In the following question, correct the equation by interchanging the two signs.
6 ÷ 17 x 51 + 6 - 12 = - 4
Answer: A
Correct answer: x and ÷
Exchanging × and ÷ gives \( 6 \times 17 \div 51 + 6 - 12 \), which works out as \[ 2 + 6 - 12 = \mathbf{-4} \]
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If "-" means "divided by", "+" means "multiplied by", "÷" means "added to", "x" means "subtracted from", then 11 ÷ 6 - 2 + 5 x 3 = ?
Answer: C
Correct answer: 23
Replacing the words by their symbols gives \( 11 + 6 \div 2 \times 5 - 3 \), and by the usual order \[ 11 + 15 - 3 = \mathbf{23} \]
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If 324⊕289 = 35, 441⊕484 = 43, then 625⊕400 = ?
Answer: D
Correct answer: 45
The operation adds the square roots: \( \sqrt{324} + \sqrt{289} = 18 + 17 = 35 \) and \( \sqrt{441} + \sqrt{484} = 21 + 22 = 43 \). So \[ \sqrt{625} + \sqrt{400} = 25 + 20 = \mathbf{45} \]
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In a certain code language, '+' represents 'x', '-' represents '+', 'x' represents '÷' and '÷' represents '-'. What is the answer to the following question?
72 x 9 - 14 + 2 = ?
Answer: D
Correct answer: 36
The code swaps the symbols: \( + \to \times \), \( - \to + \), \( \times \to \div \), \( \div \to - \). So \( 72 \times 9 - 14 + 2 \) is read as \( 72 \div 9 + 14 \times 2 \).
Applying BODMAS to the decoded expression: \[ 72 \div 9 + 14 \times 2 = 8 + 28 = \mathbf{36} \]
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If (-) stands for division, (+) stands for multiplication, (÷) stands for subtraction and (×) stands for addition, which one of the following equations is correct?
Answer: A
Correct answer: 100+5−10×250÷200 = 100
Reading + as ×, − as ÷, × as + and ÷ as − turns the left side into \( 100 \times 5 \div 10 + 250 - 200 \), which is \[ 50 + 250 - 200 = \mathbf{100} \] matching the right side. None of the other equations balances when the same substitutions are made.
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In a certain code language, '+' represents 'x', '-' represents '+', 'x' represents '÷' and '÷' represents '-'. What is the answer to the following question?
642 x 6 ÷ 25 + 4 = ?
Answer: D
Correct answer: 7
The code swaps the symbols: \( + \to \times \), \( - \to + \), \( \times \to \div \), \( \div \to - \). So \( 642 \times 6 \div 25 + 4 \) is read as \( 642 \div 6 - 25 \times 4 \).
Applying BODMAS to the decoded expression: \[ 642 \div 6 - 25 \times 4 = 107 - 100 = \mathbf{7} \]
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If the signs + and / and the numbers 2 and 4 are interchanged, which one of the following four equations would be correct?
Answer: D
Correct answer: 2+4/6 = 8
Exchanging the signs + and ÷, and the numbers 2 and 4, turns the left side into \( 4 \div 2 + 6 \), which is \[ 2 + 6 = \mathbf{8} \] None of the other equations balances after the same exchanges.
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If '+' means subtraction, '÷' means addition, '<' means multiplication and '>' means division, then find the value of the given statement,
The value of 9 ÷ 7 < 8> (4>2) + 5 will be
Answer: A
Correct answer: 32
Replace each symbol by the operation it means: \( + \to - \), \( \div \to + \), \( \lt \to \times \), \( \gt \to \div \). The expression \( 9 \div 7 \lt 8 \gt (4 \gt 2) + 5 \) therefore reads \( 9 + 7 \times 8 \div (4 \div 2) - 5 \).
Working the bracket first, then BODMAS: \[ 9 + 7 \times 8 \div 2 - 5 = 9 + 28 - 5 = \mathbf{32} \]
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If Q means ‘add’ to; J means ‘Multiply by’, T means ‘subtract from’ and K means ‘divide by’ then 30 K 2 Q 3 J 6 T 5 = ?
Answer: B
Correct answer: 28
Substituting gives \[ 30 \div 2 + 3 \times 6 - 5. \] Taking the division and multiplication first: \( 30\div2 = 15 \) and \( 3\times6 = 18 \). Then \( 15 + 18 - 5 = 28 \).
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If "K" denotes "multiplied by", "M" denotes "subtracted from", "J" denotes "added to" and "L" denotes "divided by", then
44 M 24 K 56 L 14 J 60 = ?
Answer: C
Correct answer: 8
Replacing the letters gives \( 44 - 24 \times 56 \div 14 + 60 \), and by the usual order \[ 44 - 96 + 60 = \mathbf{8} \]
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