1.With how few assistants can an intrepid explorer make a 6 day crossing on foot of an absolutelybarren desert, if he and the available assistants can each carry only enough food and water to last one man four days? Look for the simplest humane soln...
Ans: 2 assistants
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Let the explorer be 'A' and the assistants be 'x' & 'y'1. After the first day, all are left with food for 3 days. Both 'A' and 'x' will take food for one day each from 'y' and 'y' goes back. Now 'A' and 'x' are again left with food for 4 days. ('y' has food for one day which is the time required for him to reach the end from where they started)
2. After the second day, 'A' and 'x' have food for 3 days each. 'A' takes food for one day from 'x' and sends him back. ('x' goes back with food for 2 days)
3. Now 'A' has food for 4 days... and he requires only 4 days to cross the desert!!!!
101,10101,1010101,101010101,10101010101,.........
the series goes on like this.
here only 101 is prime,all others are not.how u prove it.Solution :
Though Solution is too long, it works.101 = 100+1
10101 = (100+1)*100+1 etc...
=> ((x+1)*x+1)*x+1 ....
= x^n + x^(n-1) + x^(n-2) .....
= (x^(n+1) -1) / x-1
=> (100^(n+1)-1) / 99
=> 9999/99(n=1) & 999999/99(n=2) & 99999999/99
=> 1111/11 , 111111/11 , 11111111/11.....
101*11 = 1111
1001*111 = 11111
10001*1111 = 11111111
& when odd number of 1's 100...1 is divisible by 11
& when even number of 1's occur 100...1 is indivisible by 11 but 111... is.
so one of them is divisible by 11 taking care of the dinominator in 1111/11 , 111111/11 , 11111111/11.....
Thus there remains, two terms in the numerator, making it non prime.....
The above four lines does'nt apply to 101*11 as 11/11 is 1 & there is only one term in the numerator for the first case.2.There are 5 houses.
Each house has its own unique color.
All house owners are of different nationalities.
They all have different pets.
They all drink different drinks.
They all smoke different cigarettes.
The english men lives in the red house.
The swede has a dog.
The dane drinks tea.
The green house is on the left side of the white house.
In the green house they drink coffee.
The man who smokes Pall Mall has birds.
In the yellow house they smoke Dunhill.
In then middle house they drink milk.
The norwagein lives in the first house.
The man who smokes Blend , lives in the house next to the house with cats.
In the house next to the house where they have horse, they smoke Dunhill.
The man who smokes Blue Master drinks Beer.
The german smokes Prince.
The norwegian lives next to the blue house.
They drink water in the house that lays next to the house where they smoke Blend.WHO OWNS THE ZEBRA ????
3.
1)A,B,C,D,E related.4 of them made these statements each.
i)C is my son in law's brother.
ii)B is my father's brother.
iii)E is my mother in law.
iv)A is my brother's wife.
who made these statements?(person mentioned is one of A,B,C,D,E)4.
2)e meAns belong.
All members of E e D.
All members of D e A.
Not all members of D e E.
Not all members of A e D.
All members of C e both A and B.some questions are asked about relatio
n.use venn diagram..5. A says Party was held on :Thursday ,May 8th.
B says Party was held on :Tuesday,May 10th.
C says party was held on :Friday ,June 8th.
Given April 1 st was Tuesday.one of A,B,C says 1 correct.one says 1
wrong.and one was completely wrong of date,Month and day. Find the
Day the party held.6. A ship is away from the shore by 180 miles.A plane is travelling at
10 times speed of the ship.How long from the shore will they meet?7. Every station in N railroad issue everyother station's ticket.
some stations are added.Now they have to issue 46 more tickets.
say the No.of stations after and before added.8. 3 persons say these statements.
A says either Democratic or liberal wins the elections.
B says Democratic wins.C says neither democratic nor liberal wins
the election.of these only one is wrong.who wins the election?9. A clock showing 6 o'clock takes 30 secs to strike 6 times.How long
will it take to strike 12 at midnight?Ans.66 secs.10. Only boys aged 16 wear coats.
Boys aged 15 go to watch football.some more statements are given.
What can be said about those who are watching football ? (age and costume)11. There are 3 societies A,B,C having some tractors each.
A Gives B and C as many tractors as they already have.
After some days B gives A and C as many tractors as they have.
After some days C gives A and B as many tractors as they have.
Finally each has 24 tractors.what is the original No.of
tractors each had in the beginning?
Ans.A -39.
B- 21.
C- 12.
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