The following equation is incorrect. Which two signs should be interchanged to correct the equation?
1 ÷ 14 x 30 + 20 - 10 = 12
Answer: D
Correct answer: + and ÷
Exchanging + and ÷ gives \( 1 + 14 \times 30 \div 20 - 10 \), which works out as \[ 1 + 21 - 10 = \mathbf{12} \]
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In this question, some equations are solved on the basis of a certain system. On the same basis find out the correct answer from amongst the four alternatives for the unsolved equation.
15 x 26 = 6512
29 x 36 = 6923,
46 x 54 = ?
Answer: B
Correct answer: 4645
Nothing is multiplied here - the four digits are simply rearranged. Writing the two numbers as \( a_1a_2 \) and \( b_1b_2 \), the result reads \( b_2\,a_2\,a_1\,b_1 \): the units digit of the second number, then the units digit of the first, then the tens digit of the first, then the tens digit of the second.
Checking both given equations: \( 15 \times 26 \) gives \( 6,5,1,2 = 6512 \) and \( 29 \times 36 \) gives \( 6,9,2,3 = 6923 \). So \( 46 \times 54 \) gives \[ 4,\,6,\,4,\,5 = \mathbf{4645} \]
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If "A" denotes "subtracted from", "B" denotes "added to", "C" denotes "divided by", "D" denotes "multiplied by", then which of the following statement is correct?
Answer: C
Correct answer: 13 C 13 A 13 B 13 D 13 = 157
Replacing the letters gives \( 13 \div 13 - 13 + 13 \times 13 \), and by the usual order \[ 1 - 13 + 169 = \mathbf{157} \] which matches. The other three do not balance under the same substitutions.
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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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