If 4 x 9 x 3 = 4 and 5 x 3 x 1 = 3, then
9 x 9 x 7 = ?
Answer: A
Correct answer: 5
In each case the three numbers are added and the square root taken: \( \sqrt{4+9+3} = \sqrt{16} = 4 \) and \( \sqrt{5+3+1} = \sqrt{9} = 3 \). So \[ \sqrt{9+9+7} = \sqrt{25} = \mathbf{5} \]
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Find out the two signs to be interchanged for making following equation correct
5 + 3 x 8 - 12 / 4 =3
Answer: B
Correct answer: - and /
Exchanging − and ÷ turns the equation into \( 5 + 3 \times 8 \div 12 - 4 \). Working by the usual order, \[ 5 + \frac{24}{12} - 4 = 5 + 2 - 4 = \mathbf{3} \]
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In the following question, correct the given equation by interchanging two numbers.
8 x 3 ÷ 4 + 9 - 5 = 16
Answer: C
Correct answer: 5 and 3
Exchanging the numbers 5 and 3 gives \( 8 \times 5 \div 4 + 9 - 3 \), which works out as \[ 10 + 9 - 3 = \mathbf{16} \]
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If "÷" denotes "multiplied by", "+" denotes "subtracted from", "x" denotes "added to" and "-" denotes "divided by",then
12 - 6 + 28 x 3 ÷ 9 = ?
Answer: C
Correct answer: 1
Replacing the words by their symbols gives \( 12 \div 6 - 28 + 3 \times 9 \), and by the usual order \[ 2 - 28 + 27 = \mathbf{1} \]
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If A + B = 2C and C + D = 2A, then
Answer: A
Correct answer: A + C = B + D
From \( A+B = 2C \) we get \( B = 2C-A \), and from \( C+D = 2A \) we get \( D = 2A-C \). Adding those, \[ B + D = (2C-A) + (2A-C) = A + C \] so A + C = B + D.
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If ‘-‘ stands for ‘÷’, ‘+’ stands for ‘×’, ‘÷’ stand for ‘-‘ and ‘×’ stands for ‘+’, which one of the following question is correct?
Answer: A
Correct answer: 30 – 6 + 5 × 4 ÷ 2 = 27.
Substituting in this option gives \[ 30 \div 6 \times 5 + 4 - 2. \] Taking the divide and multiply first: \( 30\div6 = 5 \), \( 5\times5 = 25 \). Then \( 25 + 4 - 2 = 27 \), which matches the stated value. The other three fail once their symbols are replaced.
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If 3 # 4 % 8 = 6 and 9 % 4 # 3 = 12, then 12 % 6 # 24 = ?
Answer: B
Correct answer: 3
The symbols stand for division and multiplication: \( 3 \div 4 \times 8 = 6 \) and \( 9 \times 4 \div 3 = 12 \), so # is ÷ and % is ×. Then \[ 12 \times 6 \div 24 = \mathbf{3} \]
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If ‘+’ stands for ‘×’, ‘-‘ for ‘÷’, ‘×’ for ‘-‘ and ‘÷’ for ‘+’, find the value of 12 + 90 - 5 × 9 ÷ 3.
Answer: C
Correct answer: 210
Substituting gives \[ 12 \times 90 \div 5 - 9 + 3. \] Multiplication and division first, left to right: \( 12\times90 = 1080 \), \( 1080\div5 = 216 \). Then \( 216 - 9 + 3 = 210 \). Stopping at 216, before the last two terms are applied, gives the second option offered.
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In a certain code language, 'x' represents '+', '÷' represents 'x', '-' represents '÷' and '+' represents '-'. Find out the answer to the following question.
5 + 10 x 21 ÷ 5 - 15 = ?
Answer: B
Correct answer: 2
Replacing the symbols gives \( 5 - 10 + 21 \times 5 \div 15 \), and by the usual order \[ 5 - 10 + 7 = \mathbf{2} \]
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What approximate value will come in place of question mark (?) in the following question ?
(49.001)² = ?
Answer: B
Correct answer: 2400
\( 49^2 = 2401 \), and 49.001 differs from 49 by so little that the square is still about 2401. To the nearest figure offered that is 2400.
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