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Logical Problems for the 11 Plus Exams

1. Logical Problems

In this article, we will look into logical problems, how to solve them, and a few applications of      them. There is no one specific formula to solve logical problems. You have to use different            formulas and logic to solve these questions. 

1.1 Magic Square

In a magic square, numbers are arranged in such as way that the sum of each row, column, and diagonal is one constant number. 

Example:

11+ Topicwise Logical Problems Article Image 01

Here the sum of numbers in each row, column, and diagonal is 15.

Steps to solve magic square questions:

  1. Try to find one missing number in a diagonal, row or column by subtracting the sum of two numbers from one constant magic number given. 
  2. Using these numbers, the rest of the missing numbers can be found. 

Example: The following magic square has all rows, columns and diagonals adding upto 18. Several numbers have been missed out. 

11+ Topicwise Logical Problems Article Image 02

Which number replaces A?

Solution:

Sum of all rows = 18

Find the missing number in the last row containing 10 and 3.

Missing number = 18 - (10 + 3)

                          = 5

Sum of all diagonal numbers = 18

Find the missing number A in diagonal elements 7, A and 5

A = 18 - (7 + 5)

A = 6

1.2 Alphabet codes

There are different logical questions involving alphabet codes. In alphabet codes, different letters are represented by different numbers. Find out the value of words by either adding or multiplying numbers as mentioned in the question. 

Example: The letters of the alphabet are assigned number values: A = 2, B = 4, C = 6 and so on. The value of a word is found by adding the value of the letters. What is the value of the word ‘MATH’?

Solution: A is the first alphabet, its value is 2 (2 × 1).

               B is the second alphabet, its value is 4 (2 × 2).

               C is the third alphabet, its value is 6 (2 × 3).

               M is the 13th alphabet, its value is 2 × 13 = 26 

               T is the 20th alphabet, its value is 2 × 20 = 40

               H is the 8th alphabet, its value is 2 × 8 = 16   

               Value of word MATH = 26 + 2 + 40 + 16 = 94

1.3 Palindromic numbers

A number that can be read the same way forwards and backwards is called a palindrome. 

 Examples:

  1. All single digit numbers are palindromes.
  2. Two digit numbers - 11, 22, 33, 44, 55, 66, 77, 88, 99
  3. Three digit numbers - 101, 202, 252, 787, etc
  4. Four digit numbers - 1111, 1221, 1771. etc
  5. Five digit numbers - 11111, 12121, 14741, etc

Example: How many palindromes are there between 100 and 200?

Solution: Palindromes between 100 and 200 are:

                      101, 111, 121, 131, 141, 151, 161, 171, 181, 191

                Total number of palindromes = 10

                 There are 10 palindromes between 100 and 200.

2. Quadratic Equations

Equations containing terms up to x² are called quadratic equations. Let us look at a couple of examples to understand how to solve such equations.

Example: 

a) a² = 49

Solution:

a × a=49

Find a number which multiplied by itself gives 49. 

7 × 7 = 49 or -7 × -7 = 49 

Hence, x=+7 or x=-7

b) x² + x = 90

x(x+1)=90

Find the factors of 90 which have a difference of 1. 

9 × 10 = 90 or -9 × -10 = 90 

Comparing the factors with x(x+1)

We get, x=9 or x=-10

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  • Frequently Asked Questions
    What is a good score in 11+ Maths ?

    What counts as a "good" score will vary depending on the school you want to attend. The standardized 11 Plus test score average across the country is roughly 100. The highest average in some areas is 111. The lowest scores would often fall between 60 and 70, while the highest scores would normally fall between 130 and 140. To achieve excellent marks on 11+ Maths Exams, practice 11+ Maths topic-wise questions.

    How to prepare for the 11+ Maths exam?

    The best way to prepare for the 11+ Maths Exam is by practicing 11+ Maths topic-wise questions regularly.

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    Maths online subscriptions are “Non-Refundable“. No refunds can be issued for any reason. This is because of the nature of digital products.

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    What kind of questions are asked in the 11 Plus Maths exam?

    The majority of the 11 Plus Maths questions are mathematical problem-solving, where pupils need to understand and apply mathematical concepts. With regular practice of 11+ Maths Topic-wise questions, you will pass the 11-plus Maths Exam with a high score.

    What do you need to know for the 11 Plus Maths exam?

    The children must master the following topics for the 11 plus exams

    • Number and place value.
    • Addition, subtraction, multiplication, and division.
    • Fractions, percentages, decimals.
    • Ratio and proportion.
    • Algebra.
    • Measurement.
    • Geometry (properties and position of shapes, coordinates)
    • Statistics.

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