If 18 (9) 3 and 36 (30) 5, then what is the value of A in 19 (A) 18?
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 \[ A = \frac{19 \times 18}{6} = \mathbf{57} \]
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5x - 6 = 3x - 8
Solve the above equation.
Answer: B
Correct answer: -1
Bringing the terms together: \( 5x - 3x = -8 + 6 \), so \( 2x = -2 \) and \[ x = \mathbf{-1} \]
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X²+X² =
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.
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If "-" means "added to", "+" means "divided by", "÷" means "multiplied by", "x" means "subtracted from", then 13 + 12 x 9 ÷ 3 - 6 = ?
Answer: D
Correct answer: -239/12
Replacing the words by their symbols gives \( 13 \div 12 - 9 \times 3 + 6 \), which is \[ \frac{13}{12} - 27 + 6 = \frac{13}{12} - 21 = \frac{13 - 252}{12} = \mathbf{-\frac{239}{12}} \]
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Select the correct set of symbols which will fit in the given equation?
5 0 3 5 = 20
Answer: B
Correct answer: -, +, x
Putting the signs in as −, + and × gives \[ 5 - 0 + 3 \times 5 = 5 - 0 + 15 = \mathbf{20} \]
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If "+" means "minus", "x" means "divided by", "÷" means "plus" and "-" means "multiplied by", then 38 x 2 - 6 + 19 ÷ 35 = ?
Answer: A
Correct answer: 130
Replacing the symbols gives \( 38 \div 2 \times 6 - 19 + 35 \), and by the usual order \[ 114 - 19 + 35 = \mathbf{130} \]
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The solution of 3(2u + v) = 7 uv and 3(u + 3v) = 11 uv is _____
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.
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In a certain code language, '+' represents 'x', '-' represents '+', 'x' represents '÷' and '÷' represents '-'. What is the answer to the following question?
24 x 6 - 8 + 2 = ?
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: \[ 24 \div 6 + 8 \times 2 = 4 + 16 = \mathbf{20} \]
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If, 1*2= 1,
2*3= 1 and
3*4= 5, Then find the value of 7*9= ?
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 \[ 7 * 9 = 7 + 9 - 63 = \mathbf{-47} \]
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If V means ‘divided by, - means ‘multiplied by’, V means ‘minus and V means ‘plus’, which of the following will be the value of the expression 16+ 8- 4 + 2 x 4?
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.
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