As we await the final list of selected people in Dunnhumby and Absolutdata, we are happy to inform you share with you guys the results of Absolutdata hunt.
Lets be share with you the solutions of some of the more difficult questions.
When a mango tree was first planted, it was 8 feet tall, and the height of the mango tree increased by a constant amount each year for the next 6 years. At the end of the 8th year, the mango tree was 1/3 taller than it was at the end of the 5th year. By how many feet did the height of the mango tree increase each year?
Let the height by which the tree increased constantly each year be x ft.
At the end of the 1st year, height of tree = 4 + x
At the end of the 2nd year, height of tree = 4 + 2x
...
At the end of the 8th year, height of the tree = 4 + 8x
It is given that at the end of the 8th year, the tree was 1/4 taller than it was at the end of the 5th year, so 4 + 8x = (1 + 1/3) * (4 + 5x)
Solving, we get, 12 + 24x = 16 + 20x
4x = 4
Consider a set [600,1000}. You are given the task of finding the numbers where two digits out of them are equal to each other and the remaining digit is different from the other two. How many such digits are there?
Since we cannot include 888 in this list, there are 9 numbers in the form 8X8
88X
880
881
882
.
.
.
889
Since we cannot include 888 in this list, there are 9 numbers in the form 88X
So, there are 27 (9+9+9) numbers from 800 to 899 inclusive that meet the given criteria.
Using the same logic, we can see that there are 27 numbers from 900 to 999 inclusive that meet the given criteria.
And there are 27 numbers from 600 to 999 inclusive that meet the given criteria. HOWEVER, the question says that we're looking at numbers greater than 600. So, there are 26 numbers from 701 to 799 inclusive that meet the given criteria.
So, our answer is 27+27+27+26
80% of the lights at Hotel Greentree are on at 8 p.m. a certain evening. However, 40% of the lights that are supposed to be off are actually 'on' and 10% of the lights that are supposed to be on are actually 'off'. What is the number of lights that are on and are supposed to be off?
Say, total number of lights in the hotel = 100
Also assume the number of lights that are supposed to be on = n.
Hence, number of lights that are supposed to be off = (100 - n)
Number of lights that are on = 80% of 100 = 80
Number of lights on that are supposed to be off = 40% of (100 - n) = 0.4(100 - n)
Number of lights off that are supposed to be on = 10% of n = 0.1n
Hence, total number of lights that are on = n - 0.1n + 0.4(100 - n) = 40 + 0.5n
Hence, (40 + 0.5n) = 80 => n = 80
Now, number of lights on that are supposed to be off = 0.4(100 - n) = 0.4(100 - 80) = 0.4*20 = 8
You choose a random set of people. You are to get 50% probability for at least two to have the same birthday(You are not in a leap yeat btw), How many people should you select?
The probability that n people have all different birthdays is 1 - (Product for i=1 to n of (365-n)/365.)
One minus this figure is the probability that there is at least one common birthday. The probability that there is at least one common birthday in 22 people is 47.57%, for 23 people it is 50.73%. Since the percentage must be at least 50% the answer is 23.
There was a case study and two data analysis problems. The case study is about identifying the right data and understanding the question. While the Data Analysis questions was to test your big data skills.
The other questions are fairly simple, so I am not publishing those answers here.
Lets be share with you the solutions of some of the more difficult questions.
When a mango tree was first planted, it was 8 feet tall, and the height of the mango tree increased by a constant amount each year for the next 6 years. At the end of the 8th year, the mango tree was 1/3 taller than it was at the end of the 5th year. By how many feet did the height of the mango tree increase each year?
Let the height by which the tree increased constantly each year be x ft.
At the end of the 1st year, height of tree = 4 + x
At the end of the 2nd year, height of tree = 4 + 2x
...
At the end of the 8th year, height of the tree = 4 + 8x
It is given that at the end of the 8th year, the tree was 1/4 taller than it was at the end of the 5th year, so 4 + 8x = (1 + 1/3) * (4 + 5x)
Solving, we get, 12 + 24x = 16 + 20x
4x = 4
Consider a set [600,1000}. You are given the task of finding the numbers where two digits out of them are equal to each other and the remaining digit is different from the other two. How many such digits are there?
Since we cannot include 888 in this list, there are 9 numbers in the form 8X8
88X
880
881
882
.
.
.
889
Since we cannot include 888 in this list, there are 9 numbers in the form 88X
So, there are 27 (9+9+9) numbers from 800 to 899 inclusive that meet the given criteria.
Using the same logic, we can see that there are 27 numbers from 900 to 999 inclusive that meet the given criteria.
And there are 27 numbers from 600 to 999 inclusive that meet the given criteria. HOWEVER, the question says that we're looking at numbers greater than 600. So, there are 26 numbers from 701 to 799 inclusive that meet the given criteria.
So, our answer is 27+27+27+26
80% of the lights at Hotel Greentree are on at 8 p.m. a certain evening. However, 40% of the lights that are supposed to be off are actually 'on' and 10% of the lights that are supposed to be on are actually 'off'. What is the number of lights that are on and are supposed to be off?
Say, total number of lights in the hotel = 100
Also assume the number of lights that are supposed to be on = n.
Hence, number of lights that are supposed to be off = (100 - n)
Number of lights that are on = 80% of 100 = 80
Number of lights on that are supposed to be off = 40% of (100 - n) = 0.4(100 - n)
Number of lights off that are supposed to be on = 10% of n = 0.1n
Hence, total number of lights that are on = n - 0.1n + 0.4(100 - n) = 40 + 0.5n
Hence, (40 + 0.5n) = 80 => n = 80
Now, number of lights on that are supposed to be off = 0.4(100 - n) = 0.4(100 - 80) = 0.4*20 = 8
You choose a random set of people. You are to get 50% probability for at least two to have the same birthday(You are not in a leap yeat btw), How many people should you select?
The probability that n people have all different birthdays is 1 - (Product for i=1 to n of (365-n)/365.)
One minus this figure is the probability that there is at least one common birthday. The probability that there is at least one common birthday in 22 people is 47.57%, for 23 people it is 50.73%. Since the percentage must be at least 50% the answer is 23.
There was a case study and two data analysis problems. The case study is about identifying the right data and understanding the question. While the Data Analysis questions was to test your big data skills.
The other questions are fairly simple, so I am not publishing those answers here.
