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 17 + 17 = 2895 18 + 18 = 3245 19 + 19 = 3615 then 23 + 23 = ?
Answer: D
Correct answer: 5295
Each answer is the square of the number written down and followed by a 5: \( 17^2 = 289 \) gives 2895, \( 18^2 = 324 \) gives 3245, \( 19^2 = 361 \) gives 3615. Since \( 23^2 = 529 \), the answer is 5295.
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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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If "+" means "minus", "x" means "divided by", "÷" means "plus" and "-" means "multiplied by", then 81 x 9 + 10 - 6 ÷ 5 = ?
Answer: B
Correct answer: -46
Replacing the symbols gives \( 81 \div 9 - 10 \times 6 + 5 \), and by the usual order \[ 9 - 60 + 5 = \mathbf{-46} \]
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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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If, 4x3=14; 5x4=18; 6x5=22; Then find the value of 7x6=?
Answer: B
Correct answer: 26
Each answer is twice the sum of the two numbers: \( 2(4+3) = 14 \), \( 2(5+4) = 18 \), \( 2(6+5) = 22 \). So \[ 2(7+6) = \mathbf{26} \]
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In the following question, correct the equation by interchanging two signs.
6 + 8 ÷ 4 - 4 = 8
Answer: D
Correct answer: + and -
Exchanging + and − gives \( 6 - 8 \div 4 + 4 \), which works out as \[ 6 - 2 + 4 = \mathbf{8} \]
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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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The following equation is incorrect. Which two signs should be interchanged to correct the equation?
10 x 4 + 5 - 30 ÷ 6 = 31
Answer: A
Correct answer: x and -
Exchanging × and − gives \( 10 - 4 + 5 \times 30 \div 6 \), which works out as \[ 10 - 4 + 25 = \mathbf{31} \]
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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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