**Campus Recruitment – Logical Reasoning – **Symbol Based Operations

Contents

**Concepts**

In this type of question an equation is given in which operators are coded into symbols. You will be given the relationship between the symbol and operator. Using that relationship you need to convert the symbol based equation into mathematical equation. Thereafter solve the equation with the help of VBODMAS rule.

**Approach**:

1) Study the relations of the symbols and mathematical operations.

2) Convert the symbols into mathematical operations.

3) Use VBODMAS rule, if necessary, for simplification.

4) Calculate the given expression.

5) Find the final value after calculation, which is the required answer.

**Conceptual Examples**

If + means -, – means x, x means÷, ÷ means + then solve the following questions.

1) 4÷8+ 2 x 3-6 = ?

**Explanation**: After interchanging the operators, we get

=>4 + 8- 2 ÷ 3 x 6

(Applying VBODMAS Rule)

=> 4+8—2/3 x 6 =>4 + 8-4=>8.

2) 16 x 8 – 6 + 15÷27 x 9

**Explanation**: After interchanging the operators, we get

=>16÷ 8 x 6-15 +27 ÷9

Applying VBODMAS Rule

=> 2 x 6 -15 + 3 => 15-15 = 0

**Exercise**

1) If + means -, – means x, x means ÷, ÷ means +.

Then (256 x 16 ÷ 49 x 7 +125 x 5 – 2 ÷289 x 17) = ?

a) 10 b) -15 c) -10 d) -17 e) 15

2) If + means -, – means +, ÷ means x, x means ÷. Then what is the value of (25 – 5 +5)÷ (3 ÷ 7 + 21)?

a) 1 b) 0 c) 2 d) 4 e) none of these

3) If + means -, – means x, x means ÷ and ÷ means +. Then (278 + 8 x 2 – 7 ÷ 316 + 7 x 28 – 364) = ?

a) 275 b) 475 c) 375 d) 575 e) none of these

4) Interchange the signs + and -, numbers 1 and 2. Based on this information, which of the following is correct?

a)12 + 21-12 = 21 b) 21 + 21 +12 = 21

c) 12 + 12-21 = 12 d) 21 -21 -21 = 33

e) 21 -12 – 12 = 50

5) If + means x, ÷ means – , x means ÷ and – means + then what will be the value of the following expression. 22 x 2 – 6 ÷ 7 + 36 x 18

a) 5 b) 15 c) 25 d)3 e)23

6) If A means +, B means -, C means x, D means ÷. Then which of the following statements is correct?

a) 10A8B7C4D2 = 6 b) 12C6A3C9D3 = 71 c)14D2C9B5C5 = 38 d) 16B5A15D3C4 = 21 e) none of these

7) Interchange the signs + and x; numbers 5 and 7. Based on this, find the value of, 5 x 15 + 7 – 20 x 6 = ?

a) 68 b) 78 c) 88 d) 98 e) 58

8) Interchange the signs – and ÷ , numbers 4 and 6. Based on this, simplify the expression,16 ÷ 8-6+12 ÷ 6.

a) 10 b) 20 c) 25 d)30 e) 15

9) If 6 Δ 5 = 341 and 7 Δ 3 = 370 then 10 Δ 8 = ?

a) 189 b) 962 c) 1024 d) 1512 e) 764

10) If 6 @ 4 = 20, and 9 @ 6 = 45 then 16 @ 11 =?

a) 125 b) 112 c) 135 d) 161 e)none

11) If x $ y = (x + y) (x – y) and a Δ b = a + b then find the value of (6 $ 3) x (9 Δ 3)?

a) 423 b) 234 c) 324 d) 824 e) none

12) If A⊕ B=(A-B)² and A%B=(A+B)².Then find the value of (16⊕12)x(l8%12) + 10=?

a) 1331 b) 1404 c) 1234 d) 1440 e) none

13) If – means x, x means +, + means ÷ and ÷ means -, then (52 +13) x (192 ÷ 86 x 46 – 21) = ?

a) 976 b) 1706 c) 1176 d) 1617 e) 1076

Directions (14 to 18): In a certain code language,+ means ÷, ÷ means x, x means -, – means +. Using this information, simplify the following expressions.

14) 10 x 5-125 + 5 ÷ 2-256 = = ?

a) 311 b) 113 c) 211 d) 131 e) 321

15) 106 -1331 +121 -56 ÷ 42 : = ?

a) 2649 b) 2946 c) 2496 d)2469 e) 2964

16) (44 – -22 ÷ 4 x 12- -36 + 4) + 3

a) 42 b) 43 c) 44 d) 46 e) none

17) (10 x 3 -2 ) x (12 — 3 + 3 x 2) = ?

a) 2 b) -2 C)1 d)-l e) 0

18) 12 ÷ 4 – 16 x 32 – 64 +16 = = ?

a) 32 b) 34 c) 63 d) 38 e) 36

Directions(19-23): Study the following sequence

carefully and answer the questions given below.

2K#7A9$3@LK62!9<8M 2

19) Find the next term in the following series. .

2 K #, 7 A $, 3 L!, ?

a) 9 < M b) 9M∧ C) 6M∧ d) 6∧M e) 9 < 2

20) Four of the following five are alike in certain way. Find the odd. one.

a) 7#K b) 9@3 c) 6#A d) 8L e) 2!M

21) How many digits are there which are immediately followed by a letter but not preceded by symbol?

a) 1 b) 2 c) 0 d) 3 e) 4

22) What is the 10th element to the left of 8th element from right end?

a) # b) M c) 7 d) K e) 2

23) What is the 6* element to the right of 16* element from right end?

a) 6 b) 2 c)! d) K e) L

Directions(24-28): Study the following sequence carefully and answer the questions that follow. 8%ML29@61#KN$73?2!P5

24) What is the 9th element to the right of 11th element from the left end?

a) 5 b) 8 c)% d) P e)M

25) Four of the following five are alike in a certain way. Find the odd one.

a) 8 M 2 b) 6# N c) 7 ? ! d)9@6 e)3 2 P

26) How many symbols are there which are preceded by a number and followed by a letter?

a) 2 b) 3 c) 1 d) 0 e) more than 3

27) Find out the next group in the series given below.

8%2, 9@6, 1#7, .

a) 9 1 # b) 2 ! P c) 3 ? 2 d)! P 5 e) 2 ? 3

28) How many consonants are there, which are immediately preceded by number but not immediately followed by a symbol?

a) 1 b) 5 c) 0 d) 2 e) 3

Directions(29-33): In an instruction system, the different computation processes are written as follows.

a) X%Y!Z means ‘X is added to the product of Y and Z’.

b) XΔY□Z means ‘product of Y&Z is subtracted from X.

c) X ↑ Y ↓ Z means ‘product of X and Y is divided by Z’.

d) X $Y #Z means ‘Z is multiplied by the sum of X & Y’. Based on the above information, simplify the following expressions.

29) 50 ↑ 40 ↓ 200 = K; 16% 12! K =?

a) 136 b) 256 c) 326 d) 112 e) 126

30) 16 $ 8 # 24 =?

a) 476 b) 675 c) 529 d) 576 e) 676

31) 48 Δ 15 □ 3 = ?

a) 2 b) 6 c)3 d) 5 e) 4

32) 62 % 24 ! 12 = ?

a) 225 b) 312 c) 350 d) 250 e) 262

33) 34 ↑ 33 ↓ 11=?

a) 201 b) 103 c) 122 d) 104 e) 102

34) c means +, d means -, e means ÷, f means x, then which of the following is true.

a) 13 d 14 c 15 f 20 e 8 = 14 b) 18 e 12 c 14 d 5 e 6 = 29

c) 24 f 6 c 2 d 13 c 4 = 36 d) 8 e 4 f 3 f 6 d 4 = 27

e) 14f3c5d6e2 = 44

35) L – M means L is equal to M.

L_M means L is smaller than M.

L & M means L is greater than M.

L # M means L is greater than or equal to M.

L Λ M means L is smaller than or equal to M.

Statements: B # A, B_C, C & D

Conclusions: (I) A_C (II) C&D (III) DC

a) only (I) is true

b) only (II) is true

c) only (III) is true

d) only (II) and (ID) true

e) (I), (II) and (III) are true

36) L – M means L is equal to M.

L_M means L is smaller than M.

L & M means L is greater than M.

L # M means L is greater than or equal to M.

L Λ M means L is smaller than or equal to M.

Statements: P∧Q,Q-R, R&S

Conclusions: (I) Q & S (II) P Λ R (HI) P_S

a) only (I) is true

b) only (II) is true

c) only (III) is true

d) only (I) and (II) true

e) only (II) and (III) true

37) L – M means L is equal to M.

L_M means L is smaller than M.

L & M means L is greater than M.

L # M means L is greater than or equal to M.

L Λ M means L is smaller than or equal to M.

Statements: E_F, F&G, G-H

Conclusions: (I) E _G (II) E # H (III) F & H

a) only (I) is true

b) only (II) true

c) only (III) true

d) only (I) and (II) true

e) none of these

**Explanations**

1) c; After interchanging the operators, we get,

= 256 ÷ 16 + 49 ÷ 7-125 ÷ 5 x 2 + 289÷17

= 16 + 7 – 25 x 2 + 17 => 23 + 17 – 50 => 40 – 50 = -10

2) b; After interchanging the operators, we get

(25 + 5 – 5) x (3 x 7 – 21) => (30 – 5) x (21 – 21) =» 25 x 0 = 0

3) b; After interchanging the operators, we get 278 – 8 ÷ 2 x 7 + 316 – 7 ÷ 28 x 364

278- 4 + 7+ 316-1/4 x 364 =>278 – 28 + 316 – 91

=>250 + 316-91 = 475

4) c; Here, + means – and 1 means 2 vice versa.

Option-a: 21-12 + 21≠21

Option-b: 12 -12 – 21≠ 21

Option-c: 21-21 + 12 = 12

Option-d: 12 + 12 + 12≠ 33

Option-e: 12 + 21 + 21 ≠ 50

5) d; 22 x 2 – 6 ÷ 7 + 36 x 18 = 22 ÷ 2 + 6 – 7 x 36 ÷ 18

11 + 6-7 x 2 = 11 + 6-14 = 17-14 = 3.

6) c; Interchange the symbols and apply VBODMAS. From option-c, 14 D 2 C 9 B 5 C 5 => 14 ÷2 x 9 -5 x 5 = 38 =>7 x 9-5 x 5 = 38=>63-25 = 38 (true)

Hence, option-c is correct choice.

7) b; Here, + means x, 5 means 7 and vice versa.

Then the expression will become 7 + 17 x 5-20 + 6.

=> 7 + 85 – 20 + 6 => 98 – 20 = 78.

8) b; Here, – means ÷, 4 means 6 and vice versa.

Then the expression will be,

14-8 ÷ 4 +12-4=> 14-2 +12-4 = 20

9) d; 6 Δ 5 => 6³ + 5³ = 341;

7 Δ 3 => 7³+ 3³ = 370

10 Δ 8 => 10³ + 8³ = 1512.

10) c; 6 @ 4 => 6³ – 4³ = 36 -16 = 20

9 @ 6 => 9³ – 6³ = 81 – 36 = 45

16 @ 11 => 16³ – 11³ = 256 -121 = 135.

11) c; 6 $ 3 => (6+3)(6-3) => 9×3 = 27

9 Δ 3 =>(9+3) = 12

(6 $3)x(9 Δ 3) = 27×12 = 324

12) d; 16 ⊕12 => (16-12)² = 4² = 16

8 % 12 => (18+12)² = 30² = 900

16 x 900 ÷10 => 16×90 = 1440

13) e; Interchange the symbols. Apply VBODMAS rule. i.e. (52÷13)+(192-86+46×21) => 4 +(192 – 86 + 966) => 1076

14) a; 10-5 + 125 ÷5 x 2 + 256 = 10 – 5 + 25 x 2 + 256 = 311

15) d; 106 +1331 ÷121 + 56 x 42 = 106 + 11 + 2352 = 2469

16) b;(44+22 x 4-12+36÷4)÷3=>(44+88-12+9 )÷3 = 129÷3=43

17) b; (10 – 3 + 2) – (12 + 3 ÷ 3 – 2) => 9 -11 = -2.

18) e; 12 x 4+16-32+64÷16 => 48 +16 – 32 + 4 = 36 .

19) b; The pattern in the series is, ‘number followed by letters and followed by next symbol in the series.Hence, the correct answer is ‘9M’.

20) b; Series pattern follows like, Number followed by symbol and followed by letters. Hence, the wrong sequence in the series is “9 @ 3”.

21) a; In this series pattern, there is one such digit which is immediately followed by a letter but not preceded by a symbol, i.e. 2 K. Hence, the answer is 1.

22) a; Let the 10th element from the left = 10L and

8th element from right = 8R (If both are either left or right, then subtract If one is left and other is right, then add).

Here, we have to combine both the values, because given, one is left and another is right. Then we get,

=> 10L + 8R => 18R

18R means 18th letter form right end i.e.#

23) d; Let the 6th element to the right = 6R and

16th element from right end = 16R’.

Here, both the letters are right, so subtract.

=> 6R+ 16R => 6R – 16R => 10R

10R means 10* letter from right end i.e. K.

24) a; 9th element to the right = 9R

11th element to the left = 11L

One is right and another one is left, so add.

=> 9R + 11L => 20L (20th element from left i.e. 5).

26) b; 8%M, 1#K, 2!P ; There are 3 such symbols which follow the pattern

27) c; The pattern in the series is, ‘symbol preceded by number and followed by number’.

.. Next number in the series is ‘3 ? 2’.

28) c; There are no such consonants which are immediately preceded by number but not immediately followed by symbol.

29) a; (50 x 40)÷200 => 2000 – 200 => K =10.

=> 16+(12 x 10) = 16 +120 =136

30) d; 24x(16 + 8) 24 x 24 = 576

31) c; 48-(15×3) => 48 -45 = 3

32) c; 62÷24 ! 12 = 62 + (24 x 12) = 62 + 288 = 350

33) e; (34 x 33)-11 = 1122÷11 = 102

34) e; From option-e, we have, 1 4 f 3 c 5 d 6 e 2 After changing to operators, we get, 14 x 3 +5 – 6 ÷ 2

Apply VBODMAS rule, 14 x 3+5-6/2=>42+5-3 =44

35) e; After changing the symbols, we get,

Statements: B≥ A, B < C, C > D.

Conclusions: A < C, C > B, D < C.

From given statements, conclusions (I), (II), III are true.

36) d; After changing the symbols, we get,

Statements: P≤Q,Q = R, R>S Conclusions: Q>S, P ≤ R, P<S

From the given statements, only conclusion (I) and (II) are true.

37) c; Statements: E<F, F>G, G = H Conclusions:E < G, E ≥ H, F > G.

From the above statements, only conclusion (III) is true.

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