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How many expressions can be formed using + or – signs between the three consecutive numbers n, n+1, n+2?
- a)4
- b)6
- c)8
- d)16
Correct answer is option 'A'. Can you explain this answer?
Most Upvoted Answer
How many expressions can be formed using + or – signs between the thre...
Understanding the Problem
To find how many expressions can be formed using + or - signs between the three consecutive numbers n, n+1, and n+2, we need to analyze the options available for the signs.
Available Signs
1. We have three numbers: n, n+1, n+2.
2. We can place either a + or a - sign between each pair of numbers.
Setting Up the Expressions
- There are two gaps between the three numbers:
- Between n and n+1
- Between n+1 and n+2
Calculating Combinations
- For each gap, we have two choices:
- First gap (between n and n+1): either + or -
- Second gap (between n+1 and n+2): either + or -
This means we can calculate the total combinations of signs as follows:
- For the first gap: 2 options (either + or -)
- For the second gap: 2 options (either + or -)
Total Expressions
- Using the multiplication principle, the total number of expressions can be calculated as:
Total expressions = 2 (first gap) * 2 (second gap) = 4
Conclusion
Thus, the total number of distinct expressions that can be formed using + or – signs between the three consecutive numbers n, n+1, and n+2 is 4.
The correct answer is option A.
To find how many expressions can be formed using + or - signs between the three consecutive numbers n, n+1, and n+2, we need to analyze the options available for the signs.
Available Signs
1. We have three numbers: n, n+1, n+2.
2. We can place either a + or a - sign between each pair of numbers.
Setting Up the Expressions
- There are two gaps between the three numbers:
- Between n and n+1
- Between n+1 and n+2
Calculating Combinations
- For each gap, we have two choices:
- First gap (between n and n+1): either + or -
- Second gap (between n+1 and n+2): either + or -
This means we can calculate the total combinations of signs as follows:
- For the first gap: 2 options (either + or -)
- For the second gap: 2 options (either + or -)
Total Expressions
- Using the multiplication principle, the total number of expressions can be calculated as:
Total expressions = 2 (first gap) * 2 (second gap) = 4
Conclusion
Thus, the total number of distinct expressions that can be formed using + or – signs between the three consecutive numbers n, n+1, and n+2 is 4.
The correct answer is option A.
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Community Answer
How many expressions can be formed using + or – signs between the thre...
There are 2 possible signs (+ or –) at 2 places, so total expressions = 22 = 4. But with 3 numbers, there are 2 gaps, so 22 = 4. Oops wait correction: Actually between 3 numbers, there are 2 sign positions → 22 = 4.
Correct Option: a) 4
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