Lokprakash M.

Financial Modeling and Machine learning enthusiast

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SQL Programming

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Question:

There is a employee table consisting of two columns a) employee_id b) manager_id where all managers are necessarily employees but all employees are not necessarily manager. Please create a table consisting of 1) employee 2) manager 3) manager's manager

Lokprakash M.

Answer:

select t2.employee_id, t2.manager_id, t1.manager_id from employee as t1 join employee as t2 on ( t2.manager_id=t1.employee_id); Thats it..

GMAT

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Question:

In what proportion must water be mixed with milk to gain 10 % by selling it at cost price ?

Lokprakash M.

Answer:

Let cost price(CP) of milk be $ 1 per liter, then selling price(SP) of mixture is also $1 per liter Now CP of mixture be = 1 - ( 10 % of $ 1 ) = 1 - ( 10 * 1 / 100 ) = 90/100= 9/10 Now, Quantity of water / Quantity of milk = (1-9/10)/(9/10) = 1:9 (Proportionality rule)

Calculus

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Question:

Lets say the functional expression of f(x) is f (x+ 1/x) = x^2 + 1/ x^2 . where x is not equal to 0. Solve for f(x).

Lokprakash M.

Answer:

The functional expression is simply put in terms of a squared terms of (x+1/x) i.e f(x+1/x) = (x+1/x)^2 - 2 . Now replace (x+1/x) = y . Then f(y)= y^2 -2 . Now changing the variables we obtain f(x) = x^2 -2 .

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