By Interchanging the given two numbers which of the following equation will be not correct? 9 and 6
9 × 7 + 4 ÷ 1 – 6 = 38
Understanding the Problem: Interchanging Numbers in Equations
The question asks us to examine four different mathematical equations. We are given two specific numbers, 9 and 6, that need to be swapped (interchanged) in each of these equations. After performing this interchange, we need to evaluate each new equation and determine which one becomes incorrect, meaning the left side of the equation will no longer equal the right side.
Step-by-Step Evaluation After Interchanging 9 and 6
We will go through each given equation, swap every instance of 9 with 6 and every instance of 6 with 9, and then calculate the result using the correct order of operations (BODMAS/PEMDAS). We will then check if the resulting equation is true.
Analysing Option 1
The original equation is: 7 + 6 × 4 ÷ 9 – 8 = 5
After interchanging 6 and 9, the equation becomes: 7 + 9 × 4 ÷ 6 – 8
Now, let's evaluate this expression:
- First, perform multiplication and division from left to right.
7 + 9 × 4 ÷ 6 – 87 + 36 ÷ 6 – 87 + 6 – 8 - Next, perform addition and subtraction from left to right.
7 + 6 – 813 – 85
The result is 5. So, the equation is 7 + 9 × 4 ÷ 6 – 8 = 5. This is a correct equation.
Analysing Option 2
The original equation is: 6 × 8 – 9 ÷ 3 + 5 = 75
After interchanging 6 and 9, the equation becomes: 9 × 8 – 6 ÷ 3 + 5
Let's evaluate this expression:
- First, perform multiplication and division from left to right.
9 × 8 – 6 ÷ 3 + 572 – 2 + 5 - Next, perform addition and subtraction from left to right.
72 – 2 + 570 + 575
The result is 75. So, the equation is 9 × 8 – 6 ÷ 3 + 5 = 75. This is a correct equation.
Analysing Option 3
The original equation is: 9 × 7 + 4 ÷ 1 – 6 = 38
After interchanging 6 and 9, the equation becomes: 6 × 7 + 4 ÷ 1 – 9
Let's evaluate this expression:
- First, perform multiplication and division from left to right.
6 × 7 + 4 ÷ 1 – 942 + 4 – 9 - Next, perform addition and subtraction from left to right.
42 + 4 – 946 – 937
The result is 37. So, the equation is 6 × 7 + 4 ÷ 1 – 9 = 38. Since 37 is not equal to 38, this is an incorrect equation.
Analysing Option 4
The original equation is: 7 × 6 ÷ 3 + 9 – 8 = 19
After interchanging 6 and 9, the equation becomes: 7 × 9 ÷ 3 + 6 – 8
Let's evaluate this expression:
- First, perform multiplication and division from left to right.
7 × 9 ÷ 3 + 6 – 863 ÷ 3 + 6 – 821 + 6 – 8 - Next, perform addition and subtraction from left to right.
21 + 6 – 827 – 819
The result is 19. So, the equation is 7 × 9 ÷ 3 + 6 – 8 = 19. This is a correct equation.
Conclusion: Which Equation is Not Correct?
After interchanging the numbers 9 and 6 in each equation and evaluating them, we found that Options 1, 2, and 4 resulted in correct mathematical statements. Option 3, however, resulted in an incorrect statement (37 = 38 is false).
Therefore, the equation that is not correct after interchanging 9 and 6 is the one from Option 3.
| Option | Original Equation | Equation after Interchanging 9 and 6 | Calculated Result | Original RHS | Correct/Incorrect |
|---|---|---|---|---|---|
| 1 | $7 + 6 \times 4 \div 9 - 8 = 5$ | $7 + 9 \times 4 \div 6 - 8$ | $5$ | $5$ | Correct |
| 2 | $6 \times 8 - 9 \div 3 + 5 = 75$ | $9 \times 8 - 6 \div 3 + 5$ | $75$ | $75$ | Correct |
| 3 | $9 \times 7 + 4 \div 1 - 6 = 38$ | $6 \times 7 + 4 \div 1 - 9$ | $37$ | $38$ | Incorrect |
| 4 | $7 \times 6 \div 3 + 9 - 8 = 19$ | $7 \times 9 \div 3 + 6 - 8$ | $19$ | $19$ | Correct |
Revision Table: Key Concepts for Interchanging Numbers
| Concept | Explanation | Relevance to Problem |
|---|---|---|
| Interchanging Numbers | Swapping the positions of two specific numbers throughout an expression or equation. | The core operation applied to the original equations. |
| Order of Operations (BODMAS/PEMDAS) | Rules that define the sequence for evaluating mathematical expressions (Brackets/Parentheses, Orders/Exponents, Division/Multiplication, Addition/Subtraction). | Essential for correctly calculating the value of the expressions after interchanging numbers. |
| Equation Validity | Checking if the left side of an equation equals the right side. | The criteria used to determine if the equation is "correct" or "not correct" after the interchange. |
Additional Information: Solving Mathematical Reasoning Problems
Problems involving interchanging numbers and checking equation validity are common in mathematical reasoning and quantitative aptitude sections of exams. Here are some tips for solving such problems efficiently:
- Understand the Rule: Clearly identify which numbers or symbols need to be interchanged. Apply the change consistently throughout the entire equation.
- Apply Order of Operations: Always follow BODMAS/PEMDAS strictly. Mistakes often happen when this order is not followed. Remember that multiplication and division have equal priority and are done from left to right. Similarly, addition and subtraction have equal priority and are done from left to right.
- Be Systematic: Evaluate each option one by one. Don't skip steps in the calculation.
- Double-Check Calculations: Even simple arithmetic can lead to errors under time pressure. Review your calculations, especially for multiplication, division, addition, and subtraction.
- Focus on the Question: Pay attention to whether the question asks which equation becomes correct or incorrect after the interchange.
Practicing such problems helps improve numerical agility and logical thinking skills required for various competitive exams.
Similar Questions
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Important Questions from Logical Puzzle
Seven persons P, Q, R, S, T, U and V like different watches namely W1, W2, W3, W4, W5, W6 and W7 (not necessarily in the same order). P and R do not like odd numbered watch. T likes W5. U does not like W2 or W3 or W6 or W7. P likes prime numbered watch. Q likes W4. S likes W2 or W7. Which of the following statement(s) is/are correct ?
I. S likes W7.
II. R likes W2.
III. U likes W1.
IV. V likes W3.
If ‘+’ means ‘×’, ‘×’ means ‘÷’, ‘÷’ means ‘–’ and ‘–’ means ‘+’, then
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In a certain code language, ‘LETTER’ is written as ‘ZLZYIO’. What is the code for ‘ACTION’ in that code language?
If ‘A’ denotes ‘+’, ‘B’ denotes ‘×’, ‘C’ denotes ‘–’ and ‘D’ denotes ‘÷’, then what will come in place of ‘?’ in the following equation?
21 A 34 C 6 B (72 D 9) A 13 B 1 + (56 D 4) = ?
