Question
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:
$7 \blacksquare 4 = 27/4$
$6 \blacksquare 1 = 5$
$4 \blacksquare 3 = 11/3$
$a \blacksquare b = ?$
This question was previously asked in
RRB NTPC 2019 CBT 1 Question Paper PDF (31-Jan-2021) (Shift 1)
The correct answer is
$(ab - 1) / b$
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:
$a \blacksquare b = \frac{ab - 1}{b}$Was this answer helpful?
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