8.Mathematical Operations

Questions on Mathematical operations will first start with either defining a new meaning to existing symbols or define a new symbol and its mathematical meaning.

You are then required to evaluate the value of an expression by assuming the meaning of the symbols as defined in the question. The following questions will make this question type clear to you.

Illustration 1:If '+' means '-', '-' means '¥', '¥' means 'Π', and 'Π' means '+' then which of the following will be the value of the expression?

32 + 8 ¥ 2 - 3 Π 4

(a) 12

(b) 20

(d) 24

Ans .

(d) 24

Explanation :
Putting the changed signs, the expression can be rewritten as
32 - 8 Π 2 ¥ 3 + 4
Using BODMAS rule, we have
=32 - 4 ¥ 3 + 4
=32 - 12 + 4 = 24
Hence, the correct option is (d).

Illustration 2: If A implies '+', B implies '-', C implies '¥', D implies 'Π', then calculate the value of the expression 2A3B4C5D1.

(a) 15

(b) 0

(d) -12

Ans .

Explanation :
Using the proper signs, the above expression can be written as 2 + 3 - 4 ¥ 5 Π 1
=5 - 20 = -15
Hence, option (c) is correct

Illustration 3: Which of the following changes would make the given expression correct?

4 + 4 ¥ 4 - 4 #928 4 = 4

(a)'+' and '¥'

(b) '-' and '#928'

(d) both 'b' and 'c'

Ans .

(d) both 'b' and 'c

Explanation :
By making inter-changes given in 'a' we get the expression as:
4 ¥ 4 + 4 - 4 #928 4 = 4 which is false.
By making interchanges given in 'b', we get expression as
4 + 4 ¥ 4 #928 4 - 4 = 4 which is true.
By making interchanges given in option 'c', we get the expression as
4 ? 4 ¥ 4 - 4 + 4 = 4 which is also true.
Hence, option (d) is correct.

Illustration 4: If A"B means add B to A, A'B implies subtract B from A, A@ B implies divide A by B, A*B means multiply A with B.

If a train travels with a speed of S₁ from point A to B and returns with a speed of S₂. The average speed will be represented using the above explained notations?

(a) (2*S₁"S₂)/(S₁"S₂)

(b) (2*S₁*S₂)/(S1"S₂)

(d) (2*S₁@S₂)/(S₁'S₂)

Ans .

(b) (2*S₁*S₂)/(S1"S₂)

Explanation :
We know that the formula for average speed is given by 2S₁S₂/(S₁ + S₂)
Hence the correct option is (b).

Illustration 5: If (l, m, n) is represented as v [(l + 1)(m + 1)/(n + 1)]: What is the value of (48, 63, 80)?

(a) 56/9

(b) 55/9

(d) 7

Ans .

(a) 56/9

Explanation :
Putting the value in the above equation we get /[(48 + 1)(63 + 1)/(80 + 1)] =/(49 ¥ 64/81) = (7 ¥ 8)/9 = 56/9 Hence, the correct option is (a).

EXERCISE

Directions for Questions 1 to 5:

If a + b implies a - b

a - b implies a ¥ b,

a ¥ b implies a Π b

a Π b implies a + b

Q.1

Calculate 5 + 8 - 25 ¥ 5 Π 40

(a) 5

(b) -5

(d) 10

Ans .

(a) 5

Explanation :
The expression will become 5 -8 ¥ 25 Π 5 + 40.
Using the BODMAS rule we will get:
5 - 40 + 40 = 5. Hence, option (a) is correct

Q.2

With which statement can you find the value of 8?

(a) 1 + 2 - 6 ¥ 3 Π 8

(b) 1 - 2 + 6 ¥ 3 Π 8

(d) none of these

Ans .

(b) 1 - 2 + 6 ¥ 3 Π 8

Explanation :
Looking at option (b), we will get, 1- 2 + 6 ¥ 3 Π 8 becomes 1 ¥ 2 - 6 Π 3 + 8 = 8. Hence, option (b) is the correct answer.

Q.3

Which of the following is true?

(a) 6 + 2 - 3 ¥ 1 Π 4 = 12

(b) 10 + 4 - 3 ¥ 1 Π 2 = 5

(d) none of these

Ans .

Explanation :
Option (c) gives us 6 - 4 ¥ 2 Π 2 + 1= 3. Hence, this is correct.

Q.4

Which of the following is true?,/br> (1 + 2 - 3 ¥ 1 Π 4)/(4 + 5 - 4 ¥ 2 Π 1) =

(a) -1/5

(b) 1/5

(d) none of these

Ans .

(b) 1/5

Explanation :
(1 + 2 -3 ¥ 1 Π 4)/(4 + 5 - 4 ¥ 2 Π 1) ? (1- 2 ¥ 3 Π 1 + 4)/(4 - 5 ¥ 4Π 2 + 1) = -1/-5 =1/5. Hence, (b) is the answer

Q.5

Find the value of (4 + 3 - 5 ¥ 1 Π 4) ¥ (5 + 2 - 3 ¥ 1 Π 4)

(a) -7/3

(b) -8/3

(d) none of these

Ans .

(a) -7/3

Explanation :
(4 + 3 - 5 ¥ 1 Π 4) ¥ (5 + 2 - 3 ¥ 1 Π 4) = (4 - 3 ¥ 5 Π 1 + 4) Π (5 - 2 ¥ 3 Π 1 + 4) = -7/3. Hence, option (a) is the answer.

Directions for Questions 6 to 8: If 'a' means+, 'b' means -, 'c' means ¥ and 'd' means Π.

Q.6

Calculate the value of 6a7b8c8d2

(a) -17

(b) 12

(d) none of these

Ans .

Explanation :
6a7b8c8d2 = 6 + 7 - 8 ¥ 8 Π 2 = -19. Hence, (c) is the answer.

Q.7

Calculate (8c7)c(7a5)b(6d3)d(3b2)

(a) 650

(b) 375

(d) none of these

Ans .

Explanation :
(8c7)c(7a5)b(6d3)d(3b2) becomes 56 ¥ 12 - 2 Π 1 = 670. Option (c) is the answer.

Q.8

What is the value of 9a10b11c15d0

(a) 1

(b) 2

(d) undefined

Ans .

(d) undefined

Explanation :
The expression contains a division by 0, hence is undefined. Option (d) is the answer.

Directions for Questions 9 to 12: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?

Q.9

Given interchanges, signs '-' and 'Π' and numbers 4 and 8 (on the LHS)

(a) 4 - 8 Π 12 = -23/4

(b) 4 Π 8 - 2 = 8

(d) none of these

Ans .

(d) none of these

Explanation :
None of these, i.e. option (d) is correct

Q.10

Given interchanges: 3 and 2, Π and -

(a) 1 + 3 ¥ 4 - 2 Π 1 = 5

(b) 1 + 2 - 3 ¥ 8 Π 4 = 9

(d) none of these

Ans .

(b) 1 + 2 - 3 ¥ 8 Π 4 = 9

Explanation :
The given expression will become 1 + 3 Π 2 ¥ 8 - 4 = 9. Option (b) is the answer

Q.11

Given interchanges: 0.4 and 0.04

(a) 1 + 2 - 0.04 ¥ 0.4 = 1

(b) 0.4 + 0.04 - 2 ¥ 2 = 1.76

(d) none of these

Ans .

(d) none of these

Explanation :
Checking each of the four options we will get none of these the answer. Hence, option (d) is the answer.

Q.12

Given interchanges, ¥ and +, 10, 1

(a) 5 ¥ 1 + 10 - 2 = 5

(b) 8 + 8 - 10 ¥ 1 = 75

(d) 3 + 4 - 12 ¥ 1 Π 10 = 10

Ans .

(d) 3 + 4 - 12 ¥ 1 Π 10 = 10

Explanation :
Option (d) becomes correct.

Q.13

Find out the two signs to be interchanged for making the following equation to be correct: 5 + 3 - 5 ¥ 5 Π 1 = 15

(a) ¥ and -

(b) ¥ and +

(d) + and -

Ans .

(a) ¥ and -

Explanation :
If the signs are changed according to the first option the equation is satisfied. Hence, option (a) is correct

Q.14

Which of the following two signs need to be interchanged to make the given equation correct? 4 + 2 - 5 ¥ 7 Π 12 = - 21

(a) Π and -

(b) Π and +

(d) ¥ and -

Ans .

(b) Π and +

Explanation :
If the signs are changed according to the second option the equation is satisfied. Hence, option (b) is correct.

Q.15

Insert proper arithmetical signs between the figures in the following equation 12_4_2_1 = 24

(a) -, Π, ¥

(b)¥, Π, ¥

(d) none of these

Ans .

(b)¥, Π, ¥

Explanation :
Insertion of ¥, Π, ¥ in that order will make 12 ¥ 4 Π 2 ¥ 1 = 24. Hence, option (b) is correct

Q.16

If 'a' implies '+', 'b' implies '-', 'c' implies '¥ ' and '¥' implies 'Π', insert proper letter between the figures in the following equation 40__ 20__ 30__6 = 55

(a) a, b, c

(b) b, c, d

(d) d, b, a

Ans .

Explanation :
40 + 20 - 30 Π 6 = 60 - 5 = 55. Hence, a, b, d. Option (c) is correct.

Q.17

If ''+' implies '-','-' implies 'Π', '¥' implies 'Π' and 'Π' implies '+' , then insert the proper signs between the figures in the given equation 12__8__4__2__1 = 15

(a) Π, ¥, -, +

(b) Π, -, +, ¥

(d) -, +, Π, ¥

Ans .

(a) Π, ¥, -, +

Explanation :
12 Π 8 ¥ 4 - 2 + 1 would mean 12 + 8 Π 4 ¥ 2 - 1 = 12 + 4 - 1 = 15. Hence, the order given in option (a) is correct

Q.18

If a = +, b = -, g = ¥, d = Π Insert the proper notations between the figures in the following sum 10__8__6__4__2 = 6

(a) b, a, d, g

(b) a, b, g, d

(d) none of these

Ans .

(b) a, b, g, d

Explanation :
Option (b) is correct.

Directions for Questions 19 to 21:

If 12 + 2 = 6
27 + 9 = 3
and 15 + 5 = 3.

Q.19

Calculate the value of 182 + 13

(a) 14

(b) 1.4

(d) none of these

Ans .

(a) 14

Explanation :
It is clear that the + sign means Π. Hence
182 + 13 would give us a value of 14. Hence, (a) is the answer

Q.20

Calculate the value of 50 + [50 + 10]

(a) 10

(b) 100

(d) 5

Ans .

(a) 10

Explanation :
50/5 = 10. Hence, (a) is the answer.

Q.21

Calculate (10 + (6 + (3 + (2 + 1))))

(a) 4

(b) 5

(d) none of these

Ans .

(a) 4

Explanation :
10/2.5 = 4. Hence, correct option is (a).

Directions for Questions 22 to 25:

If 3 ¥ 4 = 5
5 ¥ 12 = 13
Then solve the following question.

Q.22

Calculate the value of 7 ¥ 24

(a) 12

(b) 48

(d) none of these

Ans .

(a) 4

Explanation :

7 ¥ 24 = = 25. Hence, option (d) is the answer.

Q.23

Calculate the value of 8 ¥ 9

(a) 145

(b) 12.041

(d) 12.5

Ans .

(b) 12.041

Explanation :
8 ¥ 9 = = 12.041. Hence, option (b) is the answer.

Q.24

9 ¥ ? = 41

(a) 35

(b) 30

(d) none of these

Ans .

Explanation :
The required value will be got by the square root of the difference between 412 and 9² Æ 1681 - 81 = 1600. Hence, the required answer is 40. Correct answer is option (c).

Q.25

Obtain {3 ¥ (5 ¥ 6)} = ?

(a) 5

(b) 8.366

(d) none of these

Ans .

(b) 8.366

Explanation :
The required value would be square root of 61 + 9 = 8.366. Hence, option (b) is the answer

Directions for Questions 26 to 30:

If M means greater than
N means equal to
O means not less than
P means less than
Q means not equal to
and R means not greater than

Q.26

If yPz and zNa, then which of the following is true?

(a) yMa

(b) yPa

(d) none of these

Ans .

(b) yPa

Explanation :
yPz means that y is less than z and zNa means z = a. Thus, y is less than a Æ yPa. Option (b) is correct

Q.27

If 10aM6b and 12bM20c

(a) 5aMc

(b) aM5c

(d) none of these

Ans .

(d) none of these

Explanation :
10a is greater than 6b. and 12b is greater than 20c Æ 6n is greater than 10c. Thus 10a is greater than 10c or a is greater than c. Option (d) is correct

Q.28

If aP0 and b+2Pa, then which of the following is true?

(a)bM - 2

(b)bN - 2

(d) none of these

Ans .

Explanation :
a is negative and b + 2 is less than a implies that b must be below -2. Hence, option (c) is correct

Q.29

If sOt, tRu and tRv then which of the following could be true about s and u/v or u and v?

(a) sMu

(b) sPv

(d) can`t be determined

Ans .

(d) can`t be determined

Explanation :
Nothing can be said about the relationships between s, u or v or for that matter about u and v. Hence, cannot be determined. The correct answer is option (d).

Q.30

If |t - u| M0, then which of the following is/are true

(a) sMt

(b) tMs

(d) (a), (b) and (c) could be true

Ans .

(d) (a), (b) and (c) could be true

Explanation :
Since the modulus value is always positive, all the three, i.e. the first, second and third relationships are possible. Hence, option (d) is correct.

Directions for Questions 31 to 33:

If aAb implies a + b
aMb implies a - b
aPb implies a ¥ b
aQb implies a Π b

Q.31

Which of the following equations is correct?

(a) 30Q10A4P2M2 = 15

(b) 5P2A4Q2P2 = 14

(d) none of these

Ans .

(b) 5P2A4Q2P2 = 14

Explanation :
Option (b) is correct since we will get 10 + 4 = 14.

Q.32

Calculate 5A6M3P4Q8

(a) 10

(b) 9

(d) 10.5

Ans .

Explanation :
11 - 1.5 = 9.5. Option (c) is correct.

Q.33

Calculate (2A3M4P5)P(5M6P8Q4)

(a) -105

(b) -120

(d) none of these

Ans .

(d) none of these

Explanation :
(-15)(-7) = 105. Hence, option (d) is correct.

Directions for Questions 34 to 36:

A"B implies A + B
A'b implies A - B
A@B implies A Π B
A*B implies A ¥ B

Q.34

A man travels with a speed of f from A to B and returns from B to A with speed h. What is the average speed of the man over the entire journey?

(a) 2f'h/f'h

(b) 2f@h/f"h

(d) none of these

Ans .

(d) none of these

Explanation :
It can be seen that none of these is correct. Hence, (d) is the answer

Q.35

Jadugar has a jadoo box which has a length, breadth and height which can be represented by 'x', 'a', 'c' respectively. What is the formula for its total surface area?

(a) 2[(x'a)*(a"c)*(x"c)]

(b) 2[(x*a)"(a*c)"(x*c)]

(d) none of these

Ans .

(b) 2[(x*a)"(a*c)"(x*c)]

Explanation :
The surface area of a cuboid box is equal to twice the areas of each of the sides. Hence, option (b) is correct.

Q.36

At the Wave cinemas in Sector 18 in Noida, charges for parking are as follows

On a particular day there were '25' cycles, '40' scooters and '100'cars parked at the stand, what was the amount collected in that particular day?

(a) (25"2)*(40"5)*(100"20)

(b) (25'2)@(40'5)@(100'20)

(d) none of these

Ans .

Explanation :
The correct answer is option (c).

Directions for Questions 37 to 41:

If AXB implies A² + B²
AYB implies A² - B²
AZB implies (A + B)²
AMB implies (A - B)²

Q.37

Calculate the value of (4X5)Y(6X7)

(a) 5544

(b) -5544

(d) none of these

Ans .

(b) -5544

Explanation :
41² - 85² = 1681 - 7225 = -5544. Hence, option (b) is correct answer

Q.38

Calculate the value of (373)M(413)

(a) 1600

(b) 900

(d) 2500

Ans .

(a) 1600

Explanation :
(- 40)² =1600. Hence, option (a) is correct answer

Q.39

If (AMB) = (AZB) then which of the following is true.

(a) A - B = 0

(b) A²= B²

(d) A = 0

Ans .

Explanation :
The given expression tells us that (A - B)² = (A + B)². This can only occur when 2AB = - 2AB= 0. Hence, option (c) is correct.

Q.40

Calculate (3Z4) - (5M5)

(a) 49

(b) 25

(d) none of these

Ans .

(a) 49

Explanation :
7² = 49. Hence, correct answer is option (a)

Q.41

Calculate the value of (2Z2)M(4Y4)

(a) 16

(b) 256

(d) none of these

Ans .

(b) 256

Explanation :
16² = 256. Hence, correct answer is option (b).

Directions for Questions 42 and 43:

If '*' indicates either '+' or '¥', solve the following questions.

Q.42

What is the maximum value of 1*2*3*4*5*6*7

(a) 5040

(b) 5041

(d) none of these

Ans .

(b) 5041

Explanation :
The maximum value will be obtained when we use multiplication between 2 to 7 and addition between 1 and 2. Hence, option (b) is the answer.

Q.43

What is the minimum value of 1*2*3*4

(a) 10

(b) 9

(d) 14

Ans .

(b) 9

Explanation :
The minimum value will be got if we use a multiplication between 1 and 2 and addition between 2, 3, and 4. The value will be 1 ¥ 2 + 3 + 4 = 9. Hence, option (b) is the answer

Directions for Questions 44 to 46:

If A indicates >
B indicates <
C indicates =
D indicates p
E indicates +
F indicates -
G indicates *
H indicates Π

Q.44

Which of the following is false?

(a) (5E7)A(4E3)A(1E2)

(b) (5E6)A(6E12)A(13E6)

(d) all of these are false

Ans .

(b) (5E6)A(6E12)A(13E6)

Explanation :
It can be seen that options 1 and 3 are correct, but option (b) is wrong. Hence, option (b) is the correct answer

Q.45

Calculate (32H(2H(6H3)))

(a) 16

(b) 32

(d) none of these

Ans .

(b) 32

Explanation :
32/1 = 32. Hence, option (b) is correct.

Q.46

Calculate 5E3F4G6H2

(a) 1.5

(b) 1

(d) none of these

Ans .

Explanation :
5 + 3 – 12 = -4. Hence, option (c) is correct.

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Part 2:Reasoning Question Types from other MBA Exams

8.Mathematical Operations

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