If "+" denotes "divided by", "x" denotes "added to", "÷" denotes "subtracted from" and "-" denotes "multiplied by", then
54 + 162 - 18 x 12 ÷ 6 = ?
Answer: C
Correct answer: 12
Replacing the words by their symbols gives \( 54 \div 162 \times 18 + 12 - 6 \), which is \[ \frac{54}{162} \times 18 + 6 = 6 + 6 = \mathbf{12} \]
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If P means ‘division; T means ‘addition; M means ‘subtraction’ and D means ‘multiplication’, then what will be the value of the expression 12 M 12 D 28 P 7 T 15?
Answer: D
Correct answer: – 21
Substituting gives \[ 12 - 12 \times 28 \div 7 + 15. \] Multiplication and division first: \( 12\times28 = 336 \), \( 336\div7 = 48 \). Then \( 12 - 48 + 15 = -21 \). The negative result is the point of the item - the middle term is far larger than either of the others.
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If + means ÷, – means ×, ÷ means + and × means –, then 36 × 12 + 4 ÷ 6 + 2 – 3 = ?
Answer: C
Correct answer: 42
Apply the substitutions in place: + becomes \( \div \), – becomes \( \times \), \( \div \) becomes +, and \( \times \) becomes –. The expression \( 36 \times 12 + 4 \div 6 + 2 - 3 \) therefore reads \[ 36 - 12 \div 4 + 6 \div 2 \times 3 = 36 - 3 + 3\times3 = 36 - 3 + 9 = 42. \] The order of operations is applied to the *substituted* signs, not the printed ones - doing the division and multiplication before the subtraction and addition is what makes the two nines appear.
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If x stands for + stands for +, + stands for + and - stands for x, which one of the following equations is correct?
Answer: B
Correct answer: 8 + 10 – 3 + 5 x 6 = 8
This item cannot be worked as it stands: the list of substitutions in the stem has been damaged, with the same sign appearing against more than one operation and one of the four definitions lost altogether. Until the original wording is restored, no consistent set of replacements can be applied to test the four equations against one another.
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