Mathematical Operations Questions and Answers

Answer: B

The signs in order are −, ÷, +, × and =. Put them in place: \[ 45 - 44 \div 22 + 17 \times 89 = 1556 \] By BODMAS, division and multiplication come first: \[ 44 \div 22 = 2,\quad 17 \times 89 = 1513 \] \[ 45 - 2 + 1513 = 1556 \] The left side equals the right side. Substituting the other three combinations does not give 1556: for example, the first reads 45 ÷ 44 + 22 × 17 − 89, which is about 286. As a check on the first option, 45 ÷ 44 + 22 × 17 − 89 does not come to 1556, and the third and fourth options fail in the same way.

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.