Mathematical Operations Questions and Answers

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 \[ 250 - 15 = \mathbf{235} \]

Answer: D

Correct answer: None of these

Substituting gives \[ 18 + 12 \div 6 \times 2 - 5. \] Division and multiplication come first, left to right: \( 12\div6 = 2 \), then \( 2\times2 = 4 \). So the value is \( 18 + 4 - 5 = 17 \), which is not among the three figures offered.

Answer: C

Correct answer: + and –, 3 and 5

Interchanging the two signs and the numbers 3 and 5 turns \( 3 + 5 - 2 \) into \( 5 - 3 + 2 \), which is 4 as required. Swapping 2 with 3 instead gives \( 2 - 5 + 3 = 0 \), and swapping 2 with 5 gives \( 3 - 2 + 5 = 6 \) - so only the third interchange works.

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 \[ (45-5) \times 2 = \mathbf{80} \]