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INFOSYS PLACEMENT PAPERS 4
Posted Date: 26 Jun 2008 Resource Type: Articles/Knowledge Sharing Category: Placement Papers
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Posted By: sunil Member Level: Diamond
Rating:  Points: 1
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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
Answer
Assume that contents of the container is X
On the first day 1/3rd is evaporated.
(1 - 1/3) of X is remaining i.e. (2/3)X
On the Second day 3/4th is evaporated. Hence,
(1- 3/4) of (2/3)X is remaining
i.e. (1/4)(2/3)X = (1/6) X
Hence 1/6th of the contents of the container is remaining
*****
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
Answer
Vipul studied for 3 hours in candle light.
Assume that the initial lenght of both the candle was L and Vipul studied for X hours.
In X hours, total thick candle burnt = XL/6
In X hours, total thin candle burnt = XL/4
After X hours, total thick candle remaining = L - XL/6
After X hours, total thin candle remaining = L - XL/4
Also, it is given that the thick candle was twice as long as the thin one when he finally went to sleep.
(L - XL/6) = 2(L - XL/4)
(6 - X)/6 = (4 - X)/2
(6 - X) = 3*(4 - X)
6 - X = 12 - 3X
2X = 6
X = 3
Hence, Vipul studied for 3 hours i.e. 180 minutes in candle light.
*****
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)
Answer
Rs.333,062,500
To begin with, you want to know the total number of days: 365 x 50 = 18250.
By experimentation, the following formula can be discovered, & used to determine the amount earned for any particular day: 1 + 2(x-1), with x being the number of the day. Take half of the 18250 days, & pair them up with the other half in the following way: day 1 with day 18250, day 2 with day 18249, & so on, & you will see that if you add these pairs together, they always equal Rs.36500.
Multiply this number by the total number of pairs (9125), & you have the amount you would have earned in 50 years.
*****
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?
-
Answer
Rs.22176
Assume his salary was Rs. X
He earns 5% raise. So his salary is (105*X)/100
A year later he receives 2.5% cut. So his salary is ((105*X)/100)*(97.5/100) which is Rs. 22702.68
Hence, solving equation ((105*X)/100)*(97.5/100) = 22702.68
X = 22176
*****
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
It is given that the time between first and last ticks at 6'o is 30 seconds.
Total time gaps between first and last ticks at 6'o = 5
(i.e. between 1 & 2, 2 & 3, 3 & 4, 4 & 5 and 5 & 6)
So time gap between two ticks = 30/5 = 6 seconds.
Now, total time gaps between first and last ticks at 12'o = 11
Therefore time taken for 12 ticks = 11 * 6 = 66 seconds (and not 60 seconds)
*****
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
Answer
There are 7 members in Mr. Mehta's family. Mother & Father of Mr. Mehta, Mr. & Mrs. Mehta, his son and two daughters.
Mother & Father of Mr. Mehta
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Mr. & Mrs. Mehta
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One Son & Two Daughters
*****
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?
Answer
The soldier said, "You will put me to the sword."
The soldier has to say a Paradox to save himself. If his statement is true, he will be hanged, which is not the sword and hence false. If his statement is false, he will be put to the sword, which will make it true. A Paradox !!!
******
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)
Answer
As given, the person wanted to withdraw 100X + Y paise.
But he got 100Y + X paise.
After spending 20 paise, he has double the amount he wanted to withdraw. Hence, the equation is
2 * (100X + Y) = 100Y + X - 20
200X + 2Y = 100Y +X - 20
199X - 98Y = -20
98Y - 199X = 20
Now, we got one equation; but there are 2 variables. We have to apply little bit of logic over here. We know that if we interchange X & Y, amount gets double. So Y should be twice of X or one more than twice of X i.e. Y = 2X or Y = 2X+1
Case I : Y=2X
Solving two equations simultaneously
98Y - 199X = 20
Y - 2X = 0
We get X = - 20/3 & Y = - 40/2
Case II : Y=2X+1
Solving two equations simultaneously
98Y - 199X = 20
Y - 2X = 1
We get X = 26 & Y = 53
Now, its obvious that he wanted to withdraw Rs. 26.53
At 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
Answer
Statement (4) is false. There are 3 men, 8 women and 6 children.
Assume that Statements (4), (5) and (6) are all true. Then, Statement (1) is false. But then Statement (2) and (3) both can not be true. Thus, contradictory to the fact that exactly one statement is false.
So Statement (4) or Statement (5) or Statement (6) is false. Also, Statements (1), (2) and (3) all are true.
From (1) and (2), there are 11 men and women. Then from (3), there are 2 possible cases - either there are 8 men and 3 women or there are 3 men and 8 women.
If there are 8 men and 3 women, then there is 1 child. Then Statements (4) and (5) both are false, which is not possible.
Hence, there are 3 men, 8 women and 6 children. Statement (4) is false.
*****
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?
Answer
42% houses do not have tubelight, bulb and fan.
Let's assume that there are 100 houses. Hence, there should be total 300 items i.e. 100 tubelights, 100 bulbs and 100 fans.
From the given data, we know that there is shortage of atleast (67+83+73) 223 items in every 100 houses.
Also, exactly 19 houses do not have just one item. It means that remaining 81 houses should account for the shortage of remaining (223-19) 204 items. If those remaining 81 houses do not have 2 items each, there would be a shortage of 162 items. But total of 204 items are short. Hence, atleast (204-162) 42 houses do not have all 3 items - tubelight, bulb and fan.
Thus, 42% houses do not have tubelight, bulb and fan.
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?
Answer
The individual student should pay Rs. 50 for their journey.
Note that 3 persons are travelling between Bandra and Colaba.
The entire trip costs Rs. 300 to Mr. Subramanian. Hence, half of the trip costs Rs. 150.
For Andheri-Bandra-Andheri, only one person i.e. Mr. Subramaniam is travelling. Hence, he would pay Rs. 150.
For Bandra-Colaba-Bandra, three persons i.e Mr. Subramaniam and two students, are travelling. Hence, each student would pay Rs. 50.
In training for a competition, you find that swimming downstream (with the current) in a river, you can swim 2 miles in 40 minutes, & upstream (against the current), you can swim 2 miles in 60 minutes.
How long would it take you to swim a mile in still water?
Answer
You are able to swim downstream at 3 miles an hour, & upstream at 2 miles an hour. There is a difference of 1 mile an hour, which is the river helping you in 1 direction, & slowing you in the other direction.
Average the 2 rates, & you have the rate that you can swim in still water, which is 2.5 miles an hour.
You can thus swim a mile in still water in 24 minutes.
How many different ways can this be accomplished? Note that the first person can choose any of the 11 seats.
Answer
There are 1024 different ways.
This is the type of Brain Teaser that can be solved using the method of induction.
If there is just a one person and one seat, that person has only one option.
If there are two persons and two seats, it can be accomplished in 2 different ways.
If there are three persons and three seats, it can be accomplished in 4 different ways. Remember that no person can take a seat that separates him/her from at least one other person.
Similarly, four persons and four seats produce 8 different ways. And five persons with five seats produce 16 different ways.
It can be seen that with each additional person and seat, the different ways increase by the power of two. For six persons with six seats, there are 32 different ways.
For any number N, the different possible ways are 2(N-1)
Thus, for 11 persons and 11 seats, total different ways are 210 i.e. 1024
The ratio of Boys to Girls is 6:4. 60% of the boys and 40% of the girls take lunch in the canteen. What % of class takes lunch in canteen?
Answer
Assume there are 6X boys and 4X Girls
Total Students taking lunch in canteen
= (6X)(60/100) + (4X)(40/100)
= 36(X/10) + 16(X/10)
= 52(X/10)
Total students are = 6X + 4X = 10X
% of class taking lunch in canteen
= ((52X/10) * 100 ) / 10X
= 52 %
In the General meeting of "Friends Club", Sameer said, "The repairs to the Club will come to a total of Rs 3120 and I propose that this amount should be met by the members, each paying an equal amount."
The proposal was immediately agreed. However, four members of the Club chose to resign, leaving the remaining members to pay an extra Rs 26 each.
How many members did the Club originally have?
Answer
The Club originally had 24 members.
Assume that there were initially N members.
As 4 members resigned and remaining members paid Rs 26 each, it means that total amount of 4 members is equal to Rs 26 each from remaining (N-4) members. Thus,
4 * (3120 / N) = 26 * (N - 4)
12480 = 26N2 - 104N
26N2 - 104N - 12480 = 0
Solving the quadratic equation we get N=24.
Hence, the Club originally had 24 members.
*****
A tank can be filled by pipe A in 30 minutes and by pipe B in 24 minutes. Outlet pipe C can empty the full tank in one hour and twenty minutes.
If the tank is empty initially and if all the three pipes A, B and C are opened simultaneously, in how much time will the tank be full?
Answer
The tank will be full in 16 minutes.
In one minute,
pipe A can fill 1/30 part of the tank.
pipe B can fill 1/24 part of the tank.
pipe C can empty 1/80 part of the tank.
Thus, the net water level in one minute is
= 1/30 + 1/24 - 1/80
= 15/240 part of the tank
Hence, the tank will be full in 240/15 i.e. 16 minutes.
*****
A rich old Arab has three sons. When he died, he willed his 17 camels to the sons, to be divided as follows:
First Son to get 1/2 of the camels Second Son to get 1/3rd of the camels Third Son to get 1/9th of the camels.
The sons are sitting there trying to figure out how this can possibly be done, when a very old wise man goes riding by. They stop him and ask him to help them solve their problem. Without hesitation he divides the camels properly and continues riding on his way.
How did he do it?
Answer
The old man temporarily added his camel to the 17, making a total of 18 camels.
First son got 1/2 of it = 9
Second son got 1/3 of it = 6
Third son got 1/9 of it = 2
For a total of 17. He then takes his camel back and rides away......
*****
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
As it is given that only one of the given 3 statements is true; assume in turn, each statement to be true & the other 2 false and check whether the corresponding box contains the maximum amount.
Let's assume that the statement on the Blue box is true. Thus, the given 3 statements can be interpreted as
* Atmost one, a red box or a blue box contains Rs. 10000.
* Atmost one, a green box or a red box contains Rs. 25000.
* Both, a blue box and a green box contain Rs. 15000 each.
Going through all possible combinations, we can conclude that
Red Box : Rs. 10000 + Rs. 25000 = Rs. 35000
Green Box : Rs. 10000 + Rs. 15000 = Rs. 25000
Blue Box : Rs. 15000 + Rs. 25000 = Rs. 40000
You can test out for other two statements i.e. assuming Red box statement true and then Green box statement true. In both the cases, other statements will contradict the true statement.
*****
Sachin, Dravid and Ganguly played in a Cricket match between India and England.
None of them scored more than 99 runs.
If you add the digits of the runs scored by Sachin to his own score, you will get the runs scored by Dravid.
If you reverse the digits of the runs scored by Dravid, you will get the runs scored by Ganguly.
The total runs scored by them is 240.
Can you figure out their individual scores?
Answer
Sachin, Dravid and Ganguly scored 75, 87 and 78 respectively.
Sachin's score must be less than 86, otherwise Dravid's score would be more than 99. Also, he must have scored atleast 42 - incase Dravid and Ganguly scored 99 each.
Also, as none of them scored more than 99 and the total runs scored by them is 240; their individual scores must be around 80.
*****
Substitute digits for the letters to make the following relation true.
W O R L D
+ T R A D E
----
C E N T E R
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 W, no other letter can be 3 and all other W in the puzzle must be 3.
Answer
A tough one.
It is obvious that C=1. Also, the maximum possible value of E is 7. Now, start putting possible values of D, E and R as they occure frequently and use trial-n-error.
W O R L D 5 3 6 8 4
+ T R A D E + 7 6 0 4 2
--- ---
C E N T E R 1 2 9 7 2 6
*****
If you look at a clock and the time is 3:15.
What is the angle between the hour and the minute hands? ( The answer to this is not zero!)
Answer
7.5 degrees
At 3:15 minute hand will be perfactly horizontal pointing towards 3. Whereas hour hand will be towards 4. Also, hour hand must have covered 1/4 of angle between 3 and 4.
The angle between two adjacent digits is 360/12 = 30 degrees.
Hence 1/4 of it is 7.5 degrees.
*****
An apple vendor has 1000 apples and 10 empty boxes. He asks his son to place all the 1000 apples in all the 10 boxes in such a manner that if he asks for any number of apples from 1 to 1000, his son should be able to pick them in terms of boxes.
How did the son place all the apples among the 10 boxes, given that any number of apples can be put in one box.
Answer
1, 2, 4, 8, 16, 32, 64, 128, 256, 489
Let's start from scratch.
The apple vandor can ask for only 1 apple, so one box must contain 1 apple.
He can ask for 2 apples, so one box must contain 2 apples.
He can ask for 3 apples, in that case box one and box two will add up to 3.
He can ask for 4 apples, so one box i.e. third box must contain 4 apples.
Now using box number one, two and three containing 1, 2 and 4 apples respectively, his son can give upto 7 apples. Hence, forth box must contain 8 apples.
Similarly, using first four boxes containing 1, 2, 4 and 8 apples, his son can give upto 15 apples. Hence fifth box must contain 16 apples.
You must have noticed one thing till now that each box till now contains power of 2 apples. Hence the answer is 1, 2, 4, 8, 16, 32, 64, 128, 256, 489. This is true for any number of apples, here in our case only upto 1000.
*****
The letters P, Q, R, S, T, U and V, not necessarily in that order represents seven consecutive integers from 22 to 33.
U is as much less than Q as R is greater than S.
V is greater than U.
Q is the middle term.
P is 3 greater than S.
Can you find the sequence of letters from the lowest value to the highest value?
Answer
The sequence of letters from the lowest value to the highest value is TUSQRPV.
From (3), Q is the middle term.
___ ___ ___ _Q_ ___ ___ ___
From (4), there must be exactly 2 numbers between P and S which gives two possible positions.
[1] ___ _S_ ___ _Q_ _P_ ___ ___
[2] ___ ___ _S_ _Q_ ___ _P_ ___
From (1), the number of letters between U and Q must be same as the number of letters between S and R. Also, the number of letters between them can be 1, 2 or 3.
Using trial and error, it can be found that there must be 2 letters between them. Also, it is possible only in option [2] above.
[2] ___ _U_ _S_ _Q_ _R_ _P_ ___
From (2) V must be the highest and the remaining T must be the lowest number.
_T_ _U_ _S_ _Q_ _R_ _P_ _V_
Thus, the sequence of letters from the lowest value to the highest value is TUSQRPV.
A contractor had employed 100 labourers for a flyover construction task. He did not allow any woman to work without her husband. Also, atleast half the men working came with their wives.
he sequence of letters from the lowest value to the highest value?
*****
He paid five rupees per day to each man, four ruppes to each woman and one rupee to each child. He gave out 200 rupees every evening.
How many men, women and children were working with the constructor?
Answer
16 men, 12 women and 72 children were working with the constructor.
Let's assume that there were X men, Y women and Z children working with the constructor. Hence,
X + Y + Z = 100
5X + 4Y + Z = 200
Eliminating X and Y in turn from these equations, we get
X = 3Z - 200
Y = 300 - 4Z
As if woman works, her husband also works and atleast half the men working came with their wives; the value of Y lies between X and X/2. Substituting these limiting values in equations, we get
if Y = X,
300 - 4Z = 3Z - 200
7Z = 500
Z = 500/7 i.e. 71.428
if Y = X/2,
300 - 4Z = (3Z - 200)/2
600 - 8Z = 3Z - 200
11Z = 800
Z = 800/11 i.e. 72.727
But Z must be an integer, hence Z=72. Also, X=16 and Y=12
There were 16 men, 12 women and 72 children working with the constructor.
Because cigars cannot be entirely smoked, a Bobo who collects cigar butts can make a cigar to smoke out of every 3 butts that he finds.
Today, he has collected 27 cigar butts. How many cigars will he be able to smoke?
Answer
13 not 12
He makes 9 originals from the 27 butts he found, and after he smokes them he has 9 butts left for another 3 cigars. And then he has 3 butts for another cigar.
So 9+3+1=13
*****
Tanya wants to go on a date and prefers her date to be tall, dark and handsome.
Of the preferred traits - tall, dark and handsome - no two of Adam, Bond, Cruz and Dumbo have the same number.
Only Adam or Dumbo is tall and fair.
Only Bond or Cruz is short and handsome.
Adam and Cruz are either both tall or both short.
Bond and Dumbo are either both dark or both fair.
Who is Tanya's date?
Answer
Cruz is Tanya's date.
As no two of them have the same number of preferred traits - from (1), exactly one of them has none of the preferred traits and exactly one of them has all the preferred traits.
From (4) and (5), there are only two possibilities:
* Adam & Cruz both are tall and Bond & Dumbo both are fair.
* Adam & Cruz both are short and Bond & Dumbo both are dark.
But from (2), second possibility is impossible. So the first one is the correct possibility i.e. Adam & Cruz both are tall and Bond & Dumbo both are fair.
Then from (3), Bond is short and handsome.
Also, from (1) and (2), Adam is tall and fair. Also, Dumbo is the person without any preferred traits. Cruz is Dark. Adam and Cruz are handsome. Thus, following are the individual preferred traits:
Cruz - Tall, Dark and Handsome
Adam - Tall and Handsome
Bond - Handsome
Dumbo - None :-(
Hence, Cruz is Tanya's date.
Consider a game of Tower of Hanoi
*****
If the tower has 2 discs, the least possible moves with which you can move the entire tower to another peg is 3.
If the tower has 3 discs, the least possible moves with which you can move the entire tower to another peg is 7.
What is the least possible moves with which you can move the entire tower to another peg if the tower has N discs?
Answer
There are number of ways to find the answer.
To move the largest disc (at level N) from one tower to the other, it requires 2(N-1) moves. Thus, to move N discs from one tower to the other, the number of moves required is
= 2(N-1) + 2(N-2) + 2(N-3) + ..... + 22 + 21 + 20
= 2N - 1
For N discs, the number of moves is one more than two times the number of moves for N-1 discs. Thus, the recursive function is
F(1) = 1
F(N) = 2*[F(N-1)] + 1
where N is the total number of discs
Also, one can arrive at the answer by finding the number of moves for smaller number of discs and then derive the pattern.
For 1 disc, number of moves = 1
For 2 discs, number of moves = 3
For 3 discs, number of moves = 7
For 4 discs, number of moves = 15
For 5 discs, number of moves = 31
Thus, the pattern is 2N – 1
A boy found that he had a 48 inch strip of paper. He could cut an inch off every second.
*****
How long would it take for him to cut 48 pieces? He can not fold the strip and also, can not stack two or more strips and cut them together.
SubmiAnswer
47 seconds.
To get 48 pieces, the boy have to put only 47 cuts. i.e. he can cut 46 pieces in 46 seconds. After getting 46 pieces, he will have a 2 inches long piece. He can cut it into two with just a one cut in 1 second. Hence, total of 47 seconds.tted by : Kimi
*****
The cricket match between India and Pakistan was over.
Harbhajan scored more runs than Ganguly.
Sachin scored more runs than Laxman but less than Dravid
Badani scored as much runs as Agarkar but less than Dravid and more than Sachin.
Ganguly scored more runs than either Agarkar or Dravid.
Each batsman scored 10 runs more than his immediate batsman. The lowest score was 10 runs. How much did each one of them score
Answer
A simple one. Use the given facts and put down all the players in order. The order is as follow with Harbhajan, the highest scorer and Laxman, the lowest scorer.
Harbhajan
Ganguly
Dravid
Badani, Agarkar
Sachin
Laxman
Also, as the lowest score was 10 runs. Laxman must have scored 10, Sachin 20, Badani & Agarkar 30 and so on.
Harbhajan - 60 runs
Ganguly - 50 runs
Dravid - 40 runs
Badani, Agarkar - 30 runs each
Sachin - 20 runs
Laxman - 10 runs
*****
There are 10 statements written on a piece of paper:
At least one of statements 9 and 10 is true.
This either is the first true or the first false statement.
There are three consecutive statements, which are false.
The difference between the numbers of the last true and the first true statement divides the number, that is to be found.
The sum of the numbers of the true statements is the number, that is to be found.
This is not the last true statement.
The number of each true statement divides the number, that is to be found.
The number that is to be found is the percentage of true statements.
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.
There are no three consecutive true statements.
Find the minimal possible number?
Answer
The numebr 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, atleast 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:
The numebr is divisible by 5 (Statement 4)
The numebr is divisible by 2, 3, 4, 6, 7 (Statement 7)
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.
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Ankit and Tejas divided a bag of Apples between them.
Tejas said, "It's not fair! You have 3 times as many Apples I have." Ankit said, "OK, I will give you one Apple for each year of your age." Tejas 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 Ankit.
Ankit went to Kitchen to drink water. While Ankit was in Kitchen, Tejas took apples from Ankit's pile equal to Ankit's age.
Who have more apples now?
Answer
At the end, Ankit and Tejas, both have the same number of apples.
Let's assume that initially Tejas got N apples and his age is T years. Hence, initially Ankit got 3N apples and his age is 2T years.
Operation Ankit's Apples Tejas's Apples
Initially 3N N
Ankit gave T apples to Tejas
(equals age of Tejas) 3N - T N + T
Tejas took 2T apples from Ankit's pile
(equals age of Ankit) 3N - 3T N + 3T
It is given that after Ankit gave T apples to Tejas, Ankit had twice as many apples as Tejas had.
3N - T = 2*(N + T)
3N - T = 2N + 2T
N = 3T
From the table, at the end Ankit have (3N - 3T) apples and Tejas have (N + 3T) apples. Substituting N = 3T, we get
Ankit's apples = 3N - 3T = 9T - 3T = 6T
Tejas's apples = N + 3T = 3T + 3T = 6T
Thus, at the end Ankit and Tejas, both have the same number of apples.
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