Infosys Questions

1. Lucia is a wonderful grandmother.Her age is between 50 and 70.Each of her sons have as many sons as they have brothers.Their combined number gives Lucia’s age.What is the age?

2. There are two towers A and B.Their heights are 200ft and 150ft respectively and the foot of the towers are 250ft apart.Two birds on top of each tower fly down with the same speed and meet at the same instant on the ground to pick a grain.What is the distance between the foot of tower ** the grain?

3. Grass in lawn grows equally thick and in a uniform rate.It takes 40 days for 40 cows and 60 days for 30 cows to eat the whole of the grass.How many days does it take for 20 cows to do the same?

4. Four tourists A,B,C,D and four languages English,German,French and Italian.They are not able to converse among themselves in one language.Though A does not know English he can act as an interpreter between B and C.No one spoke both French and German.A knows German and was able to converse with D who doesn’t know a word in German.Only one language was spoken by more than two persons.Each spoke two languages.Find who spoke what.

5. There is a five digit number.It has two prime digits(1 is not a prime number).Third digit is the highest.Second digit is the lowest.First digit is one less than the third digit.The fifth digit is half of the fourth.The sum of 4th and 5th is less than the first.Find the number.

6. Four persons A, B, C and D are playing cards.Each person has one card, laid down on the table below him,which has two different colours on either side.No card has the same color on both sides.The colours visible on the table are Red, Green, Red and Blue respectively.They see the color on the reverse side and give the following comment.

A: Yellow or Green
B: Neither Blue nor Green
C: Blue or Yellow
D: Blue or Yellow

Given that out of the 4 people 2 always lie find out the colours on the
cards each person.

7. A software engineer returns from America. As he is fat he decided to have evening walk…..he started at 3pm. he walks along the road at 4km/hr for some time then he climbs a upward slope area at 3km/hr then downwards at the rate of 6km/hr. then back to the home through the road at 4km/hr. what is the distance he covered in one way if he reaches back home at 9pm

8. A 1 k.m. long wire is held by n poles. If one pole is removed,the length of the gap becomes 12/3m. What is the number of poles initially?
9. Find the digits X,Y,Z
X X X X
Y Y Y Y +
Z Z Z Z
————–
Y X X X Z
—————-

10. In a race Andrew beats Jim.Jack is not the last.Dennis loses to both Jack and Lucia.Jim beats Jack.Who won the race?

Answers

1. Let the no. of Lucia’s sons = n
No. of brothers for each son = n-1
No. of sons for each of Lucia’s son = n-1

Lucia’s age = n-1 * n-1
= a perfect square between 50 and 70
= 64

2.
200
150 Since the two birds travel with the same
speed and meet at the same instant the
distance traveled by them is equal.
By Pythagoras theorem,

200*200 + x*x = (250-x)*(250-x)+150 * 150
x = 90ft

3. 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

g + 40*r = 40 * 40 * y——- 1
g + 60*r = 30 * 60 * y——- 2
g + n*r = 20 * n * y——– 3

from 1 and 2
r=10y g=120r
from 3
nr=120r

Solving, n = 120

4. Think logically.
Ans -

A B C D
German
Italian French
Italian German
English Italian
English

5. Ans - 71842
Hint - Start with the last condition.

6. Try all possible combinations.Keep in mind two things.THE combination obtained should satify the conditions
1.Two are lying and two are telling the truth
2.Neither two cards are similar nor are two sides of a card are of same color

Ans
A Yellow
B Yellow
C Green
D Red

7. Let the dist traveled on level ground = x and on the hill be y.
x/4 + y/3 + y/6 + x/4 = 6
(x+y)/2 = 6km

8. Let the no. of poles originally = n
After taking away one pole
(n-1)*12/3 = 1000
n = 251

9. x+y+z = z ==> x+y = 10
max value for y = 1
hence x = 1
also, (carry)1+x+y+z = x ==> 1+y+z = 10
hence z=8
X Y Z
9 1 8

10. The possible positions in the race are,

Andrew Andrew
Jim Jim
Jack Lucia
Lucia Jack
Dennis Dennis

In either case Andrew is the winner.

Adam and Bob have exact speeds for walking and running - neither Adam outwalks Bob, nor Bob outruns Adam.

But for a given distance, Adam runs half the time, then walks another half. Bob runs half the distance, then walks another half.

If they were to compete, which distance would Adam win at, and which distances would Bob be the winner at?

Solution:

For Adam,
Ta/2*Vr+Ta/2*Vw=d
For Bob,
Tb = d/(2*Vr) +d/(2*Vw)
Distance difference:
(Ta-Tb)*Vw=2*d*Vw/(Vr+Vw)-(d*Vw/2)*(1/Vr+1/Vw)
=2*d*Vw/(Vr+Vw)-(d*Vw/2)*(Vr+Vw)/(Vv*Vw)
=-d*(Vr-Vw)^2/(2*Vr*(Vr+Vw))

So actually Bob will win.

how many trailing zeroes are there in 100! (100 factorial)?

solution: 100!

One per factor of 10, and one per factor of 5 (there are more than enough 2’s to pair with the 5’s), plus one per factor of ten squared (one occurrence) and one per factor of 5 squared (three occurrences).

 bad king has a cellar of 1000 bottles of delightful and very expensive wine. a neighbouring queen plots to kill the bad king and sends a servant to poison the wine. (un)fortunately the bad king’s guards catch the servant after he has only poisoned one bottle. alas, the guards don’t know which bottle but know that the poison is so strong that even if diluted 1,000,000 times it would still kill the king. furthermore, it takes one month to have an effect. the bad king decides he will get some of the prisoners in his vast dungeons to drink the wine. being a clever bad king he knows he needs to murder no more than 10 prisoners - believing he can fob off such a low death rate - and will still be able to drink the rest of the wine at his anniversary party in 5 weeks time.explain how….

solution: bad king

problem: a bad king has a cellar of 1000 bottles of delightful and very expensive wine. a neighbouring queen plots to kill the bad king and sends a servant to poison the wine. (un)fortunately the bad king’s guards catch the servant after he has only poisoned one bottle. alas, the guards don’t know which bottle but know that the poison is so strong that even if diluted 1,000,000 times it would still kill the king. furthermore, it takes one month to have an effect. the bad king decides he will get some of the prisoners in his vast dungeons to drink the wine. being a clever bad king he knows he needs to murder no more than 10 prisoners - believing he can fob off such a low death rate - and will still be able to drink the rest of the wine at his anniversary party in 5 weeks time.

explain how…

solution: i’ll give you a hint. 1000 is less than 1024. if there were
1024 or more bottles of wine it would take more than 10 prisoners.

number the bottles 1 to 1000, and write the number in binary format.

bottle 1    = 0000000001 bottle 250
= 0011111010 bottle 1000 = 1111101000

now take your prisoner’s 1 through 10 and let prisoner 1 take a sip from every bottle that has a 1 in its least significant bit. let prisoner 10 take a sip from every bottle with a 1 in its most significant bit. etc.

prisoner    10 9 8 7 6 5 4 3 2 1 bottle 924
  1 1 1 0 0 1 1 1 0 0

for instance, bottle #924 would be sipped by 10,9,8,5,4
and 3. that way if bottle #924 was the poisoned one, only those prisoners would die.

after four weeks, line the prisoners up in their bit order and read each living prisoner as a 0 bit and each dead prisoner as a 1 bit. the number that you get is the bottle of wine that was poisoned.

additional question: to increase your chance of living, which prisoner would you want to be?

if there were 1023 bottles, it wouldn’t matter since everyone would have to take 512 sips. but there are 23 bottles less, so the people whose bits would have been on from 1001 to 1023 won’t have to take a sip. 1001 is [11111 01001] in binary and
1023 is [11111 11111]. the most five significant bits are the most interesting because they would always be on from 1001 to 1023, so all those people are missing out on 23 bottles of wine that they otherwise would have had to drink. so in order to increase your chance of living, you’d probably want to be prisoner 6 to 10. (but depending on how the king determines who is least significant and who is most significant you could get shafted.)

note that if the king was really trying to kill the least number of prisoners, he should have let 999 prisoners each take a sip from their respective bottle numerically (if he had that many prisoners at his disposal). that way only one prisoner would die, and there’s a chance of 1/1000 that no one would die, but then the puzzle isn’t very fun.