If A means ‘plus’, B means ‘minus’, C means ‘divided by’ and D means ‘multiplied by’, then 18 A 12 C 6 D 2 B 5 = ?
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.
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Which one of the four interchanges in signs and numbers would make the given equation correct? 3 + 5 – 2 = 4
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.
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If 25 + 5 ÷ 2 = 40 , and 35 + 5 ÷ 2 = 60 , then 45 + 5 ÷ 2 = ?
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 \[ (45-5) \times 2 = \mathbf{80} \]
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The value of -4-(-10) is how much greater then the value of -10-(-4) ?
Answer: C
Correct answer: 12
\( -4 - (-10) = -4 + 10 = 6 \) and \( -10 - (-4) = -10 + 4 = -6 \). The first exceeds the second by \[ 6 - (-6) = \mathbf{12} \]
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If - means x, x means +, + means 4, and + means then 40x 12 + 3- 6 + 60 = ?
Answer: D
Correct answer: None of these
Substituting turns the expression into one whose value falls outside every figure offered, so the answer is none of them. The stem’s list of definitions has been damaged - one sign appears against two different operations - but on any consistent reading of it the result is a value the three numbered options do not contain.
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If "÷" denotes "multiplied by", "+" denotes "subtracted from", "-" denotes "added to" and "x" denotes "divided by", then which of the following equation is true?
Answer: D
Correct answer: 18 x 6 ÷ 8 - 12 = 36
Replace every symbol by the operation it denotes: \( \div \to \times \), \( + \to \) subtracted from, \( - \to \) added to, \( \times \to \div \).
The correct option becomes \( 18 \div 6 \times 8 + 12 \), and by BODMAS \[ 18 \div 6 \times 8 + 12 = 24 + 12 = \mathbf{36} \]
The others fail: \( 5 \times 6 + 4 \div 3 \) becomes \( 12 - \tfrac{5}{6} = \tfrac{67}{6} \), not \( \tfrac{37}{6} \); and \( 6 \times 3 + 12 \div 3 \) becomes \( 36 - 2 = 34 \), not 21.
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In a certain code language, '-' represents 'x', '÷' represents '+', '+' represents '÷' and 'x' represents '-'. Find out the answer to the following question.19 ÷ 2 - 35 + 10 x 6 = ?
Answer: A
Correct answer: 20
Replacing the symbols gives \( 19 + 2 \times 35 \div 10 - 6 \), and by the usual order \[ 19 + 7 - 6 = \mathbf{20} \]
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If P denotes ÷; Q denotes ×, R denotes + and S denotes -, then what is the value of 18 Q 12 P 4 R 5 S 6 ?
Answer: A
Correct answer: 53
Substituting gives \[ 18 \times 12 \div 4 + 5 - 6. \] The multiplication and division are taken first, left to right: \( 18\times12 = 216 \), \( 216\div4 = 54 \). Then \( 54 + 5 - 6 = 53 \).
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In the following question, by using which mathematical operator will the expression become correct?
18 ? 6 ? 9 ? 27
Answer: B
Correct answer: ÷, x and =
Putting the operators in as ÷, × and = gives \[ 18 \div 6 \times 9 = 3 \times 9 = \mathbf{27} \] which is what the right-hand side requires.
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If × means ÷, - means ×, ÷ means + and + means- than (3 - 15 ÷ 19) × 8 + 6 = ?
Answer: C
Correct answer: 2
Replacing the symbols gives \( (3 \times 15 + 19) \div 8 - 6 \), and working the bracket first, \[ \frac{45+19}{8} - 6 = 8 - 6 = \mathbf{2} \]
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