Mathematical Operations Questions and Answers

Answer: C

Correct answer: 5 ÷ 3 - 25 + 20 = 20 x 39

The substitutions are \( = \to \div \), \( + \to - \), \( \times \to = \), \( - \to + \) and \( \div \to \times \). Note that \( \times \) becomes the equals sign, so it marks where the two sides of the equation meet.

Decoding the correct option gives \( 5 \times 3 + 25 - 20 \div 20 = 39 \), and by BODMAS \[ 15 + 25 - 1 = 39 \] which is true. For contrast, \( 96 \div 2\ \text{x}\ 6 \div 105 + 1 \) decodes to \( 192 = 630 - 1 \), which is false.

Answer: C

Correct answer: 12

Replacing the words by their symbols gives \( 54 \div 162 \times 18 + 12 - 6 \), which is \[ \frac{54}{162} \times 18 + 6 = 6 + 6 = \mathbf{12} \]

Answer: B

Correct answer: 262

The two operators are not arithmetic in the usual sense. Square the bracketed number, then \( @ \) writes the next number immediately after it (digits joined, not added), and \( * \) adds the final number.

Checking both worked examples: \( (3)^2 = 9 \), joined with 1 gives 91, and \( 91 + 7 = 98 \). \( (4)^2 = 16 \), joined with 2 gives 162, and \( 162 + 16 = 178 \).

So \( (5)^2 = 25 \), joined with 3 gives 253, and \[ 253 + 9 = \mathbf{262} \] The option 253 is the value before the last addition, offered as a distractor.

Answer: C

Correct answer: 5 and 3

Exchanging the numbers 5 and 3 gives \( 8 \times 5 \div 4 + 9 - 3 \), which works out as \[ 10 + 9 - 3 = \mathbf{16} \]

Answer: B

Correct answer: ÷, x and =

Putting the operators in as ÷, × and = gives \[ 18 \div 6 \times 9 = 3 \times 9 = \mathbf{27} \] which is what the right-hand side requires.

Answer: B

Correct answer: 3

The symbols stand for division and multiplication: \( 3 \div 4 \times 8 = 6 \) and \( 9 \times 4 \div 3 = 12 \), so # is ÷ and % is ×. Then \[ 12 \times 6 \div 24 = \mathbf{3} \]

Answer: C

Correct answer: 8

Replacing the letters gives \( 44 - 24 \times 56 \div 14 + 60 \), and by the usual order \[ 44 - 96 + 60 = \mathbf{8} \]

Answer: D

Correct answer: 7

The code swaps the symbols: \( + \to \times \), \( - \to + \), \( \times \to \div \), \( \div \to - \). So \( 642 \times 6 \div 25 + 4 \) is read as \( 642 \div 6 - 25 \times 4 \).

Applying BODMAS to the decoded expression: \[ 642 \div 6 - 25 \times 4 = 107 - 100 = \mathbf{7} \]

Answer: B

Correct answer: x and +, 8 and 2

Making both exchanges - the signs × and +, and the numbers 8 and 2 - turns the left side into \( 2 + 9 \times 8 \), which is \[ 2 + 72 = \mathbf{74} \]

Answer: D

Correct answer: 20

The code swaps the symbols: \( + \to \times \), \( - \to + \), \( \times \to \div \), \( \div \to - \). So \( 24 \times 6 - 8 + 2 \) is read as \( 24 \div 6 + 8 \times 2 \).

Applying BODMAS to the decoded expression: \[ 24 \div 6 + 8 \times 2 = 4 + 16 = \mathbf{20} \]