Mathematical Operations Questions and Answers

Answer: A

The value is 22.

Apply the rule a * b = 2a - 3b + ab to each part, taking care that the operation is not symmetric:

\[ \begin{aligned} 3 * 5 &= 6 - 15 + 15 = 6 \\ 5 * 3 &= 10 - 9 + 15 = 16 \\ 6 + 16 &= 22 \end{aligned} \]

Treating 5 * 3 as equal to 3 * 5 would give 12, which is not offered, and the other options come from sign or arithmetic slips.

Answer: B

The value is \(9\tfrac{1}{3}\).

Replace each sign by its meaning: '+' becomes '÷', '-' becomes '×' and '×' becomes '+'. The expression becomes

\[ 12 \div 6 \div 3 \times 2 + 8 \]

Working left to right for division and multiplication, then adding:

\[ \begin{aligned} 12 \div 6 &= 2,\quad 2 \div 3 = \tfrac{2}{3} \\ \tfrac{2}{3} \times 2 &= \tfrac{4}{3} \\ \tfrac{4}{3} + 8 &= 9\tfrac{1}{3} \end{aligned} \]

\(8\tfrac{1}{3}\) is one less than the correct value, and none of the other options results from applying the substitutions and then the usual order of operations.

Answer: D

The correct equation is 24 \(\gt\) 4 × 20 \(\lt\) 2 # 16.

Replace each symbol: \(\gt\) becomes ÷, \(\lt\) becomes +, × becomes =, and # becomes −. The last option then reads

\[ \begin{aligned} 24 \div 4 &= 20 + 2 - 16 \\ 6 &= 6 \end{aligned} \]

which is true. The others fail:

• 24 = 4 ÷ 20 + 2 − 16 gives 24 = −13.8.
• 24 + 4 ÷ 20 − 2 = 16 gives 22.2 = 16.
• 24 − 4 + 20 = 2 ÷ 16 gives 40 = 0.125.

Answer: C

Correct answer: 35

Each second number is two and a half times the first: \( 12 \times 2.5 = 30 \), so \[ 14 \times 2.5 = \mathbf{35} \]

Answer: C

Correct answer: 8 R 8 P 8 S 8 Q 8 = 57

Substituting gives \[ 8 \times 8 + 8 \div 8 - 8 = 64 + 1 - 8 = 57. \] The multiplication and the division are evaluated before the addition and subtraction, which is what makes the middle term contribute 1 rather than being folded into a running total.

Answer: D

Correct answer: 36 -6 + 3 × 5 ÷ 3 = 74

Substituting in this option gives \[ 36 \times 6 \div 3 + 5 - 3. \] Multiplication and division first, left to right: \( 36\times6 = 216 \), then \( 216\div3 = 72 \). Then \( 72 + 5 - 3 = 74 \), which matches. The other three options do not balance once their signs are replaced.

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: D

Correct answer: 14

The code swaps the symbols: \( - \to + \), \( + \to \times \), \( \times \to \div \), \( \div \to - \). So \( 2 - 12 + 10 \times 5 \div 12 \) is read as \( 2 + 12 \times 10 \div 5 - 12 \).

Applying BODMAS to the decoded expression: \[ 2 + 12 \times 10 \div 5 - 12 = 2 + 24 - 12 = \mathbf{14} \]

Answer: B

Correct answer: 30

Substituting gives \[ 28 \div 7 \times 8 - 6 + 4. \] Division and multiplication first, left to right: \( 28\div7 = 4 \), \( 4\times8 = 32 \). Then \( 32 - 6 + 4 = 30 \).

Answer: B

Correct answer: 235

Replacing the symbols gives \( 25 \times 10 - 240 \div 16 \), and by the usual order \[ 250 - 15 = \mathbf{235} \]