The goal is to find the correct interchange of numbers and signs to satisfy the given equation.
Checking Equation Interchanges
The original equation is $8 \times 3 + 4 = 28$. We need to test the options by applying the specified interchanges to the numbers and signs.
Option C: Swap operators '+' and '$\times$', and swap numbers 8 and 4.
- Original equation structure: $Number1$ $Operator1$ $Number2$ $Operator2$ $Number3$
- Original values: $8$ $\times$ $3$ $+$ $4$
- Applying the swaps from Option C:
- Operators: '$\times$' becomes '+' and '+' becomes '$\times$'.
- Numbers: '8' becomes '4', '4' becomes '8'. The number '3' remains unchanged.
- Constructing the new equation with swapped values in the original positions:
$4 + 3 \times 8$
- Evaluating the new equation using the order of operations (multiplication before addition):
$4 + (3 \times 8) = 4 + 24 = 28$
The result $28$ matches the right side of the original equation. Therefore, this interchange makes the equation correct.
Verifying Other Options
Let's briefly check why other options are incorrect using the same logic.
- Option A: Swap '+' $\leftrightarrow$ '$\times$', swap 3 $\leftrightarrow$ 4. Equation: $8 + 4 \times 3 = 8 + 12 = 20 \neq 28$.
- Option B: Swap '+' $\leftrightarrow$ '$\times$', swap 8 $\leftrightarrow$ 3. Equation: $3 + 8 \times 4 = 3 + 32 = 35 \neq 28$.
- Option D: Swap '+' $\leftrightarrow$ '$\times$', swap 4 $\leftrightarrow$ 3. Equation: $8 + 4 \times 3 = 8 + 12 = 20 \neq 28$.
Only Option C results in the correct equation value.
Similar Questions
- Which two signs should be interchanged to make the following equation CORRECT?
$[(15 \div 3) - (4 \times 2)] + [4 - 6] = 5 \times 10$ - If "+" means "$\div$", "-" means "+", "$\times$" means "-" and "$\div$" means "$\times$", which of the following options is CORRECT?
- If 5 @ 2 = 17 and 6 @ 3 = 27, what is 7 @ 4?
- If 9 @ 1 = 82 and 6 @ 2 = 38, what is the value of 7 @ 3?
- You are given a mathematical expression with basic operations. However, the symbols used are not their usual meaning.
You must follow these symbol substitution rules:
'+' means '-'
'-' means 'x'
'x' means '÷'
'÷' means '+'
$120 \div 6 \times 3 - 10 + 4 = ?$ - If $\times$ stands for addition, $\div$ stands for subtraction, + stands for multiplication, and - stands for division, then $12 \times 6 \div 3 - 2 + 5 = ?$
- Which two signs need to be interchanged?
$22 - 4 \times 2 \div 2 + 6 = 20$ - Select the CORRECT sequence of mathematical signs to sequentially replace the A and B to balance the given equation.
15 A 5 B 4 = 35 - The following equation is incorrect. Which two signs should be interchanged to correct the equation?
$14 - 7 \times 30 \div 10 + 4 = 54$ By interchanging the given two signs which of the following equation will NOT be correct?
$+$ and $\div$
I. $27 \div 3 - 18 \times 3 + 9 = 24$
II. $12 \div 8 \times 12 + 16 - 7 = 19$
Important Questions from Mathematical Operations
What will come in the place of ‘?’ in the following equation if ‘+’ and ‘−’ are interchanged and ‘×’ and ‘÷’ are interchanged?
18 ÷ 9 + 24 × 3 − 16 = ?If ‘A’ stands for ‘÷’, ‘B’ stands for ‘×’, ‘C’ stands for ‘+’, and ‘D’ stands for ‘−’, what will come in place of the question mark (?) in the following equation?
88 B 3 D 12 A 4 C 6 = ?Select the set in which the numbers are related in the same way as are the numbers of the given sets.
(NOTE: Operations should be performed on whole numbers without breaking down the numbers into their 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.)
Given sets:
(9, 21, 193)
(12, 15, 184)What will come in the place of the question mark (?) in the following equation, if ‘÷’ and ‘+’ are interchanged and ‘−’ and ‘×’ are interchanged?
44 ÷ 78 + 6 − 3 × 19 = ?Two sets of numbers are given below. In each set of numbers, certain mathematical operation(s) on the first number result(s) in the second number. Similarly, certain mathematical operation(s) on the second number result(s) in the third number and so on. Which of the given options follows the same set of operations as in the given sets?
(NOTE: Operations should be performed on the whole numbers, without breaking down the numbers into their constituent digits. E.g. 13 – Operations on 13 such as adding/subtracting/multiplying to 13 can be performed. Breaking down 13 into 1 and 3 and then performing mathematical operations on 1 and 3 is not allowed.)
