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
- Read the given paragraph and answer the question.
There are five persons A, G, M, J and D. Every person has to select one item each from a box containing items numbered from 1 to 5. A and J selected items 5 and 2 respectively. G cannot select item 3, while M cannot select item 3 or 5.
Which item can G select? - Read the given information carefully and answer the question that follows.
- There are four persons: P, Q, R and S.
- One of them is a doctor and plays football and cricket.
- P and Q are teachers.
- P plays badminton.
- The lawyer and both the teachers are swimmers.
- One of them also plays tennis.
- S plays carrom and is a lawyer.
- All the four persons play two games each and follow one profession.
- Four girls, Radha, Neena, Mohita and Jyoti, are to be served in a sequence by a service provider. However, there are some limitations as follows: Mohita and Jyoti cannot be served one after the other; Neena cannot be served at the third number in sequence; and Radha and Neena are to be served one after the other. Considering the given information, which of the following statements is compulsorily true?
- In a school there were 6 teachers. A and B taught Hindi and English. D and A taught Mathematics and Science. C and E taught English and Mathematics. F and B taught Hindi and French. Who taught the maximum number of subjects?
- Five children A, B, C, D and E ate mangoes. A ate 8 mangoes less than B. C and E together ate 37 mangoes. D ate 8 mangoes more than C. B ate 5 mangoes more than C. B and A together ate 40 mangoes. Considering the above information, which of the following statements is correct?
- Huma's mother gave Huma 4 baskets of blueberries each labelled A, B, C, D. Each berry weighs 5 g, except for the basket, which has all rotten berries, where each berry has a weight of 3 g. Huma took out 1, 2, 3 and 4 berries from the baskets A, B, C and D respectively and weighed them to be 44 grams. Which basket has the rotten berries?
- In a test paper, correct answers fetch three marks and there is a penalty of one mark for each wrong answer. A student who attempts 76 questions gets 144 marks. How many questions did the student get right?
- In a test series, South Africa defeated England twice, Bangladesh defeated South Africa twice, England defeated Bangladesh twice, South Africa defeated Pakistan twice and Bangladesh defeated Pakistan twice. Which country lost the highest number of times?
Important Questions from Problem Solving
A tight fitting band is wrapped around the Equator. Another circular band whose length is 15 m more lies at a certain height over the first band. A group of human beings attempt to pass under the longer band. Can they walk under it?
(Earth’s circumference is roughly 40000 km. The height of human beings is between 1 & 2m)
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)
- Arrange the problem-solving strategy.
(A) Generate many possible solutions
(B) Determine how to implement the solution and evaluate the success of the solution
(C) Make a decision
(D) Evaluate each solution
(E) Define the problem
Choose the correct answer from the options given below. - A cyclist starting from point $X$ travels straight towards east for 3km and then turns right and covers 4km and reaches point $Y$. What is the shortest distance between point $X$ and $Y$?
- Read the given paragraph and answer the question.
There are five persons A, G, M, J and D. Every person has to select one item each from a box containing items numbered from 1 to 5. A and J selected items 5 and 2 respectively. G cannot select item 3, while M cannot select item 3 or 5.
Which item can G select?
