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: \(13 + (65 \div 2) \times 8 - 21 = 13 + 32.5 \times 8 - 21 = 13 + 260 - 21 = 252\)
Similar Questions
The two expressions on either side of the equal sign will have the same value if two numbers on the left-hand side are interchanged and two signs on the right-hand side are interchanged.
What are those two numbers (not digits) and the two signs?
4 × 3 ÷ 6 + 2 - 8 = 10 + 2 × 3 ÷ 5 - 18
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If + means ×, × means −, − means ÷, and ÷ means +, what will be the value of the given expression?
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Important Questions from Mathematical Operations
Select the set, from the given options, in which the numbers are related in the same way as are the numbers of the following sets.
(NOTE: Operations should be performed on the whole numbers, without breaking down the numbers into its constituent digits. E.g. 13 – Operations on 13 such as adding/subtracting/multiplying etc. to 13 can be performed. Breaking down 13 into 1 and 3 and then performing mathematical operations on 1 and 3 is not allowed.)
(6, 13, 78)
(5, 22, 110)
If + means -, - means ×, × means ÷, ÷ means +, then what will come in place of the question mark (?) in the following equation?
28 - 6 ÷ 4 + 14 × 14 = ?
In the following number-pairs, the second number is obtained by applying certain mathematical operations to the first number. Which numbers should replace X and Y so that the pattern followed by the two numbers on the left side of :: is the same as that on the right side of :: ?
(NOTE: Operations should be performed on the whole numbers, without breaking down the numbers into its constituent digits. E.g. 13 Operations on 13 such as adding/subtracting /multiplying etc. to 13 can be performed. Breaking down 13 into 1 and 3 and then performing mathematical operations on 1 and 3 is not allowed.)
X : 649 :: 956 : Y
Which two numbers should be interchanged to make the given equation correct?
75 ÷ 5 + 15 × 4 - 17 × 3 + (60 ÷ 6) × 10 = 100
(Note: Interchange should be done of the entire number and not individual digits of a given number.)
If '+' means minus, '-' means multiplication, '÷' means plus, and 'x' means division, then solve the equation:
15 - 3 + 10 x 5 ÷ 5
