CAT Quantitative Aptitude Questions | CAT Algebra - Functions questions

The question is about Function of a function. This is about deriving a new function from given functions. Functions is a simple topic which involves a lot of basic ideas. Make sure that you a get of hold of them by solving these questions. A range of CAT questions can be asked based on this simple concept of Functions questions in the CAT Exam. Make sure you practice a lot of questions in CAT Functions Algebra to push your CAT preparation in the right direction. Functions as an idea is a fabulous idea if one can wrap their head around it the right way, and it has been one of the staple ideas tested by the CAT exam historically.

Question 13: For this question, assume the following operators:
A*B = A² - B²
A-B = \\frac{A}{B}\\)
A+B = A * B
\\frac{A}{B}\\) = A+B
Which of the following expression would yield the result as x subtracted by y?

1. (x*y)-(x+5)
2. (\\frac{x}{y}\\))*(x-y)
3. (x*y) - (\\frac{x}{y}\\))
4. (x+y)*(x-y)

Explanatory Answer

Method of solving this CAT Question from CAT Algebra - Functions: Were you able to solve this one by the given way?

Never solve each expression. Solve by assigning values of x and y

Let x = 6, y = 2 Therefore, required x – y = 4
x*y = 6² – 2² = 32
x-y = \\frac{6}{2}\\) = 3
x+y = 6 * 2 = 12
x+5 = 6 * 5 = 30
\\frac{x}{y}\\) = 6 + 2 = 8

a) (x*y)-(x+5) = 32-30 = \\frac{32}{30}\\) not equal to 4
b) (\\frac{x}{y}\\))*(x-y) = 8*3 = 8² - 3² = 55 not equal to 4
c) (x*y) - (\\frac{x}{y}\\)) = 32 - 8 = \\frac{32}{8}\\) = 4
d) (x+y)*(x-y) = 12*3 = 12² - 3² not equal to 4

The question is "Which of the following expression would yield the result as x subtracted by y?"

Hence the answer is "(x*y) - (\\frac{x}{y}\\)) "

Choice C is the correct answer.