bought great quantities of Wheat to sell to poor people at prices they could afford. He started out as a billionaire, but lost so much money in his good works that he became a millionaire!

39. Three of the glasses are filled with Orange juice and other three are empty. Three filled glasses are placed side by side and three empty glasses are placed side by side all in a single line.
like : Full Full Full empty empty empty
By moving only one glass can you arrange them so the full glasses and empty classes are alternate.

Take the second glass from the left and put it contents into the second glass from the right. And then put it to it’s original position

40. A police officer saw a truck driver clearly going the wrong way down a one-way street, but did not try to stop him. Why not?
It’s said no where that he was driving a truck. The truck driver was walking.

41. The following is what seems to be a mathematical proof that ten equals 9.999999…. What’s wrong with it?

a = 9.999999…
10a = 99.999999…
10a – a = 90
9a = 90
a = 10

Actually there’s nothing wrong with it. Ten does equal 9.99999…, as this proof clearly shows.

42. A horse is tied to a 15 ft. rope and there is a bail of hay 25 ft. away from him. Yet the horse is able to eat from the bail of hay. How is this possible. [ The bail of hay was not moved by any external force]
The rope isn’t tied to anything, so the horse can go freely to anywhere it pleases.

43. A man holidaying abroad fell off a boat into deep water. He could not swim and he was not wearing anything to keep him afloat. It took 40 minutes for the people on the boat to realize someone was missing. The missing man was rescued 1and 1/2 hour later. Why didn’t he drown?
He fell into the Dead Sea, which lies between Israel and Jordan. The water is so salty and dense that anyone in it floats very easily.

44. What would you estimate to be the result if you multiply the number of hairs of all the people on the earth?[Assume there are 5 billion people in the world, and average number of hair / person is 1 million]
As there are people with no hair. And any number multiplied by 0 will result in 0.

45.What does
E
K
A
M
REPRESENT…
Makeup

46. If a doctor gives you three pills, telling you to take one every half hour, how many minutes will the pills last?

60 minutes. You take first pills now, 2nd pills after 30 minutes. And 3rd pill after another 30 minutes. Total time elapsed is 60 minutes.

47. You must cut a birthday cake into exactly eight pieces, but you’re only allowed to make three straight cuts, and you can’t move pieces of the cake as you cut. How can you do it?
Use the first two cuts to cut an ‘X’ in the top of the cake. Now you have four pieces. Make the third cut horizontal, which will divide the four pieces into eight

48. A butcher is 5′10″ tall and has a muscular body. What does he weigh?
Meat.

49. A table tennis ball fell into a deep hole. The hole was only a bit wider then the ball, so you can not use your hand or any other mechanical instrument. How would you take it out, with no damage?

All you have to do is pour some water into the pipe so that the ball swims up on the surface.

50. Ram is in the final of a match at the Olympic Games. At the moment he reaches the finish, all the other contestants are behind his back. He did not play unfair and did also not use doping, but he does not get the gold medal? Why is that? [He was not running on a circular track]

Ram was in the final of a rowing match. When rowing, you always go backwards. So since all other contestants were behind his back, he became last and therefore did not get a gold medal.

51. Light as a feather, even the strongest man can’t hold it for much more than 3 minutes.
Breath

52. What do you serve that you can’t eat?

A tennis ball.

53. A Beggar’s Brother Died, But The Man Who Died Had No Brother How Could This Be…?

The Beggar Was a Female

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Saturday, January 22, 2011

Reasoning Puzzle

Reasoning Puzzle


Reasoning Puzzle

Posted: 21 Jan 2011 12:18 PM PST

This is an arrangement related reasoning problem for you. Similar questions frequently appear in various competitive examinations. You will probably need a pen and paper to solve this.

So go ahead and solve it. All the best!!

Arrangement related Logical Reasoning Question

Information

Bimla, champa, Tina and Alica are sitting around a table discussing their favorite sports.

a. Bimla sits directly across from the jogger.

b. Champa sits to the right of the racquetball player.

c. Alica sits across from Ted.

d. The golfer sits to the left of the tennis player.

e. A man sits on Tina right.

Question - What sport does each of the four prefer?

Leave your answers below.

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Common Mistakes in English Usage

Common Mistakes in English Usage


Common Mistakes in English Usage

Posted: 22 Jan 2011 12:10 AM PST

Whether you like it or not, any management entrance examination like CAT, XAT, SNAP, etc. will judge you by your quality of using right word in right context. The first thing you should do is to avoid the most common spelling mistakes. Below you'll find 10 such mistakes to get you started.

10 common spelling mistakes

1. accept / except

INCORRECT: Please except this gift.
CORRECT: Please accept this gift.

Except, as a verb, means to exclude or leave out. As a preposition it means "with the exception of." Accept means "to receive willingly." For example: We visited every landmark except the Eiffel Tower. The school is accepting only those students who have had their shots; all others are excepted.

2. advice / advise

INCORRECT: He refused to take my advise.
CORRECT: He refused to take my advice.

Advise is a verb. The s has the sound of "z." Advice is a noun. The c has the sound of "s."

3. all right / alright

INCORRECT: He's alright after his fall.
CORRECT: He's all right after his fall.

Although arguments are advanced for the acceptance of the spelling, alright is still widely regarded as nonstandard. Careful writers avoid it.

4. effect / affect

INCORRECT: His death really effected me.
CORRECT: His death really affected me.

The most common use of effect is as a noun meaning "something produced by a cause." The most common use of affect is as a transitive verb meaning "to act upon." For example: The disease had a lasting effect on the child. The family's lack of money affected his plans.

5. every day / everyday

INCORRECT: Dan walks the dog everyday at six p.m.
CORRECT: Dan walks the dog every day at six p.m.

Everyday is an adjective that means "daily." Every day is a phrase that combines the adjective every with the noun day. For example: Walking the dog is an everyday occurrence. I practice the flute every day.

6. its / it's

INCORRECT: Put the saw back in it's place.
CORRECT: Put the saw back in its place.

It's is a contraction that represents two words: it is. Its is a one-word third-person singular possessive adjective, like his. For example: The man lost his hat. The dog wagged its tail.

7. passed / past

INCORRECT: The car past the train.
CORRECT: The car passed the train.

Past is used as an adverb of place, or as a preposition. Passed is the past tense of the verb to pass. For example: The past few days have been hectic. The deadline has passed. He passed her the biscuits. The boys ran past the gate. As we stood in the doorway, the cat ran past.

8. quiet / quite

INCORRECT: We spent a quite evening reading.
CORRECT: We spent a quiet evening reading.

Quiet is an adjective meaning "marked by little or no activity." Quite is an adverb meaning "to a considerable extent." For example: The children are quite amiable today. Quiet can also be used as a noun. For example: We enjoyed the quiet by the lake. (The suffix "ness" should never be added to the abstract nouns quiet and calm.)

9. then / than

INCORRECT: I have more eggs then you.
CORRECT: I have more eggs than you.

Then is an adverb that indicates time. It can go anywhere in a sentence. For example: The man paused by the door and then entered. Then the noise started. As conjunction or preposition, than will always be followed by a noun or a pronoun. For example: I like Melville better than Hawthorne.

10. who's / whose

INCORRECT: I don't know who's dog you're talking about.
CORRECT: I don't know whose dog you're talking about.

Who's is the contracted form of "who is." Whose is the possessive adjective form of who. For example: Who's your daddy? Whose car are we going in?

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Wednesday, January 19, 2011

3 Men and 5 Hats – Brainteaser

3 Men and 5 Hats – Brainteaser


3 Men and 5 Hats – Brainteaser

Posted: 18 Jan 2011 04:20 PM PST

Interesting Brainteaser

3 innocent prisoners were sitting in a jail. One day, the cruel jailer takes them out and places them in a line on three chairs, in such a way that man C can see both man A and man B, man B can see only man A, and man A can see none of the other men.

The jailer shows them 5 hats, 2 of which are black and 3 of which are white. After this, he blindfolds the men, places one hat on each of their heads, and removes the blindfolds again. The jailer tells his three prisoners that if one of them is able to determine the color of his hat within one minute, all of them are released. Otherwise, they will all be executed. None of the prisoners can see his own hat, and all are intelligent. After 59 seconds, man A shouts out the (correct) color of his hat!

What is the color of man A's hat, and how does he know?

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Data Sufficiency Sample Questions

Data Sufficiency Sample Questions


Data Sufficiency Sample Questions

Posted: 19 Jan 2011 03:30 AM PST

Direction for next 5 Data Sufficiency Sample Questions: Each Data Sufficiency Sample Questions n is followed by some data.

Mark [a], if I alone is sufficient to answer the question.
Mark [b], if II alone is sufficient to answer the question.
Mark [c], if both I and II needed to answer the question.
Mark [d], if neither I nor II is sufficient to answer the question.
Mark [e], if either I or II is sufficient to answer the question but not both.

1. Will the new mayor prove more useful than the last one?
I. The new mayor has preformed a number of urgently required tasks for the benefit of the city.
II. The new mayor is disciplined and is achievement-oriented.

2. Are colleges today understaffed?
I. The paucity of teachers is reflected in the unmanageably high number of students per teacher.
II. Many posts in colleges lie vacant as there is a dearth of qualified personnel.

3. How has the trading business fared in the last two months?
I. Due to rising demands from other countries in the last couple of months the actual market size increased for traders.
II. Thanks to increased capacities, traders were able to meet the rise in demand.

4. Is the study of Philosophy necessary for children today?
I. Philosophy acquaints one with the purpose of life.
II. Children need to understand the implications of their environment, which they can get only from philosophy.

5. Are writers of pulp fiction intelligent people?
I. Pulp fiction relies on an astute understanding of human nature and sharp perspective on the current environment.
II. Pulp fiction is widely read by some of the most intelligent people in the world.

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Monday, January 17, 2011

You have 12 coins, one of which is fake.

You have 12 coins, one of which is fake.


You have 12 coins, one of which is fake.

Posted: 16 Jan 2011 10:56 AM PST

Hey friends, try and solve this intricate puzzle. You can use your skills to explain this puzzle using a flow chart. If you make one send it to me on my email address, I will include it in the body of this post itself.

12 coins 3 weighings

You have 12 coins, one of which is fake. The fake coin is indistinguishable from the rest except that it is either heavier or lighter, but you don't know which. Can you determine which is the fake coin and whether it is lighter or heavier using a balance scale and only 3 weighing?

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Verbal Sample Questions

Verbal Sample Questions


Verbal Sample Questions

Posted: 16 Jan 2011 09:47 AM PST

Verbal Sample Questions: Directions for next 3 Verbal Sample Questions: Read the passage given below and answer the verbal sample questions accordingly.

In a certain society, there are two marriage groups, Red and Brown. No marriage is permitted within a group. On marriage, males become part of their wife's group: women remain in their own group. Children belong to the same group as their parents. Widowers and divorced males revert to the group of their birth. Marriage to more than one person at the same time and marriage to a direct descendant are forbidden.

1. A Brown female could have had
I. a grandfather born Red
II. a grandmother born Red
III. two grandfathers born Brown.
a. I only
b. II only
c. I and II only
d. I, II and III

2. A male born into the Brown group may have
a. an uncle in either group
b. a Brown daughter
c. a son-in-law born into the Red group
d. a daughter-in-law in the Red group.

3. Which of the following is not permitted under the rules started?
a. A Brown male Marrying his father's sister
b. A Red female marrying her mother's brother
c. A man born Red, who is now a widower, marrying his brother's widow
d. A widow marrying her divorced daughter's ex-husband

To buy Complete Verbal Ability Preparation Module @ Just for Rs.  490Click Here

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Saturday, January 15, 2011

Interesting Picture Puzzle

Interesting Picture Puzzle


Interesting Picture Puzzle

Posted: 14 Jan 2011 12:48 PM PST

If you like picture puzzles, this is post is for you.  What do you see?  The first picture below has faces hidden - but

Where are they?

How many are there?

How Many Faces Can You Find In This Picture? Post your observations in form of comments below-

Click on the image to enlarge


Click here to know the answer

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Quantitative Questions

Quantitative Questions


Quantitative Questions

Posted: 15 Jan 2011 12:59 AM PST

Sample Quantitative Questions: Direction for next 2 Quantitative questions: Answer the following quantitative questions on the basis of data given below. x , y , z are positive integers such that x + y + z = 100,

1. Find the probability that x > 20, y > 10 , z > 20 .
a) 23/99
b) 1/7
c) 7/33
d) 1/8
e) 8/33

2. Find the number of possible solutions for the equation in the previous question, If 25 < x < 51, y > 10 and z > 15.
a) 900
b) 1176
c) 4075
d) 236
e) None of these

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