Which two numbers (not digits) and which two signs should be interchanged to yield the value ‘zero’ for the following expression? 13 + 65 ÷ 2 × 8 – 21
To solve this question, we need to systematically test the interchanges proposed in the options to see which yields a result of zero.
Option 1: (+ and ÷; 13 and 21)
The expression becomes: 21 + 65 ÷ 13 × 8 – 65 = 21 + 5 × 8 – 65 = 21 + 40 – 65 = -4. This is not zero.
Option 2: (– and ÷; 8 and 13)
The expression becomes: 13 + 65 ÷ 13 × 8 – 21 = 13 + 5 × 8 – 21 = 13 + 40 – 21 = 32. This is not zero.
Option 3: (× and –; 21 and 65)
The expression becomes: 13 + 21 ÷ 2 × 8 – 65 = 13 + 10.5 × 8 – 65 = 13 + 84 – 65 = 32. This is not zero.
Option 4: (+ and ÷; 13 and 65)
The expression becomes: 65 + 13 ÷ 2 × 8 – 21 = 65 + 6.5 × 8 – 21 = 65 + 52 – 21 = 96. This is not zero.
Let's re-examine Option 4. There seems to be a mistake in the initial assessment. Let's recalculate:
Original expression: \(13 + 65 \div 2 \times 8 - 21\)
Interchanging 13 and 65, and + and ÷:
\(65 \div 13 + 2 \times 8 - 21\)
\(5 + 16 - 21 = 0\)
Therefore, interchanging 13 and 65, and + and ÷ gives a result of 0.
The correct option is 4. The crucial step is to correctly apply the order of operations (BODMAS/PEMDAS) after the interchange. The original calculation using BODMAS would be: \(13 + (65 \div 2) \times 8 - 21 = 13 + 32.5 \times 8 - 21 = 13 + 260 - 21 = 252\)
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X : 649 :: 956 : Y
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