Mathematical Operations Questions and Answers

Q: If "÷" denotes "multiplied by", "+" denotes "subtracted from", "-" denotes "added to" and "x" denotes "divided by", then which of the following equation is true?

Correct answer: 18 x 6 ÷ 8 - 12 = 36Replace every symbol by the operation it denotes: \( \div \to \times \), \( + \to \) subtracted from, \( - \to \) added to, \( \times \to \div \).The correct option becomes \( 18 \div 6 \times 8 + 12 \), and by BODMAS \[ 18 \div 6 \times 8 + 12 = 24 + 12 = \mathbf{36} \]The others fail: \( 5 \times 6 + 4 \div 3 \) becomes \( 12 - \tfrac{5}{6} = \tfrac{67}{6} \), not \( \tfrac{37}{6} \); and \( 6 \times 3 + 12 \div 3 \) becomes \( 36 - 2 = 34 \), not 21.

Q: If 25 + 5 ÷ 2 = 40 , and 35 + 5 ÷ 2 = 60 , then 45 + 5 ÷ 2 = ?

Correct answer: 80The rule is to take five from the first number and double the result: \( (25-5)\times2 = 40 \) and \( (35-5)\times2 = 60 \). So \[ (45-5) \times 2 = \mathbf{80} \]

Q: If "-" means "divided by", "+" means "multiplied by", "÷" means "added to", "x" means "subtracted from", then 11 ÷ 6 - 2 + 5 x 3 = ?

Correct answer: 23Replacing the words by their symbols gives \( 11 + 6 \div 2 \times 5 - 3 \), and by the usual order \[ 11 + 15 - 3 = \mathbf{23} \]

Q: If 13*45 = 29 , 24*58 = 41 , 74*32 = 53 , what should 97*47 be?

Correct answer: 72Each answer is the average of the two numbers: \( \tfrac{13+45}{2} = 29 \), \( \tfrac{24+58}{2} = 41 \), \( \tfrac{74+32}{2} = 53 \). So \[ \frac{97+47}{2} = \mathbf{72} \]

Q: If the signs + and / and the numbers 2 and 4 are interchanged, which one of the following four equations would be correct?

Correct answer: 2+4/6 = 8Exchanging the signs + and ÷, and the numbers 2 and 4, turns the left side into \( 4 \div 2 + 6 \), which is \[ 2 + 6 = \mathbf{8} \] None of the other equations balances after the same exchanges.

Q: If 18 (9) 3 and 36 (30) 5, then what is the value of A in 19 (A) 18?

Correct answer: 57The number in brackets is the product of the outer two divided by six: \( \tfrac{18\times3}{6} = 9 \) and \( \tfrac{36\times5}{6} = 30 \). So \[ A = \frac{19 \times 18}{6} = \mathbf{57} \]

Q: If 19 (36) 13 and 37 (81) 28, then what is the value of 'A' in 43 (A) 38?

Correct answer: 25The number in brackets is the square of the difference of the outer two: \( (19-13)^2 = 36 \) and \( (37-28)^2 = 81 \). So \[ A = (43-38)^2 = \mathbf{25} \]

Q: If "÷" denotes "multiplied by", "+" denotes "subtracted from", "x" denotes "added to" and "-" denotes "divided by",then 12 - 6 + 28 x 3 ÷ 9 = ?

Correct answer: 1Replacing the words by their symbols gives \( 12 \div 6 - 28 + 3 \times 9 \), and by the usual order \[ 2 - 28 + 27 = \mathbf{1} \]

Q: The following equation is incorrect. Which two signs should be interchanged to correct the equation? 15 x 12 + 40 ÷ 40 - 6 = 21

Correct answer: + and xExchanging + and × gives \( 15 + 12 \times 40 \div 40 - 6 \), which works out as \[ 15 + 12 - 6 = \mathbf{21} \]

Q: In a certain code language, '+' represents 'x', '-' represents '+', 'x' represents '÷' and '÷' represents '-'. What is the answer to the following question? 72 x 9 - 14 + 2 = ?

Correct answer: 36The code swaps the symbols: \( + \to \times \), \( - \to + \), \( \times \to \div \), \( \div \to - \). So \( 72 \times 9 - 14 + 2 \) is read as \( 72 \div 9 + 14 \times 2 \).Applying BODMAS to the decoded expression: \[ 72 \div 9 + 14 \times 2 = 8 + 28 = \mathbf{36} \]

Important Instructions

71.

If "÷" denotes "multiplied by", "+" denotes "subtracted from", "-" denotes "added to" and "x" denotes "divided by", then which of the following equation is true?

A.16 + 19 x 21 - 5 = 201
B.5 x 6 + 4 ÷ 3 = 37/6
C.6 x 3 + 12 ÷ 3 = 21
D.18 x 6 ÷ 8 - 12 = 36

Answer: D

Correct answer: 18 x 6 ÷ 8 - 12 = 36

Replace every symbol by the operation it denotes: \( \div \to \times \), \( + \to \) subtracted from, \( - \to \) added to, \( \times \to \div \).

The correct option becomes \( 18 \div 6 \times 8 + 12 \), and by BODMAS \[ 18 \div 6 \times 8 + 12 = 24 + 12 = \mathbf{36} \]

The others fail: \( 5 \times 6 + 4 \div 3 \) becomes \( 12 - \tfrac{5}{6} = \tfrac{67}{6} \), not \( \tfrac{37}{6} \); and \( 6 \times 3 + 12 \div 3 \) becomes \( 36 - 2 = 34 \), not 21.

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72.

If 25 + 5 ÷ 2 = 40 , and 35 + 5 ÷ 2 = 60 , then 45 + 5 ÷ 2 = ?

A.90
B.70
C.60
D.80

Answer: D

Correct answer: 80

The rule is to take five from the first number and double the result: \( (25-5)\times2 = 40 \) and \( (35-5)\times2 = 60 \). So \[ (45-5) \times 2 = \mathbf{80} \]

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73.

If "-" means "divided by", "+" means "multiplied by", "÷" means "added to", "x" means "subtracted from", then 11 ÷ 6 - 2 + 5 x 3 = ?

A.17
B.21
C.23
D.26

Answer: C

Correct answer: 23

Replacing the words by their symbols gives \( 11 + 6 \div 2 \times 5 - 3 \), and by the usual order \[ 11 + 15 - 3 = \mathbf{23} \]

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74.

If 13*45 = 29 ,
24*58 = 41 ,
74*32 = 53 ,
what should 97*47 be?

A.73
B.72
C.63
D.64

Answer: B

Correct answer: 72

Each answer is the average of the two numbers: \( \tfrac{13+45}{2} = 29 \), \( \tfrac{24+58}{2} = 41 \), \( \tfrac{74+32}{2} = 53 \). So \[ \frac{97+47}{2} = \mathbf{72} \]

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75.

If the signs + and / and the numbers 2 and 4 are interchanged, which one of the following four equations would be correct?

A.4/2+3 = 6
B.2+4/3 = 3
C.4+2/6 = 1.5
D.2+4/6 = 8

Answer: D

Correct answer: 2+4/6 = 8

Exchanging the signs + and ÷, and the numbers 2 and 4, turns the left side into \( 4 \div 2 + 6 \), which is \[ 2 + 6 = \mathbf{8} \] None of the other equations balances after the same exchanges.

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76.

If 18 (9) 3 and 36 (30) 5, then what is the value of A in 19 (A) 18?

A.33
B.57
C.75
D.96

Answer: B

Correct answer: 57

The number in brackets is the product of the outer two divided by six: \( \tfrac{18\times3}{6} = 9 \) and \( \tfrac{36\times5}{6} = 30 \). So \[ A = \frac{19 \times 18}{6} = \mathbf{57} \]

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77.

If 19 (36) 13 and 37 (81) 28, then what is the value of 'A' in 43 (A) 38?

A.49
B.36
C.25
D.16

Answer: C

Correct answer: 25

The number in brackets is the square of the difference of the outer two: \( (19-13)^2 = 36 \) and \( (37-28)^2 = 81 \). So \[ A = (43-38)^2 = \mathbf{25} \]

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78.

If "÷" denotes "multiplied by", "+" denotes "subtracted from", "x" denotes "added to" and "-" denotes "divided by",then

12 - 6 + 28 x 3 ÷ 9 = ?

A.-24
B.-53
C.1

Answer: C

Correct answer: 1

Replacing the words by their symbols gives \( 12 \div 6 - 28 + 3 \times 9 \), and by the usual order \[ 2 - 28 + 27 = \mathbf{1} \]

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79.

The following equation is incorrect. Which two signs should be interchanged to correct the equation? 15 x 12 + 40 ÷ 40 - 6 = 21

A.+ and x
B.+ and ÷
C.- and +
D.÷ and x

Answer: A

Correct answer: + and x

Exchanging + and × gives \( 15 + 12 \times 40 \div 40 - 6 \), which works out as \[ 15 + 12 - 6 = \mathbf{21} \]

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80.

In a certain code language, '+' represents 'x', '-' represents '+', 'x' represents '÷' and '÷' represents '-'. What is the answer to the following question?

72 x 9 - 14 + 2 = ?

A.26
B.80
C.30
D.36

Answer: D

Correct answer: 36

The code swaps the symbols: \( + \to \times \), \( - \to + \), \( \times \to \div \), \( \div \to - \). So \( 72 \times 9 - 14 + 2 \) is read as \( 72 \div 9 + 14 \times 2 \).

Applying BODMAS to the decoded expression: \[ 72 \div 9 + 14 \times 2 = 8 + 28 = \mathbf{36} \]

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Mathematical Operations Questions and Answers

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Mathematical Operations Questions and Answers

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