3 Integers.

Written on 11:32 pm by Vja Students

In how many ways can you choose 3 integers such that their sum and product have the same value and none of the 3 integers are equal?

Answer:
Infinite ways
{-a,0,-a}
3,2,1
-3,-2,-1

Playing game

Written on 12:03 am by Vja Students

There are 6 players A B C D E F.Mr. Chaitu , the coach asked them , who are interested to play the game ?
A= no one is interested to play
B= only one of us is interested to play
C= only 2 of us is interested to play
D = only 3 of us
E = only 4 of us is
F = only 5 of us is...
Now Mr Chaitu knows that those who are interested to play the game always lie/s.So how many of them are interested to play the game or data is inconsistent ?

Answere::
This problem has two solutions
First:When 5 people are interested in playing and those 5 people are A B C D E as A B C D E lies and F is telling truth.

Second:When 6 people are interested in playing and those 6 people are A B C D E F as all of them lies.

4 4's

Written on 11:15 pm by Vja Students

How can u get 280 by using 4 4's n by using any mathematical symbol??


Answer:
[(square root of 4*4)^4 ]+ 4! = 280

Time Plzzz

Written on 11:43 pm by Vja Students

Karthik, Balaji, Chaitu and Dileep visited Sunil on 14th February.

1. The time of each visit was as follows: - Karthik at 8:00 - Balaji at 9:00 - Chaitu at 10:00 - Dileep at 11:00 Each time mentioned above may be either AM or PM.
2. Chaitu did not visit Sunil between Balaji and Dileep.
3. At least one female visited Sunil between Karthik and Balaji.
4. Karthik did not visit Sunil before both Chaitu and Dileep.
Can you tell at what time did they individually visit Sunil?

Answer::Balaji (9:00AM) - Dileep (11:00AM) - Karthik (8:00PM) - Chaitu (10:00PM)

Secret mail

Written on 11:44 pm by Vja Students

The secret agent X emailed a code word to his head office. They are "AIM DUE OAT TIE MOD". But four of these five words are fake and only one contains the information. The agent X also mailed a sentence as a clue - if I tell you any one character of the code word, you would be able to tell the number of vowels in the code word. Can you tell which is the code word?

Answer::
The code word is TIE.

If you were told any one character of MOD, then you would not be able to determine whether the number of vowels are one or two. e.g. if you were told M, there are two words with M - AIM with 2 vowels and MOD with 1 vowel.

So you would not be able to say the number of vowels. same arguments can be given for characters O and D. Hence, the word with any one of M, O or D is not a code word i.e. AIM, DUE, OAT and MOD are not the code word.

Thus, TIE is the code word. T : two words - TIE and OAT, both with 2 vowels I : two words - TIE and AIM, both with 2 vowels E : two words - TIE and DUE, both with 2 vowels.

Tea Money

Written on 10:35 pm by Vja Students

A drinks machine offers three selections - Tea, Coffee or Random (Either tea or Coffee) but the machine has been wired up wrongly so that each button does not give what it claims.

If each drink costs 50p, how much minimum money do you have to put into the machine to work out which button gives which selection?


Answer::

You have to put just 50p.

Put 50p and push the button for Random. There are only 2 possibilities. It will give either Tea or Coffee.

· If it gives Tea, then the button named Random is for Tea. The button named Coffee is for Random selection. And the button named Tea is for Coffee.
· If it gives Coffee, then the button named Random is for Coffee. The button named Tea is for Random selection. And the button named Coffee is for Tea.
Thus, you can make out which button is for what by putting just 50p and pressing Random selection first.

Hat & Get out

Written on 12:16 am by Vja Students

Three convicts are brought into the warden's office. He says he can parole one of them and to decide which one he will parole he takes out 5 hats (3 red and 2 white). He stands behind them and places a hat on each one of their heads and puts the other two remaining hats in a drawer. He tells the prisoners they can look at the others hats and if they can tell which hat they have on they will be the one who is paroled. The first man looks at the other two and says, "I don't know." The second man looks at the others hats and says, "I don't know." The third man who is blind says, "Even though I have not the gift of sight I can tell by what the others have said that the color of my hat is..." What color is the blind mans hat and how does he know?

Answer:: The color of blind man's hat is Red.

Weight

Written on 11:25 pm by Vja Students

Everyday in his business a merchant had to weigh amounts from 1 kg to 121 kgs, to the nearest kg. What are the minimum number of different weights required and how heavy should they be?


Answer:
The minimum number is 5 and they should weigh 1, 3, 9, 27 and 81 kgs

Age OR False

Written on 12:57 am by Vja Students

Naim and Manikanth have a conversation.
· Naim says I am certainly not over 40
· Manikanth says I am 38 and you are at least 5 years older than me
· Now Naim says you are at least 39
All the statements by the two are false. How old are they really?


Answer::
Naim is 41 and Manikanth is 37.

Stake

Written on 11:30 pm by Vja Students

Chaitu and Sunil are playing cards for a stake of Rs 100 a game. At the end of the evening, Chaitu has won 3 games and Sunil has won Rs 300. How many games did they play?

For solution visit the blog tomorrow..................

Car

Written on 12:17 am by Vja Students

I bought a car with a peculiar 5 digit numbered license plate which on reversing could still be read.On reversing value is increased by 78633.What is the original number if all the digits are different?


Answer
10968




Water

Written on 11:08 pm by Vja Students

A farmer needs 8 gallons of water. He has only three unmared buckets, two 6 gallon and one 11 gallon bucket.

How can he collect 8 gallons of water using three unmarked buckets? Provide solution with minimal water wastage.

Answer

Here is the solution with 10 gallon water wastage.

OPERATIONS

6

6

11

Fill 6 gallon bucket with water

6

0

0

Empty 6 gallon bucket into 11 gallon bucket

0

0

6

Fill 6 gallon bucket with water

6

0

6

Fill 11 gallon bucket to full using filled 6 gallon bucket. This will leave 1 gallon water in 6 gallon bucket

1

0

11

Empty 11 gallon bucket into second 6 gallon bucket.

1

6

5

Empty 11 gallon bucket - wastage of 5 gallon water

1

6

0

Empty second 6 gallon bucket into 11 gallon bucket

1

0

6

Fill seccond 6 gallon bucket with water

1

6

6

Fill 11 gallon bucket to full using filled second 6 gallon bucket. This will leave 1 gallon water in second 6 gallon bucket

1

1

11

Fill first 6 gallon bucket with 1 gallon water which is in second 6 gallon bucket

2

0

11

Empty 11 gallon bucket into second 6 gallon bucket.

2

6

5

Empty 11 gallon bucket - wastage of 5 gallon water

2

6

0

Fill 11 gallon bucket with water in both the 6 gallon buckets

0

0

11

Rook

Written on 11:38 pm by Vja Students

Consider a chessboard with a single Rook.A Rook can move any number of square sideways/forward,but not diagonally.What is the minimum number of moves the Rook needs to make in order to pass over all the squares on the chessboard and return to the original position?


Answer
16 moves

Truth

Written on 10:54 pm by Vja Students

Chaitu lies a lot.He tells the truth on only one day in a week.
One day he said:"I lie on Mondays and Tuesdays."
The next day he said :"Today is either Sunday,Saturday or Thursday."
The next day he said :"I lie on Fridays and Wednesdays."
On which day of the week does Chaitu tell the truth?


Answer:
Tuesday


Groups

Written on 11:20 pm by Vja Students

Major Chaitu is forming five-person Special Task Group. The group must contain one leader, two bomb-experts and two soldiers. P, Q and R are possible bomb-experts. R, S and T are possible leaders. U, V and W are possible soldiers. Also, P and R prefers to work with each other in the same team. T prefers to work only if V works. How many different possible Groups, Major Chaitu can make?

Answer
Major Chaitu can make 8 different possible groups

Rain

Written on 10:54 pm by Vja Students

A group of friends went on a holiday to a hill station. It rained for 13 days. But when it rained in the morning, the afternoon was lovely. And when it rained in the afternoon, the day was preceded by clear morning. Altogether there were 11 very nice mornings and 12 very nice afternoons. How many days did their holiday last?

Answer
The holiday last for 18 days

House

Written on 12:07 am by Vja Students

Chaitu lives in "Friends Society" where all the houses are in a row and are numbered sequentially starting from 1. His house number is 109. Karthik lives in the same society. All the house numbers on the left side of Karthik's house add up exactly the same as all the house numbers on the right side of her house. What is the number of Karthik's house? Find the minimal possible answer.

Answer
There are 288 houses and Karthik's house number is 204

Eggs

Written on 12:02 am by Vja Students

A woman took a certain number of eggs to the market and sold some of them. The next day, through the industry of her hens, the number left over had been doubled, and she sold the same number as the previous day. On the third day the new remainder was tripled, and she sold the same number as before. On the fourth day the remainder was quadrupled, and her sales the same as before. On the fifth day what had been left over were quintupled, yet she sold exactly the same as on all the previous occasions and so disposed of her entire stock. What is the smallest number of eggs she could have taken to market the first day, and how many did she sell daily? Note that the answer is not zero.


Answer She took 103 eggs to market on the first day and sold 60 eggs everyday.

Coins

Written on 12:19 am by Vja Students

A rich man died. In his will, he has divided his gold coins among his 5 sons, 5 daughters and a manager.

According to his will: First give one coin to manager. 1/5th of the remaining to the elder son. Now give one coin to the manager and 1/5th of the remaining to second son and so on..... After giving coins to 5th son, divided the remaining coins among five daughters equally.

All should get full coins. Find the minimum number of coins he has?



Answer

3121 coins.

Truth

Written on 12:00 am by Vja Students

Shahrukh speaks truth only in the morning and lies in the afternoon, whereas Salman speaks truth only in the afternoon and lies in the morning.

A says that B is Shahrukh.

Is it morning or afternoon and who is A - Shahrukh or Salman?



Answer


It is Afternoon and A can be Salman or Shahrukh

Time

Written on 10:50 pm by Vja Students

Sunil has 3 timepieces in his house - a wall clock, an alarm clock and a wristwatch. The wristwatch is always accurate, whereas the wall clock gains 2 minutes everyday and the alarm clock loses 2 minutes everyday.

At exactly midnight last night, all three watches were showing the same time.

If today is 25 July 2007, then on which date all three clocks will show the same time again?



Answer

All three clocks will show the same time again on midnight between 19 July 2008 and 20 July 2008.

A clock finishes on round in 12*60 i.e. 720 minutes.

If a clock gains 2 minutes everyday, then it would be 720 minutes ahead after 360 days. Thus, after 360 days, it will show the same time again.

Similarly, if a clock loses 2 minutes everyday, then it would be 720 minutes behind after 360 days. Thus, after 360 days, it will show the same time again.

Thus, after 360 days all three clocks will show the same time again i.e. midnight between 19 July 2008 and 20 July 2008.

Balls

Written on 10:23 pm by Vja Students

There are six boxes containing 5, 7, 14, 16, 18, 29 balls of either red or blue in color. Some boxes contain only red balls and others contain only blue.

One sales man sold one box out of them and then he says, "I have the same number of red balls left out as that of blue."

Which box is the one he solds out?


Answer

29


Cube

Written on 11:23 pm by Vja Students

A cube is made of a white material, but the exterior is painted black.

If the cube is cut into 125 smaller cubes of exactly the same size, how many of the cubes will have at least 2 of their sides painted black?


Answer

44

Counterfeit

Written on 11:22 pm by Vja Students

A man went into a fast food restaurant and ate a meal costing Rs. 105, giving the accountant a Rs. 500 note. He kept the change, came back a few minutes later and had some food packed for his girl friend. He gave the accountant a Rs. 100 note and received Rs. 20 in change. Later the bank told the accountant that both the Rs. 500 and the Rs. 100 notes were counterfeit.

How much money did the restaurant lose? Ignore the profit of the food restaurant.



Answer

He lost Rs.600

Apples

Written on 12:01 am by Vja Students

Sunil and Dileep divided a bag of Apples between them.

Dileep said, "It's not fair! You have 3 times as many Apples I have." Sunil said, "OK, I will give you one Apple for each year of your age." Dileep replied, "Still not fair. Now, you have twice as many Apples as I have." "Dear, that's fair enough as I am twice older than you.", said Sunil.

Sunil went to Kitchen to drink water. While Sunil was in Kitchen, Dileep took apples from Sunil's pile equal to Sunil's age.

Who have more apples now?


Answer

At the end, Sunil and Dileep, both have the same number of apples.

Number

Written on 11:27 pm by Vja Students

There are 10 statements written on a piece of paper:

1. At least one of statements 9 and 10 is true.

2. This either is the first true or the first false statement.

3. There are three consecutive statements, which are false.

4. The difference between the numbers of the last true and the first true statement divides the number, that is to be found.

5. The sum of the numbers of the true statements is the number, that is to be found.

6. This is not the last true statement.

7. The number of each true statement divides the number, that is to be found.

8. The number that is to be found is the percentage of true statements.

9. The number of divisors of the number, that is to be found, (apart from 1 and itself) is greater than the sum of the numbers of the true statements.

10. There are no three consecutive true statements.

Find the minimal possible number?

Answer

The number is 420.

If statement 6 is false, it creates a paradox. Hence, Statement 6 must be true.

Consider Statement 2:

  • If it is true, it must be the first true statement. Otherwise, it creates a paradox.
  • If it is false, it must be the second false statement. Otherwise, it creates a paradox.

In both the cases, Statement 1 is false.

As Statement 1 is false, Statement 9 and Statement 10 both are false i.e. there are three consecutive true statements.

1

2

3

4

5

6

7

8

9

10

False

-

-

-

-

True

-

-

False

False


Let\'s assume that Statement 3 is false i.e. there are no three consecutive false statements. It means that Statement 2 and Statement 8 must be true, else there will be three consecutive false statements.

1

2

3

4

5

6

7

8

9

10

False

True

False

-

-

True

-

True

False

False


Also, at least two of Statements 4, 5 and 7 must be true as there are three consecutive true statements.

According to Statement 8, the number that is to be found is the percentage of true statements. Hence, number is either 50 or 60. Now if Statement 7 is true, then the number of each true statement divides the number, that is to be found. But 7 and 8 do not divide either 50 or 60. Hence, Statement 7 is false which means that Statement 4 and 5 are true. But Statement 5 contradicts the Statement 8. Hence, our assumption that Statement 3 is false is wrong and Statement 3 is true i.e. there are 3 consecutive false statements which means that Statement 8 is false as there is no other possibilities of 3 consecutive false statements.

Also, Statement 7 is true as Statement 6 is not the last true statement.

1

2

3

4

5

6

7

8

9

10

False

-

True

-

-

True

True

False

False

False


According to Statement 7, the number of each true statement divides the number, that is to be found. And according to Statement 5, the sum of the numbers of the true statements is the number, that is to be found. For all possible combinations Statement 5 is false.

There 3 consecutive true statements. Hence, Statement 2 and Statement 4 are true.

1

2

3

4

5

6

7

8

9

10

False

True

True

True

False

True

True

False

False

False


Now, the conditions for the number to be found are:

1. The number is divisible by 5 (Statement 4)

2. The number is divisible by 2, 3, 4, 6, 7 (Statement 7)

3. The number of divisors of the number, that is to be found, (apart from 1 and itself) is not greater than the sum of the numbers of the true statements. (Statement 9)

The minimum possible number is 420.

The divisors of 420, apart from 1 and itself are 2, 3, 4, 5, 6, 7, 10, 12, 14, 15, 20, 21, 28, 30, 35, 42, 60, 70, 84, 105, 140, 210. There are total of 22 divisors. Also, the sum of the numbers of the true statements is 22 (2+3+4+6+7=22), which satisfies the third condition.

Boxes

Written on 3:07 am by Vja Students

There are 3 colored boxes - Red, Green and Blue. Each box contains 2 envelopes. Each envelope contains money - two of them contain Rs. 25000 each, two of them contain Rs. 15000 each and remaining two contain Rs. 10000 each.

There is one statement written on the cover of each box.

* Red Box: Both, a red box and a blue box contain Rs. 10000 each.

* Green Box: Both, a green box and a red box contain Rs. 25000 each.

* Blue Box: Both, a blue box and a green box contain Rs. 15000 each.

Only one of the above 3 statements is true and the corresponding box contains the maximum amount.

Can you tell which box contains the maximum amount and how much?

Answer

Blue box contains the maximum amount Rs. 40000

Ages

Written on 12:07 am by Vja Students

There were two men standing on a street. The one says to the other, "I have 3 daughters, the product of their ages is 36. What are the ages of my daughter?"

The second guy says, "I need more information." So, the first guy says, "The sum of their ages is equal to the address of the house across the street."

The second guy looks at the address and says, "I still need more information." So, the first guy says, "My oldest daughter wears a red dress."

What are the ages of his daughter

Answer

The ages are 9,2,2 years.

First you need to find all the possible sets of three numbers that when multiplied equals 36:

1 1 36
1 2 18
1 3 12
1 4 9
1 6 6
2 2 9
2 3 6
3 3 4

Then you add the numbers together to find the sum
1 1 36 = 38
1 2 18 = 21
1 3 12 = 16
1 4 9 = 14
1 6 6 = 13
2 2 9 = 13
2 3 6 = 11
3 3 4 = 10

Even though we don't know the address the guy knows it. For him to need more information that means that at least two of the sets of numbers has

the same sum. Two of them do, 1 6 6 and 2 2 9.

When the first guy said that his OLDEST daughter wears a red dress that meant that there had to be the oldest. So 1 6 6 can't possibly be the answer. So the answer is 2 2 9

Load

Written on 12:14 am by Vja Students

A mule and a donkey were carrying full sacks on their backs.

The mule started complaining that his load was too heavy. The donkey said to him "Why are you complaining? If you gave me one of your sacks I'd have double what you have and if I give you one of my sacks we'd have an even amount."

How many sacks were each of them carrying? Give the minimal possible answer.


Answer
The mule was carrying 5 sacks and the donkey was carrying 7 sacks.

Fraction

Written on 2:43 am by Vja Students

In a certain year, the number of girls who graduated from KL College OF Engineering was twice the number of boys. If 3/4 of the girls and 5/6 of the boys went to college immediately after graduation, what fraction of the graduates that year went to college immediately after graduation?


Answer

7/9

Game

Written on 1:03 am by Vja Students

In a certain game, if 2 wixsomes are worth 3 changs, and 4 changs are worth 1 plut, then 6 plutes are worth how many wixsomes?


Answer

6 plutes = 16 wixsomes

Express

Written on 11:26 pm by Vja Students

Addanki Express runs between Addanki and Vijayawada, For the up as well as the down journey, the train leaves the starting station at 10:00 PM everyday and reaches the destination at 11:30 PM after three days.

Mr. Sunil once travelled by Addanki Express from Vijayawada to Addanki. How many Addanki Express did he cross during his journey?


Answer


Mr. Sunil crossed 7 Addanki Expresses during his journey

Clinic

Written on 7:31 am by Vja Students

Dr. Rajesh always goes walking to the clinic and takes the same time while going and while coming back. One day he noticed something.

When he left the home, the hour hand and the minute hand were exactly opposite to each other and when he reached the clinic, they were together.

Similarly, when he left the clinic, the hour hand and the minute hand were together and when he reached the home, they were exactly opposite to each other.

How much time does Dr. Rajesh take to reach home from the clinic? Give the minimal possible answer.



Answer


32 minutes 43.6 seconds

Suits

Written on 5:10 am by Vja Students

Mr. Black, Mr. White and Mr. Grey were chatting in the Yahoo conference. They were wearing a black suit, a white suit and a grey suit, not necessarily in the same order.

Mr. Grey sent message, "We all are wearing suit that are of the same color as our names but none of us is wearing a suit that is the same color as his name."

On that a person wearing the white suit replied, "What difference does that make?"

Can you tell what color suit each of the three persons had on?

Answer

Mr. Grey is wearing Black suit.
Mr. White is wearing Grey suit.
Mr. Black is wearing White suit.

Eggs

Written on 1:59 pm by Vja Students

Rajesh says to Jay, "Can you figure out how many Eggs I have in my bucket?" He gives 3 clues to Jay: If the number of Eggs I have

1. If it is a multiple of 5, it is a number between 1 and 19
2. If it is not a multiple of 8, it is a number between 20 and 29
3. If it is not a multiple of 10, it is a number between 30 and 39

How many Eggs does Rajesh have in his bucket?

Answer

32 eggs

Let's apply all 3 condition separately and put all possible numbers together.

First condition says that if multiple of 5, then the number is between 1 and 19. Hence, the possible numbers are (5, 10, 15, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39)

Second condition says that if not a multiple of 8, then the number is between 20 and 29. Hence, the possible numbers are (8, 16, 20, 21, 22, 23, 25, 26, 27, 28, 29, 32)

Third condition says that if not a multiple of 10, then the number is between 30 and 39. Hence, the possible numbers are (10, 20, 31, 32, 33, 34, 35, 36, 37, 38, 39)

Only number 32 is there in all 3 result sets. That means that only number 32 satisfies all three conditions. Hence, Rajesh have 32 eggs in his bucket.

Lamp

Written on 10:12 pm by Vja Students

Mrs. Sindhuhad a garage sale. A custmer named Lata bought an old lamp and a rug. She paid a total of Rs 5.25 for everything. The rug cost 25 paise more than the lamp. How much did each cost?

Ans:
The lamp cost Rs 2.50 and the rug cost Rs 2.75

Stations & Tickets

Written on 11:25 pm by Vja Students

There were N stations on a railroad. After adding X stations 46 additional tickets have to be printed. Find N and X.

Answer
Case I: (46,1)
Case II: (23,2)
there are 2 possible answers.
.

Get Whole number

Written on 11:59 pm by Vja Students

Given any whole number take the sum of the digits, and the product of the digits, and multiply these together to get a new whole number. For example, starting with 6712, the sum of the digits is (6+7+1+2) = 16, and the product of the digits is (6*7*1*2) = 84. The answer in this case is then 84 x 16 = 1344. If we do this again starting from 1344, we get (1+3+4+4) * (1*3*4*4) = 576 And yet again (5+7+6) * (5*7*6) = 3780
At this stage we know what the next answer will be (without working it out) because, as one digit is 0, the product of the digits will be 0, and hence the answer will also be 0. Can you find any numbers to which when we apply the above mentioned rule repeatedly, we never end up at 0?

Ans:There are no such numbers

Exchange

Written on 11:38 pm by Vja Students

You have 14 apples. Your Friend Marge takes away 3 and gives you 2. You drop 7 but pick up 4. Bret takes 4 and gives 5. You take one from Marge and give it to Bret in exchange for 3 more. You give those 3 to Marge and she gives you an apple and an orange. Frank comes and takes the apple Marge gave you and gives you a pear. You give the pear to Bret in exchange for an apple. Frank then takes an apple from Marge, gives it to Bret for an orange, gives you the orange for an apple. How many pears do you have?

Answer::
None
Frank gave you a pear in exchange of the apple which Marge gave you. And you gave that pear to Bret in exchange for an apple. All the others exchanges involved apples and/or oranges.

Sprite

Written on 9:31 pm by Vja Students

A man is stranded on a desert island. All he has to drink is a 20 litre bottle of sprite.

To conserve his drink he decides that on the first day he will drink one litre the refill the bottle back up with water. On the 2nd day he will drink 2 litre and refill the bottle. On the 3rd day he will drink 3 litre and so on...

By the time all the sprite is gone, how much water has he drunk?


Answer::The man drunk 190litre of water.

Base..

Written on 11:17 pm by Vja Students

A class of 100 students. 24 of them are girls and 32 are not. Which base am I using

Answer

Let the base be X.

Therefore
(X*X + X*0 + 0) = (2*X +4) + (3*X + 2)
X*X = 5*X + 6
X*X - 5*X -6 = 0
(X-6)(X+1) = 0

Therefore base is 6

Population of Rabbits.

Written on 11:21 pm by Vja Students

Scientist decided to do a study on the population growth of rabbits. Inside a controlled environment, 1000 rabbits were placed.

Six months later, there were 1000Z rabbits. At the beginning of the 3rd year, there were roughly 2828Z rabbits, which was 4 times what the scientists placed in there at the beginning of the 1st year.

If Z is a positive variable, how many rabbits would be there at the beginning of the 11th year?

Answer::At the beginning of the 11th year, there would be 1,024,000 rabbits.

Stamps

Written on 11:31 pm by Vja Students

My friend collects antique stamps. She purchased two, but found that she needed to raise money urgently. So she sold them for Rs. 8000 each. On one she made 20% and on the other she lost 20%.

How much did she gain or lose in the entire transaction?

Answer:: She lost Rs 666.67

Constants Alphabets

Written on 11:31 pm by Vja Students

Imagine that you have 26 constants, labeled A through Z. Each constant is assigned a value in the following way: A = 1; the rest of the values equal their position in the alphabet (B corresponds to the second position so it equals 2, C = 3, etc.) raised to the power of the preceding constant value. So, B = 2 ^ (A's value), or B = 2^1 = 2. C = 3^2 = 9. D = 4^9, etc.

Find the exact numerical value to the following equation: (X - A) * (X - B) * (X - C) * ... * (X - Y) * (X - Z).

Answer ::
(X - A) * (X - B) * (X - C) * ... * (X - Y) * (X - Z) equals 0 since (X - X) is zero

Remainder

Written on 12:02 am by Vja Students

What is the remainder left after dividing 1!+2!+3!+.....+100! by 7 ?

Answer::

7! onwards all terms are divisible by 7 as 7 is one of the factor. So there is no remainder left for those terms i.e. remainder left after dividing 7! + 8! + 9! + ... + 100! is 0.

1!+2!+3!+...+100!=

1+2+6+24+120+720+0=873

Calculate the water

Written on 12:14 am by Vja Students

A man at river has 9 gallon bucket and a 4 gallon bucket.He needs exactly 6 gallons of water.
how can he use both the buckets to get exactly 6 gallons of water?
Note:: He cannot estimate my dumping some of the water from 9 gallons bucket or of 4 gallons bucket.

Answer ::Steps to perform




















































steps4 gallons(P)9 gallons(Q)
initialiy00
fill the 9 gallon bucket09
pour 4 gallons from Q to P45
Empty bucket P05
pour 4 gallons from Q to P41
empty bucket p01
pour 1 gallon from Q yo P10
fill the bucket 9 gallon bucket19
pour 3 gallons of water from Q to P46

Ages

Written on 10:06 pm by Vja Students

Difference between Valenka's and Angil's age is 2 years and the difference between Anil's and Raman's age is 5 years.
What is the maximum possible value of the sum of the difference in their ages, taken two at a time?

Answer::The maximum possible values of the sum of the difference in their ages -taken two at a time is 14 yrs

Hotel Rooms

Written on 12:18 am by Vja Students

In a hotel, rooms are numbered from 101 to 550. A room is chosen at random. What is the probability that room number starts with 1, 2 or 3 and ends with 4, 5 or 6?

Solution:
0.20

Socks

Written on 11:15 pm by Vja Students

In your sock drawer, you have a ratio of 5 pairs of blue socks, 4 pairs of brown socks, and 6 pairs of black socks. In complete darkness, how many socks would you need to pull out to get a matching pair of the same color?

Answere::4

People and Hair

Written on 11:23 pm by Vja Students

In a town called Alibaug, following facts are true

1. No two inhabitants have exactly the same number of hair.
2. No two inhabitants have 2025 hairs.
3. There are more inhabitants than there are hairs on head of any one inhabitant.

What is the largest possible number of inhabitants of town Alibaug?

Answere :: 2025

Sleeping & Distance

Written on 12:09 am by Vja Students

Mr. Wagle goes to work by a bus. One day he falls asleep when the bus still has twice as far to go as it has already gone. Halfway through the trip he wakes up as the bus bounces over some bad potholes. When he finally falls asleep again, the bus still has half the distance to go that it has already travelled. Fortunately, Mr. Wagle wakes up at the end of his trip. What portion of the total trip did Mr. Wagle sleep?

Answere:: Mr.Wagle slept through half his journey.

Playing caroms

Written on 7:21 am by Vja Students

A blindfolded man is asked to sit in the front of a carom board. The holes of the board are shut with lids in random order, i.e. any number of all the four holes can be shut or open.

Now the man is supposed to touch any two holes at a time and can do the following.
Open the closed hole.
Close the open hole.
Let the hole be as it is.

After he has done it, the carom board is rotated and again brought to some position. The man is again not aware of what are the holes which are open or closed.
How many minimum number of turns does the blindfolded man require to either open all the holes or close all the holes?
Note that whenever all the holes are either open or close, there will be an alarm so that the blindfolded man will know that he has won.

Answere::

The blindfolded man requires 5 turns.
1. Open two adjacent holes.


2. Open two diagonal holes. Now atleast 3 holes are open. If 4th hole is also open, then you are done. If not, the 4th hole is close.


3. Check two diagonal holes.
If one is close, open it and all the holes are open.
If both are close, open any one hole. Now, two holes are open and two are close. The diagonal holes are in the opposite status i.e. in both the diagonals, one hole is open and one is close.

4. Check any two adjacent holes.
If both are open, close both of them. Now, all holes are close.
If both are close, open both of them. Now, all holes are open.
If one is open and one is close, invert them i.e. close the open hole and open the close hole. Now, the diagonal holes are in the same status i.e. two holes in one diagonal are open and in other are close.

5. Check any two diagonal holes.
If both are open, close both of them. Now, all holes are close.
If both are close, open both of them. Now, all holes are open.

Never leave me

Written on 11:33 pm by Vja Students

Substitute digits for the letters to make the following addition true.






N E V E R

L E A V E

* * * M E

------------------

A L O N E



Answere::

2 1 4 1 9

3 1 5 4 1


* * * 6 1
--------------
5 3 0 2 1

Get the number

Written on 11:25 pm by Vja Students

What is the four-digit number in which the first digit is 1/3 of the second, the third is the sum of the first and second, and the last is three times the second?

Answere::The 4 digit number is 1349.

Twins

Written on 9:25 pm by Vja Students

There are 20 people in your applicant pool, including 5 pairs of identical twins. If you hire 5 people randomly, what are the chances you will hire at least 1 pair of identical twins?


Answere::The probability to hire 5 people with at least 1 pair of identical twins is 25.28%

Ants

Written on 12:32 am by Vja Students

There are 3 ants at 3 corners of a triangle, they randomly start moving towards another corner.

What is the probability that they don't collide?

Answer

1/4

Let's mark the corners of the triangle as A,B,C. There are total 8 ways in which ants can move.

1. A->B, B->C, C->A

2. A->B, B->C, C->B

3. A->B, B->A, C->A

4. A->B, B->A, C->B

5. A->C, C->B, B->A

6. A->C, C->B, B->C

7. A->C, C->A, B->A

8. A->C, C->A, B->C


Out of which, there are only two cases under which the ants won't collide :

  • A->B, B->C, C->A
  • A->C, C->B, B->A

Cards

Written on 11:21 pm by Vja Students

Two identical pack of cards A and B are shuffled thoroughly. One card is picked from A and shuffled with B. The top card from pack A is turned up. If this is the Queen of Hearts, what are the chances that the top card in B will be the King of Hearts?

Answer

52 / 2703

Smallest Number

Written on 11:51 pm by Vja Students

Find the smallest number such that if its rightmost digit is placed at its left end, the new number so formed is precisely 50% larger than the original number.


The answer is 285714

Number

Written on 11:44 pm by Vja Students

Consider a number as 235, where last digit is sum of first two digits i.e. 2+3=5.
How many such 3 digit numbers are there?


Ans: There are 45 such numbers

Chess board

Written on 11:48 pm by Vja Students

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


Answere::= (16!) / (8! * 2! * 2! * 2!) =6,48,64,800 ways

Men & Sheeps

Written on 12:11 am by Vja Students

Four friends - Arjan, Bhuvan, Guran and Lakha were comparing the number of sheep that they owned.

It was found that Guran had ten more sheep than Lakha.

If Arjan gave one-third to Bhuvan, and Bhuvan gave a quarter of what he then held to Guran, who then passed on a fifth of his holding to Lakha, they would all have an equal number of sheep.

How many sheep did each of them possess? Give the minimal possible answer.


Solution:
Arjan, Bhuvan, Guran and Lakha had 90, 50, 55 and 45 sheep respectively

Clock with Hands....

Written on 11:22 pm by Vja Students

At what time after 4.00 p.m. is the minutes hand of a clock exactly aligned with the hour hand?

Answere:: 4:21:49.5

Party

Written on 7:42 am by Vja Students

At the Party:

1. There were 9 men and children.

2. There were 2 more women than children.

3. 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:

4. There were 4 of one group.

5. There were 6 of one group.

6. 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





Answere::Statement (4) is false. There are 3 men, 8 women and 6 children.

Money Gets Double . . .

Written on 11:33 pm by Vja Students

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).


Ans: X = 26 & Y = 53

Telling a ' Lie '.....

Written on 11:50 pm by Vja Students

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?


Answere :: The soldier said, "You will put me to the sword."

Cubes,Corners,Edges

Written on 11:56 pm by Vja Students

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?


Answere::9

Houses

Written on 7:26 am by Vja Students

There is a shortage of tube lights, bulbs and fans in a village - Addanki. It is found that

All houses do not have either tube light or bulb or fan.

exactly 19% of houses do not have just one of these.

at least 67% of houses do not have tube lights.

at least 83% of houses do not have bulbs.

at least 73% of houses do not have fans.

What percentage of houses do not have tube light, bulb and fan?


Answere:: 42% houses do not have tubelight, bulb and fan..




Safe

Written on 7:09 pm by Vja Students

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

Ticks

Written on 11:12 pm by Vja Students

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.


Answer

66 seconds

Who Married Whom

Written on 11:27 pm by Vja Students

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.


Answere::Carrie is wife of Cam

Cows & Grass

Written on 11:11 pm by Vja Students

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?

Answere::20

9 Digit Number

Written on 11:45 pm by Vja Students

A number of 9 digits have the following properties:

1. 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.
2. Each digit in the number is different i.e. no digits are repeated.
3.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?

The answer is 381654729.

Medals

Written on 12:26 am by Vja Students

In a sports contest there were m medals awarded on n successive days (n > 1).

1. On the first day 1 medal and 1/7 of the remaining m-1 medals were awarded.
2. On the second day 2 medals and 1/7 of the now remaining medals was awarded; and so on.
3. 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?


Answere::Yes,answere is right 6 days & 36 medals

Candles

Written on 12:01 am by Vja Students

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?

Answer

Vipul studied for 3 hours in candle light

Zeroes

Written on 12:39 am by Vja Students

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?

Answere ::192

Bullets

Written on 12:24 am by Vja Students

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.

Answer

18

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