Concept 1:

Problem Solving by Substitution

Eg: 1) If ‘+’ means ‘minus’ ,’×’ means ‘divided by’, ‘÷’ means ‘plus’ and ‘-’ means ‘multiplied by’, then which of the following will be the value of the expression

252 × 9 – 5 + 32 ÷ 92?    

a) 95                 b) 168                           c) 192               d) 200               e) None of these

2) If ÷ implies =, × implies ˂, + implies ˃, - implies ×, ˃ implies  ÷, < implies +, = implies -, identify the correct expression.    

a) 1 – 3 > 2 + 1 – 5 = 3 – 1 < 2

b) 1 – 3 > 2 + 1 × 5 = 3 × 1 > 2

c) 1 × 3 > 2 + 1 × 5 × 3 – 1 > 2

d) 1 – 3 > 2 + 1 × 5 + 3 – 1 > 2      

3) Directions: In an imaginary language, the digits 0, 1, 2, 3, 4, 5, 6, 7, 8 and 9 are substituted by a, b, c, d, e, f, g, h, i and j. And 10 is written as ba.

bee + fg - (ca × h/be) is equal to   

a) bhc                b) bic                c) bib                d) bja 

4) Directions: In the following question, different alphabets stand for various symbols as indicated below:

Addition: O       Subtraction: M              Multiplication: A

Division: Q      Equal to: X                    Greater than: Y             Lees than: Z

Out of the four alternatives given in these questions, only one is correct according to the above letter symbols. Identify the correct answer.

a) 32 X 8 Q 2 A 3 Q 1 A 2          b) 14 X 2 A 4 A 2 M 2 Q 1

c) 2 Y 1 A 1 Q 1 O 1 A 1           d) 16 Y 8 A 3 O 1 A 2 M 2 

Concept 2:

Interchanging of Signs and Numbers

Eg: 1) Directions: In each of the following questions, if the given interchanges are made in signs and numbers, which one of the four equations would be correct?

Given interchanges: Signs + and × and numbers 4 and 5.

a) 5 × 4 + 20 = 40            b) 5 × 4 + 20 = 85             c) 5 × 4 + 20 = 104            d) 5 × 4 + 20 = 95

2) Directions: In each of the following questions, which one of the four interchanges in signs and numbers would make the given equation correct?

6 ×  4 + 2 = 16

a) + and ×,  2 and 4                    b) + and ×, 2 and 6      

c) + and ×, 4 and 6                      d) None of these 

Concept 3:

Finding the Appropriate Conclusions

Eg: 1) Directions: In the following question, the symbols *, %, $, # and © are used with the following meanings as illustrated below:

‘P $ Q’ means ‘P is smaller than Q’;                   ‘P % Q’ means ‘P is greater than Q’;     

‘P * Q’ means ‘P is neither smaller than nor greater than Q’;

‘P # Q’ means ‘P is either greater than or equal to Q’;                

‘P © Q’ means ‘P is either smaller than or equal to Q’.

Now, in each of the following questions, assuming the given statements to be true, find which of the two conclusions I and II given below them is /are definitely true?

Give answer (a) if only conclusion I is true;                    (b) if only conclusion II is true;            

(c) if either conclusion I or II is true;

(d) if neither conclusion I nor II is true; and                    (e) if both conclusions I and II are true

Statements: B # D,                   D * F,               F % H

Conclusions: I. F * B                II. F $ B

In a certain code language, ‘+’ represents ‘×’, ‘-’ represents ‘÷’,  ‘×’ represents ‘- ’ and ‘÷’ represents ‘+’. Find out the answer to the following question considering that language as base.

10 ÷ 18 + 25 x 20 - 5 = ?

A) 384             B) 450              C) 454              D) 400              E) 500

SOLUTION:

Given expression is 10 ÷ 18 + 25 x 20 - 5

After substituting the signs as given in the question, the equation becomes

= 10 + 18 × 25 – 20 ÷ 5

Apply the rule BODMAS,

= 10 + 18 × 25 – 4 = 10 + 450 – 4 = 460 – 4 = 454

ANSWER: C

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