**SSC CHSL Topic Wise Study Material – General Intelligence – Mathematical/Numerical Operation**

Contents

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Mathematical operation can be defined as the simplification of expression containing numbers and different mathematical signs. There are four fundamental of mathematical operation such as.

[Addition, ‘+’], [Subtraction’-‘], [Division, ‘÷’] and [Multiplication, ‘x’] and also statements such as [Less than, ‘<’], [ Greater than, ‘>’], [Equal to, =’], [Not equal to, ≠], [Not greater than >/, ], [Not less than, /<] etc, are also represented by symbols.

In these type of questions, an equation is represented by different symbols and signs which may be different from the usual ones. The equation involving these operation are a set, using artificial symbols. In other words, the equation may also be used by giving a proper definition of the symbol used. The candidate is required to substitute the real signs in place of artificial symbols to solve the questions.

In this type of questions, to find the value of given expression are must replace the symbol by mathematical operations. Then, apply the BODMAS rule

B- Bracket

O – Of

D – Division

M – Multiplication

A – Addition

S – Subtraction

Basically two types of questions covered in this chapter are as follows

**1. Symbol Substitution**

In this type of questions, a candidate is provided with substitutes for various mathematical symbols, followed by a question involving calculation of an expression or choosing the correct/incorrect equation. The candidate is required to put in the real signs in the given equation and then solve the questions as required.

**Example If + means ‘minus’, -’ means ‘multiply’, ÷ means ‘plus’ and x means ‘divide’, then 10 x 5 ÷ 3 – 2 + 3 is equal to SSC (10 + 2) 2013**

(a) 5

(b) 53/3

(c) 21

(d) 36

**Answer:**

(a) As, 10 x 5 ÷ 3 – 2 + 3 = ?

After using the correct symbols, we have 10 ÷ 5 + 3 x 2 – 3 = 2 + 3 x 2 – 3 = 2 + 6 – 3 = 8 – 3 = 5 (By using BODMAS rule)

**2. Interchange of Signs and Numbers**

In this type of questions, the given equation become correct and fully balanced, when either two signs of the equation or both the numbers and the signs of the equation are interchanged. The candidate is required to find the correct pair of signs and numbers from the given alternatives.

**Example If + and – signs are interchanged, similarly ‘x’ and ÷ are interchanged, then find the answer of the following equation.**

**10 – 2 + 12 x 1 ÷0 SSC (10 + 2) 2012**

(a) 8

(b) 12

(c) 1

(d) 0

**Answer:**

(b) Given equation,

= 10 – 2 + 12 x 1÷0

According to the question, after interchanging the . signs

10 + 2 – 12 ÷ 1 x 0 = 12 – 12 x 0 = 12 – 0=12

**Example Which interchange of signs will make the following equation correct?**

**(16-4) x 6 ÷ 2 + 8= 30 SSC (10 + 2) 2012**

(a) ÷ and –

(b) 4 and 2

(c) – and +

(d) 16 and 6

**Answer:**

(a) Given equation, (16 – 4) x 6 ÷ 2 + 8 = 30

From option (a), after interchanging signs

(16÷4) x 6-2 + 8 = 30

= 4 x 6 – 2 + 8=30

= 32 – 2 = 30 => 30=30

**Reference Corner**

**1. Insert the arithmetical operations in the following numerical figure.**

**4_3_4 = 48 SSC (10+2) 2015**

(a) x x

(b) + +

(c) x +

(d) + –

**Answer:**

(a) From the option (a), 4 x 3 x 4 = 48

**2. Some equations are solved on the basis of a certain system. On the same basis, find out the correct answer for the unsolved equation.**

**2 x 3 x 4= 432, 5 x 6 x 7= 765,**

**7 x 8 x 9 = 987, 2 x 5 x 7 = ? SSC (10+2) 2014**

(a) 572

(b) 752

(c) 725

(d) 257

**Answer:**

**3.If 3 x 9 x 7 = 379, 5 x 4 x 8= 584, then 1 x 2 x 3 = ? SSC (10 + 2) 2013**

(a) 123

(b) 231

(c) 213

(d) 132

**Answer:**

**4. If 526 = 9 and 834 = 9, then 716 = ? SSC (10+2) 2013**

(a) 20

(b) 15

(c) 9

(d) 12

**Answer:**

(d) As, 526 in 5 + 6 – 2 = 9 and 834 in 8 + 4 – 3 = 9 Similarly 716 in 7 + 6-1=12

**5. If ‘+’ means ‘minus’, ‘-’, means ‘multiply’, ‘÷’ means ‘plus’ and ‘x’ means ‘divide’, then**

**10 x 5 ÷ 3 – 2 + 3 = ? SSC (10 + 2) 2013**

(a) 5

(b) 53/3

(c) 21

(d) 36

**Answer:**

(a) ? = 10 x 5 ÷ 3 – 2 + 3 = 10 ÷ 5 + 3 x 2 – 3 (By question)

=2 + 3 x 2 – 3 = 2 + 6 – 3 = 8 – 3 = 5

**6. If – mean x, x means +, + means ÷ and ÷ means -, then 40 x 12 x 3 – 6 ÷ 60 = ? SSC (10+2) 2013**

(a) 44

(b) 16

(c) 7.95

(d) 4

**Answer:**

(d)40 x 12 + 3 – 6 ÷ 60

According to the question, putting the real values of signs,

40 + 12 ÷ 3 x 6 – 60

= 40 + 4 x 6 – 60

= 40 + 24 – 60 = 64 – 60 = 4

**7. If 4 x 6 x 9 = 694, 5 x 3 x 2 = 325, then 7 x 8 x 2 = ? SSC (10 + 2) 2013**

(a) 729

(b) 872

(c) 827

(d) 279

**Answer:**

**8. If 2463 = 36 and 5552 = 30, then 6732 = ? SSC-(10 + 2) 2013**

(a) 32

(b)36

(c) 34

(d)39

**Answer:**

(a) As, 2463–>(2 + 4 + 6) x 3 = 12 x 3 = 36

and 5552–> (5 + 5 + 5) x 2 = 15 x 2 = 30

Similarly, 6732–>(6 + 7 + 3) x 2 = 16 x 2 =[32]

**Practice Exercise**

**1.If x means -, + means ÷, – means x and ÷ means +, then 15 – 2 ÷ 900 + 90 x 100 is equal to**

(a) 190

(b) 180

(c) 90

(d) -60

**2.If + means ÷,÷ means-, – means x, x means +, then 12 + 6 ÷ 3 – 2 x 8 is equal to**

(a) – 2

(b) 2

(c) 4

(d) 8

**3.If x means ÷, – means x, ÷ means + and + means – then (3-15÷19) x 8 + 6 is equal to**

(a) -1

(b) 2

(c) 4

(d) 8

**4.If ÷ means x, x means +, + means – and – means ÷, find the value of 16 x 3 + 5 – 2 ÷ 4.**

(a) 9

(b) 10

(c) 19

(d) 12

**5.If + means -, – means x, ÷ means + and x means ÷, then 15-3+10 x 5÷5 is equal to**

(a) 5

(b) 22

(c) 48

(d) 52

**6.If x means +, + means ÷, – means x and ÷ means – then 8 x 7 – 8 + 40 ÷ 2 is equal to**

(a) 1

(b) 7 2/5

(c) 8 3/5

(d) 44

**7.If + means -, – means x, ÷ means + and x means ÷ then 25 – 3 + 15 x 5 ÷ 5 is equal to**

(a) 5

(b) 62

(c) 77

(d) 12

**8.If + means -, – means x, x means ÷ and ÷ means +, then what is the value of 40 ÷ 360 x 24 – 4 + 18 is equal to**

(a) 118

(b) 82

(c) 72

(d) 90

**9.If $ means +, # means -, @ means x and * means ÷, then what is the value of 16 $ 4 @ 5 # 72 * 8?**

(a) 25

(b) 27

(c) 29

(d) 36

**10.If + means divided by, – means add, x means minus and / means multiplied by, what will be the value of the following expression?****[{(17×12)-(4/2)}+ (23-6)]/0**

(a) Infinite

(b)0

(c) 118

(d) 219

**11.If Q means ‘add to’, J means ‘multiply by’, T means ‘subtract from’ and K means ‘divide by’, then 30 K2 Q 3 J 6T 5 is equal to
**(a) 18

(b) 28

(c) 31

(d) 103

**12.If ÷ means +, – means ÷,x means – and + means x, then (36 x 4)-8 x 4/4 + 8 x 2 + 16 ÷ 1 equal to**

(a) 0

(b) 8

(c) 12

(d) 16

**13. If + means ‘minus’, x means ‘divided by’, ÷ means “plus’ and – means ‘multiplied by’, then which of the following will be the value of the expression 252 x 9 – 5 + 32 ÷ 92?**

(a) 95

(b) 168

(c) 192

(d) 200

**14. If P means ‘division’, T means ‘addition’, M means ‘subtraction’ and D means ‘multiplication’, then what will be the value of the expression 12 M 12 D 28 P 7 T 15 ?**

(a) – 30

(b) – 15

(c)-21

(d) 45

**15. If P means x, R means +, T means ÷ and S means -, then 18 T 3 P 9 S 8 R 6 is equal to **

(a)-1 1/3

(b)2/3

(c) 46

(d) 52

**16. If + stands for ‘division’, ÷ stands for ‘multiplication’, x stands for ‘subtraction’, – stands for ‘addition’, which one of the following is correct?**

(a)18 ÷ 6 x 7 + 5 – 2=22

(b)18 x 6+ 7 ÷ 5 – 2 =16

(c)18 ÷ 6 – 7 + 5 x 2 = 20

(d)18 + 6 ÷ 7 x 5 – 2 =18

**17. If “x’ stands for ‘addition’, “<’ for ‘subtraction’, + for division’, > for ‘multiplication, ‘-’for ‘equal to,‘÷’ for ‘greater than’ and ‘=’ for less than’, then state which of the following is true.**

(a)3 x 4 > 2 – 9 + 3 < 3

(b)5 x 3 < 7 ÷ 8 + 4 x 1

(c)5 > 2 + 2 =10 < 4 x 8

(d)3 x 2 < 4 ÷ 16 > 2 + 4

**18. If “+’ stands for ‘division’, ÷ stands for ‘multiplication’, x stands for ‘subtraction’ and – stands for ‘addition’, which one of the following is correct?**

(a) 18 ÷ 6 x 7 + 5 – 2 =22

(b) 18 x 6 + 7 ÷ 5 – 2 =16

(c) 18 ÷ 6 – 7 + 5 x 2 = 20

(d) 18 + 6 ÷ 7 x 5 – 2=18

**19. If – means ÷, + means x, ÷ means -, x means +, then which of the following equations is correct?**

(a)52 ÷ 4 + 5 x 8 – 2 =36

(b) 43 x 7 ÷ 5 + 4 – 8 =25

(c) 36 x 4 – 12 + 5 ÷ 3 = 420

(d) 36 – 12 x 6 ÷ 3 + 4 = 60

**20.**

**21. If ‘-’ stands for ‘division’, “+’ for ‘multiplication’, ÷ for ‘subtraction’ and x for ‘addition’, which one of the following equations is correct?**

(a) 6 + 20 -12 ÷ 7 -1 = 38

(b) 6 – 20 ÷ 12 x 7 +1 = 57

(c) 6 + 20-12 ÷ 7 x 1 = 62

(d) 6 ÷ 20 x 12 + 7 – 1 = 70

**Directions (Q. NOS. 22-25) Read the information carefully and answer the questions that follow.**

**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.**

**22. (cd + ef) x be is equal to**

(a) 684

(b) 816

(c) 916

(d) 1564

**23. dc x f – (bf – d) x d is equal to**

(a) abb

(b) ade

(c) bce

(d) bef

**24. baf ÷ bf x d is equal to**

(a) df

(b) cb

(c) be

(d)d

**25. bee + fg – (ca x h /be) is equal to**

(a) bhc

(b) bic

(c) bib

(d) bja

**26. Some equations are solved on the basis of a certain system. On the same basis, find out the correct answer for the unsolved equation. SSC (10 + 2) 2011**

**4 x 6 x 9= 649**

**7 x 3 x 2 = 372**

**8 x 9 x 4=?**

(a) 489

(b) 849

(c) 948

(d) 984

**27. Which of the following interchanges of signs would make the given equation correct? SSC (10 + 2) 2011**

**24+ 6 x 3 ÷ 3 – 1 = 14**

(a) + and x

(b) x and –

(c) ÷ and +

(d) – and ÷

**Answers**

**Hints & Solutions**

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