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6 employees Abhishek, Bhuvan, Chetan, Dilip, Eshan and Faraz of XYZ Corp Ltd are sports enthusiasts who all go to a sports complex near their office after working hours. Each of them plays exactly one sport out of Cricket, Badminton, Tennis, Football, Swimming and Basketball. Each of them has been the member of the complex for a different amount of time. It is known that everyone joined the complex in consecutive months. They all arrive at the complex in their own cars. The complex offers a discount in membership fees for people who remain a member there for more than a quarter of a year. It is also known that : - Half of the people pay less than the others. - Chetan, who plays basketball does not drive Logan and does not pay as much as Bhuvan as membership fees for the complex. - The people playing football and badminton pay less than half of the employees and arrive at the complex in Logan and Swift respectively. - The one who plays tennis drives Amaze and has been a member of the complex for 3 months. - Bhuvan plays cricket and is the newest member of the complex when compared with others with only 1 month of membership. - Faraz, who plays football has been a member for half a year, the most amongst the given group of people and Dilip who comes in a Polo has been a member for a third of Faraz’s time. - Eshan does not come in a Swift
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If the person coming in a Verna has been a member of the complex for more than 3 months, which sport does he play ?
Let us draw a basic table and then we can try to fill it from the information given. The basic table will look like this :
Chetan plays basketball and Bhuvan plays cricket. Bhuvan has 1 month of membership. Since he is the newest member, we can say that the others have been a member of the complex for longer time. Faraz plays football and has been a member for 6 months. Dilip drives a Polo and has been a member for 13×6=2\dfrac{1}{3} \times 6 = 231×6=2 months. The table will look like this :
Chetan does not pay as much as Bhuvan ie he pays less than Bhuvan ie he has been a member of the complex for more than 3 months. The three people who pay less are : Chetan, the person playing badminton and Faraz (the person playing football). The person playing football has a Logan ie Faraz has a Logan. We know that Eshan does not own a swift and the person playing badminton has a Swift. Looking at the table above, the person playing badminton has to be Abhishek. Now the table will look like this :
The one who plays tennis drives Amaze. Looking at the table, the only possibility is that Eshan plays tennis. Since the only remaining sport is Swimming, we can say that Dilip does swimming at the complex. Since we know that Chetan and Abhishek have more than 3 months of membership but less than 6 months, they can have membership of 5 months or 4 months. Now the table will look like this :
From the table, we know that the person coming in a Verna has been a member for more than 3 months, it has to be Chetan. So, the sport played by the person coming in Verna is Basketball.
For which of the following people, does their name and the name of the sport they play start with consecutive letters in the alphabet ?
From the given options, we can see that since Abhishek plays badminton, he satisfies the given conditions.
The complex offers more discount to the members who remain a member for more than half a year. How many of the given people will be availing that discount after 2 months ?
People who will be availing extra discount two months from now will then have more than 6 months of membership.
Thus, they must have more than 4 months of membership today. Therefore, a total of 2 people amongst the given 6 will be able to avail the discount after 2 months.
Amongst the given options, which is a correct pairing of the car of the person and the sport that they play ?
From the table, we can see that option A is the only correct combination.
If the sum of months of membership of Faraz and Dilip is equal to that of Chetan and Eshan, for how long was Chetan a member of the complex?
From the table, we can see that sum of membership months of Faraz & Dilip = 8 months & that of Eshan & Chetan should also be 8
Here Chetan can have both 4 & 5 months
But for this question 5 months is the correct answer.
In the below table, the number of employees working in the Marketing, Finance and Administration departments of a company ABC Technologies is given in each age group. The numbers in the ordered pair are the lowest pay and the highest pay a person is getting in that age group in that department. For example, consider the cell that corresponds to Marketing department and the age of employees less than 25. There are 8 employees in Marketing department who are less than 25 years of age. Also, the lowest pay an employee is getting in this combination is 4 lakhs and the highest pay an employee is getting in this combination is 8 Lakhs. Answer the following questions based on the given information.
What is the maximum number of employees who are more than 39 years of age and have a pay of at least 19 Lakhs in any of the departments?
Age Group of 35-45: Marketing => At least 1 employee must have 12 Lakhs => It is possibile that all the remaining employees have a salary of greater than 19 Lakhs => 8 employees Finance => At least 1 employee must have 15 Lakhs => It is possibile that all the remaining employees have a salary of greater than 19 Lakhs => 3 employees Administration => At least 1 employee must have 10 Lakhs => It is possibile that all the remaining employees have a salary equal to 19 Lakhs => 6 employees Age Group 45-55: Markteting => All 6 employees may have salary greater than or equal to 19 Lakhs. Finance => All the 8 employess satisfy the criteria. Administration => At least 1 employee must have 17 Lakhs => It is possibile that all the remaining employees have a salary of greater than 19 Lakhs => 6 employees Age Group 55-60: All the employees in this age group satisfy the given criteria. => Total number of people = 8 + 3 + 6 + 6 + 8 + 6 + 4 + 4 + 5 = 50 Hence, option B is the answer.
What is the minimum number of employees who earn more than 10 Lakhs but less than 18 Lakhs in any department and are of more than 31 years of age?
It is possible that none of those who belong to age group 25-35 are paid more than 10 Lakhs => 0 employees.
Age group 31-35:
In Marketing, at least one employee should have 13lakhs. But this employee could be from the age group 25-30. Thus, the min for marketing is 0 employees. Similar is the case for Finance and Administration. Thus, a min of 0 employees from the age group 30-35 has salary between 10 and 18 lakhs.
Age group 35-45: In Marketing, at least one employee must be paid 12 Lakhs => Remaining can have more than 18 Lakhs => 1 employee In Finance, at least one employee must be paid 15 Lakhs => Remaining can have more than 18 Lakhs => 1 employee In Administration, at least one employee must be 10 lakhs and the remaining can have more than 18 lakhs. But we need more than 10 lakhs => 0 employees. Age Group 45-55: One employee in Administration must be paid 17 Lakhs => 1 employee => Total number of employees that satisfy the condition = 1 + 1 + 1 = 3.
The average salary(in Lakhs) of Finance department is at least how much?
Least sum of salaries for employees less than 25 yrs of age = 6*5 + 12 = 42 Least sum of salaries for employees greater than 25 yrs of age but less than 35 yrs of age = 6*7 + 15 = 57 Least sum of salaries for employees greater than 35 yrs of age but less than 45 yrs of age = 3*15 + 31 = 76 Least sum of salaries for employees greater than 45 yrs of age but less than 55 yrs of age = 7*28 + 43 = 239 Least sum of salaries for employees greater than 55 yrs of age but less than 60 yrs of age = 3*42 + 57 = 183 Total sum = 42 + 57 + 76 + 239 + 183 = 597 Total number of employees in Finance = 29 => Average Salary = 597/29 = 20.58 Lakhs
What is the maximum possible average salary(In Lakhs) of the employees who are more 45 years old and less than 55 years old?
Maximum sum of salaries in Marketing = 19 + 31 + 31 + 31 + 31 + 31 = 174 Maximum sum of salaries in Finance = 28 + 43 + 43 + 43 + 43 + 43 + 43 + 43 = 329 Maximum sum of salaries in Administration = 17 + 35 + 35 + 35 + 35 + 35 + 35 = 227 Total sum = 174 + 329 + 227 = 730 Total number of employees = 21 Average salary = 730/21 = 34.76 Lakhs
What is the minimum average salary of employees over 47 years of age?
To get the minimum average salary, we have to minimize the salary of the particular group as much as possible ( keeping in mind whether all the conditions are satisfied or not.) In the (45,55] age group: For marketing, a minimum of one employee will surely get 19L (the lowest salary); similarly, a minimum of one employee will get 31L (the highest salary). But the employee who is getting 31L can be younger than age 47. (45,47) in this age group. So, the minimum salary of employees in marketing over 47 years to 55 years will be = 5*19=95 L for 5 employees. Applying the same conditions, we can say that the minimum salary of employees in Finance over 47 years to 55 years will be= 7*28=196 L for 7 employees, and the minimum salary of employees in Administration over 47 years to 55 years will be = 6*17=102 L for 6 employees. In the (55,60] age group: The minimum salary of employees in marketing will be = (3*30+1*47)=137 L for 4 employees. In Finance, the minimum salary will be = (3*42+1*57)=183 L for 4 employees. In Administration, the minimum salary will be = (4*29+1*41)=157 L for 5 employees. So, the average minimum salary will be = (95+196+102+137+183+157)/(5+7+6+4+4+5)= 870/31=28.06 L
The first pie chart shows the population of each of the 6 countries, A, B, C, D, E and F as the percentage of the total population of the 6 countries. The second pie chart shows the number of billionaires in each country as a percentage of the total number of billionaires in these 6 countries.
Based on the information given, answer the following questions.
Which country has the highest billionaire to population ratio?
Let the total population be x and the total number of billionaires be y.
Now, let the billionaire to population ratio be r.
r for A = 35y20x=1.75yx\frac{35y}{20x}=\frac{1.75y}{x}20x35y=x1.75y
r for B = 10y25x=0.4yx\frac{10y}{25x}=\frac{0.4y}{x}25x10y=x0.4y
r for C = 10y5x=2yx\frac{10y}{5x}=\frac{2y}{x}5x10y=x2y
r for D = 20y15x=1.33yx\frac{20y}{15x}=\frac{1.33y}{x}15x20y=x1.33y
r for E = 10y20x=0.5yx\frac{10y}{20x}=\frac{0.5y}{x}20x10y=x0.5y
r for F = 15y15x=yx\frac{15y}{15x}=\frac{y}{x}15x15y=xy
So, it is maximum for C.
If the total billionaire to population percentage is 0.3%, then for the 3 most populated countries, find the ratio of the total number of billionaires to their total population.
Therefore
yx=31000\frac{y}{x}=\frac{3}{1000}xy=10003
The top 3 populated countries are A, B and E.
Total billionaires = 35% + 10% + 10% of y = 55100y\frac{55}{100}y10055y
Total population = 20% + 25% + 20% of x = 65100x\frac{65}{100}x10065x
Ratio = 55y65x=1113yx=1113× 31000=3313000\frac{55y}{65x}=\frac{11}{13}\frac{y}{x}=\frac{11}{13}\times\ \frac{3}{1000}=\frac{33}{13000}65x55y=1311xy=1311× 10003=1300033
The highest billionaire to population ratio for any country is H and the lowest billionaire to population ratio for any country is L. What percentage of L is H?
Highest = 2yx\frac{2y}{x}x2y
Lowest = 0.4yx\frac{0.4y}{x}x0.4y
Percentage = 2yx0.4yx× 100%=500%\frac{\frac{2y}{x}}{\frac{0.4y}{x}}\times\ 100\%=500\%x0.4yx2y× 100%=500%
If the billionaire to population percentage for the most populated country is 0.15%, find the billionaire to population ratio for the country with the highest number of billionaires.
The most populated country is B.
10%y25%x=0.15100\frac{10\%y}{25\%x}=\frac{0.15}{100}25%x10%y=1000.15
y10x4=1510000\frac{\frac{y}{10}}{\frac{x}{4}}=\frac{15}{10000}4x10y=1000015
yx× 410=1510000\frac{y}{x}\times\ \frac{4}{10}=\frac{15}{10000}xy× 104=1000015
yx=154000\frac{y}{x}=\frac{15}{4000}xy=400015
The country with most billionaires = A
Billionaire to population ratio = 3520yx=3520.154000=213200\frac{35}{20}\frac{y}{x}=\frac{35}{20}.\frac{15}{4000}=\frac{21}{3200}2035xy=2035.400015=320021
If the billionaires of the most populous country increased by 150 % and the billionaires of the least populous country decreased by 50%, what would be the ratio of BPRs (billionaire to population ratio) of the most populous country to the least populous country?
Let the total population be x, and the total number of billionaires be y.
r for A = 35y/20x=1.75y/x
r for B = 10y/25x=0.4y/x
r for C = 10y/5x=2y/x
r for D = 20y/5x=1.33y/x
r for E = 10y/20x=0.5y/x
r for F = 15y/15x=y/x
But now the billionaire of the most populous country (B) increased by 150% = 10y + 10y *(150/100) = 10y+15y=25y. The billionaire of the least populous country (C) decreased by 50% = 10y - 10y * (50/100) = 10y-5y = 5y So, the new ratio would be = (25y/25x) for country B and (5y/5x) for country C. so the final ratio would be = (25y/25x)/(5y/5x) = 1 (answer)
Geralt was roaming through the woods when he saw an unusual hut. When he entered the hut, he saw a 5x5 grid in front of him on the ground as shown:
Suddenly the door behind him shut and a voice resonated from above: 'The grid in front of you has 25 identical white tiles. Below each tile is either a precious diamond or nothing. If you remove a tile, and find a diamond under it, you can keep the diamond and you will be given another chance to choose another tile. This would continue till you pick a tile that has nothing under it, or you quit. If you quit of your own will, you will be allowed to take the diamonds you have collected till then. But if you choose a tile that has nothing under it, all the diamonds you have collected till now will be gone, the game will be over.'
While the tiles were identical in all aspects, the voice provided 10 identical potions, which when used provide clues as to what lies underneath. To demonstrate the power of these potions, the mysterious voice chanted some incantations, and three potions flew and fell on 3 of the tiles. The tiles (1,3) (4,1) and (4,3) changed to Orange, Green and Blue respectively. Additionally, the tile (4,1) was embossed with a diamond symbol. The following 5 rules must be followed to use the potions:
1. Each potion needs to be poured completely over a tile. Then it would change the colour of the tile from white to one of the following colours:
a) Red: Of all the tiles touching the selected tile, only 1 of them has a diamond underneath.
b) Blue: Of all the tiles touching the selected tile, only 2 of them have a diamond underneath.
c) Yellow: Of all the tiles touching the selected tile, only 3 of them have a diamond underneath.
d) Green: Of all the tiles touching the selected tile, only 4 of them have a diamond underneath.
e) Orange: Of all the tiles touching the selected tile, only 5 of them have a diamond underneath.
(Touching a tile means a tile that touches its sides or corners. For example, (2,2) has 8 tiles touching it.)
2. The embossed diamond indicates that the tile contains a diamond beneath it and no embossing indicates the absence of diamond. However, if a potion is poured over a tile, that tile can no longer be selected by Geralt to be removed.
3. The potions can only be used on a tile where the result is NOT already known - i.e. whether the tile will be embossed or what the colour will be on pouring the potion. If Geralt uses the potion on a tile where he knows either the resulting colour or if it contains a diamond or not, then the game ends and Geralt loses all his diamonds.
4. When the potion is poured, the tile necessarily changes to one of the five mentioned colours.
The tiles are numbered as (i,j), where i is the row number and j is the column number. The leftmost, topmost tile is numbered (1,1). The row number increases downwards and the column number increases towards the right.
What is the minimum number of diamonds?
We know the colour of 3 of the tiles:
An orange tile has 5 diamonds in nearby tiles. Since only 5 tiles are touching (1,3), all 5 of them must contain diamonds.
A green tile has 4 diamonds in adjacent tiles. Since only 5 tiles are touching (4,1), only one of them does not have a diamond. But (4,3) has the colour blue. Hence, only 2 of its adjacent tiles can have the diamonds. Since 3 of the tiles touching (4,1) are also touching (4,3), only two of them must have diamonds, and all the other tiles touching (4,3) must be empty. Thus, we can make the following table:
Under rule number 4, it has been given that any of the tiles will necessarily change its colour to one of the 5 given colours without violating any condition. What this implies is that all the tiles have only 1-5 diamonds in their vicinity, as changing to one of the colours without having 1-5 diamonds in the vicinity would violate the condition for that colour.
(5,5) has 3 adjacent tiles and 2 of them do not have any diamonds underneath. Hence, (4,5) necessarily contains a diamond, and he can deduce that (5,5) must necessarily be Red since only 1 tile in the vicinity has a diamond underneath. Hence, only on the basis of the 3 potions that the mysterious voice poured, Geralt has the following knowledge about the tiles:
The minimum condition arises when we have only the diamonds necessary to satisfy the above conditions. We have 9 diamonds for which we know the positions, and 2 diamonds in the second column for which we do not know the position. But, in this condition, we would have no tile touching (4,5) that contains a diamond. So, hypothetically, if one were to pour the potion on it, it would not achieve any of the given colours. Hence, we would need to have a diamond underneath (3,5) or (5,5).
Thus, we have 12 diamonds overall.
What is the maximum number of diamonds Geralt can leave with?
For the maximum condition, we will have Geralt pour the potion on (2,1) and (2,5), and have them turn Orange and Green respectively.
In this case, we do not know which among the two of (4, 2) and (5,2) contains the diamond. Hence, if Geralt pours the potion on the tile which does not contain the diamond, he would walk away with 13 diamonds.
Geralt leaves with 8 diamonds. The number of potions that he could have used lie in the range [a,b]. What is the value of a+b?
If Geralt walks away with 8 diamonds, he did not find any more diamonds under the other tiles.
Hence, in the minimum condition, he uses 0 potions and only deduces the position of the diamonds using the potions the voice poured.
We can pour a potion on only 1 of the two tiles in the first column, as pouring on one gives us the information about the other. Similarly, we can pour only 1 potion in the two tiles in the second column.
Also, we can pour only 1 potion in the three tiles in column 5:
1. If we pour on (2,5): It tells us whether there is a diamond in the other two tiles or not. Hence, we cannot pour a potion on them.
2. If we pour on (1,5): It tells us whether there is a diamond in (2,5) or not. Hence, we can infer the colour of (3,5) too, and we cannot pour a potion on it.
3. If we pour on (3,5): It tells us whether there is a diamond in (2,5) or not. Hence, we can infer the colour of (1,5) too, and we cannot pour a potion on it.
Thus, Geralt can pour at most 3 more potions.
Thus, the minimum number of potions (a): 0.
The maximum number of potions (b): 3.
a+b = 0+3= 3.
If Geralt leaves with 10 diamonds, what is the maximum number of tiles that turned red after a potion was poured on them?
Here, we can see that none of the tiles on which the potion can be poured has only 1 diamond in their vicinity. There are at least 2 diamonds touching each of the remaining tiles. Hence, there cannot be a tile that turns Red after a potion was poured over it.
What is the maximum possible number of potions that are used, including the ones used by the voice?
Thus, Geralt can pour at most 3 more potions. Hence, a total of 6 potions can be used.
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