Mathematical Operations Questions and Answers

Answer: B

Correct answer: 57

The number in brackets is the product of the outer two divided by six: \( \tfrac{18\times3}{6} = 9 \) and \( \tfrac{36\times5}{6} = 30 \). So \[ A = \frac{19 \times 18}{6} = \mathbf{57} \]

Answer: B

Correct answer: -1

Bringing the terms together: \( 5x - 3x = -8 + 6 \), so \( 2x = -2 \) and \[ x = \mathbf{-1} \]

Answer: C

Here the given expression, 

X² + X²  is an algebraic expression. Here in this expression the terms are like terms. Now to add them, add their coefficients.

Here in the given expression, the like terms are two X² 

Hence, adding their coefficients i.e, 1 + 1 = 2

Therefore, 

X² + X² = 2X².

Answer: D

Correct answer: -239/12

Replacing the words by their symbols gives \( 13 \div 12 - 9 \times 3 + 6 \), which is \[ \frac{13}{12} - 27 + 6 = \frac{13}{12} - 21 = \frac{13 - 252}{12} = \mathbf{-\frac{239}{12}} \]

Answer: B

Correct answer: -, +, x

Putting the signs in as −, + and × gives \[ 5 - 0 + 3 \times 5 = 5 - 0 + 15 = \mathbf{20} \]

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.