Mathematical Operations Questions and Answers

Answer: A

Correct answer: 130

Replacing the symbols gives \( 38 \div 2 \times 6 - 19 + 35 \), and by the usual order \[ 114 - 19 + 35 = \mathbf{130} \]

Answer: B

Correct answer: u = 1, v = 3/2

Putting \( u = 1 \) and \( v = \tfrac32 \) into the first equation gives \( 3(2 + \tfrac32) = 10.5 \) and \( 7uv = 7 \times \tfrac32 = 10.5 \); into the second, \( 3(1 + \tfrac92) = 16.5 \) and \( 11uv = 11 \times \tfrac32 = 16.5 \). Both hold, so that is the solution.

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: \[ 24 \div 6 + 8 \times 2 = 4 + 16 = \mathbf{20} \]

Answer: A

Correct answer: -47

The rule is \( a * b = a + b - ab \): \( 1+2-2 = 1 \), \( 2+3-6 = -1 \) and \( 3+4-12 = -5 \). So \[ 7 * 9 = 7 + 9 - 63 = \mathbf{-47} \]

Answer: B

Correct answer: 28

The substitution table has been destroyed in this record - three of the four symbol names were lost and are shown as the letter V, so it cannot be known which sign stands for which operation. What can be said is that the keyed value follows from reading the expression at face value: \[ 16 + 8 - 4 + 2\times4 = 16 + 8 - 4 + 8 = 28, \] taking multiplication before addition. As an operator-substitution question the item cannot be worked until the original table is restored, and no assignment consistent with the one surviving clue - that the dash means multiplied by - produces 28.

Answer: D

Correct answer: 5295

Each answer is the square of the number written down and followed by a 5: \( 17^2 = 289 \) gives 2895, \( 18^2 = 324 \) gives 3245, \( 19^2 = 361 \) gives 3615. Since \( 23^2 = 529 \), the answer is 5295.

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: C

Correct answer: 20 < 2 + 10 ÷ 4 – 6 × 100

Substituting gives \( 20 \div 2 \times 10 - 4 + 6 \) on the left, and the final symbol means greater than. Working left to right through the divide and multiply: \( 20\div2 = 10 \), \( 10\times10 = 100 \), then \( 100 - 4 + 6 = 102 \). Since 102 exceeds 100 the statement holds.

Answer: C

Correct answer: 24

Substituting gives \[ 20 + 8 - 8 \div 4 \times 2. \] The division and multiplication are taken first, left to right: \( 8\div4 = 2 \), then \( 2\times2 = 4 \). What remains is \( 20 + 8 - 4 = 24 \). Working strictly left to right instead would give 22, which is why the order of operations has to be respected after the symbols are replaced.

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 \[ \frac{97+47}{2} = \mathbf{72} \]