The rectangle represents a set of calculations that are common across all the given equations. Identify the calculations involved and solve the fourth equation on the same basis:
$7 \blacksquare 4 = 27/4$
$6 \blacksquare 1 = 5$
$4 \blacksquare 3 = 11/3$
$a \blacksquare b = ?$
Solving the Algebraic Pattern
The problem presents a series of equations with a symbolic operator '$\blacksquare$'. We need to identify the rule governing this operator based on the given examples and apply it to find the expression for '$a \blacksquare b$'.
Analyzing the Given Equations
The provided equations are:
- $7 \blacksquare 4 = 27/4$
- $6 \blacksquare 1 = 5$
- $4 \blacksquare 3 = 11/3$
Identifying the Operator Rule
Let's assume the operation '$a \blacksquare b$' follows a specific algebraic pattern. We test the pattern $a \blacksquare b = (ab - 1) / b$, derived from the options and verified against the examples.
- For the first equation, $a=7, b=4$: $(7 \times 4 - 1) / 4 = (28 - 1) / 4 = 27/4$ This matches the given result.
- For the second equation, $a=6, b=1$: $(6 \times 1 - 1) / 1 = (6 - 1) / 1 = 5/1 = 5$ This also matches the given result.
- For the third equation, $a=4, b=3$: $(4 \times 3 - 1) / 3 = (12 - 1) / 3 = 11/3$ This matches the given result as well.
Solving for '$a \blacksquare b$'
Since the pattern $a \blacksquare b = (ab - 1) / b$ holds true for all given examples, we can conclude this is the correct rule for the operator.
Therefore, for '$a \blacksquare b$', the expression is:
$a \blacksquare b = \frac{ab - 1}{b}$Similar Questions
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Important Questions from Problem Solving
Six numbers, 7, 8, 9, 10, 11 and 12 are written on different faces of a dice. Three positions of this dice are shown here. Find the number on the face opposite 12.
Select the set in which the numbers are related in the same way as are the numbers of the following sets.
(NOTE: Operations should be performed on the whole numbers, without breaking down the numbers into its constituent digits. E.g. 13 - Operations on 13 such as adding/subtracting/multiplying etc. to 13 can be performed. Breaking down 13 into 1 and 3 and then performing mathematical operations on 1 and 3 is not allowed.)
(84, 73, 157) (96, 88, 184)
Rahul invests his savings, which is Rs. 25,000 in his bank that pays 7 per cent annual interest. How much will he earn by way of interest in one year?
Which two signs need to be interchanged to make the following equation correct? 5 × 4 + 12 - 3 ÷ 6 = 18
In a company there are 3 departments - IT, HR and Help Desk. In the IT department there are 125 employees and in the HR department the number of employees is 1/5th of IT. The helpdesk department has 20 employees less than total employees in IT and HR together. What is the total number of employees working in all three departments?
