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Teacher said that there were 100 students in his class, 24 of whom were boys and 32 were girls. Which base system did the teacher use in this statement?
- a)9
- b)5
- c)6
- d)8
Correct answer is option 'C'. Can you explain this answer?
Most Upvoted Answer
Teacher said that there were 100 students in his class, 24 of whom wer...
To determine the base system used by the teacher, we will analyze the numbers provided in the context of different base systems. The numbers given are 24 boys, 32 girls, and a total of 100 students. We will convert these numbers from their respective base systems to decimal (base 10) and check if the sum equals 100.
We are provided with the equation (32) + (24) = (100). Let us assume our base be 'b'
Then,we can say:
Then,we can say:
⇒ 32 = 3 x b1 + 2 x b0 = 3b+2
⇒ 24 = 2 x b1+ 4 x b0 = 2b+4
⇒ 100 = 1 x b2 + 0 x b1 + 0 x b0 = b2
⇒ 24 = 2 x b1+ 4 x b0 = 2b+4
⇒ 100 = 1 x b2 + 0 x b1 + 0 x b0 = b2
Now, according to our question:
⇒ 32 + 24=100
⇒ (3b + 2) + (2b + 4) = (b2)
⇒ 5b + 6 = b2
⇒ b2 - 5b - 6 = 0
⇒ b2 - 6b + b - 6 = 0
⇒ b(b - 6) + 1(b - 6) = 0
⇒ (b - 6) * (b + 1) = 0
⇒ b = 6,- 1
⇒ (3b + 2) + (2b + 4) = (b2)
⇒ 5b + 6 = b2
⇒ b2 - 5b - 6 = 0
⇒ b2 - 6b + b - 6 = 0
⇒ b(b - 6) + 1(b - 6) = 0
⇒ (b - 6) * (b + 1) = 0
⇒ b = 6,- 1
Base can't be negative. Hence b = 6.
∴ Base assumed in the asked question must be 6.
∴ Base assumed in the asked question must be 6.
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Community Answer
Teacher said that there were 100 students in his class, 24 of whom wer...
Understanding the Statement
The teacher mentioned that there were 100 students in the class, comprising 24 boys and 32 girls. To determine the base system used, we need to analyze the numbers.
Breaking Down the Numbers
- The total number of students is stated as 100.
- The number of boys is 24.
- The number of girls is 32.
Calculating the Total
When we add the number of boys and girls:
- 24 (boys) + 32 (girls) = 56.
Since the total students mentioned is 100, it indicates a discrepancy because 56 does not equal 100 in the decimal (base 10) system.
Exploring Base Systems
Now, we will explore the base system that would make 24 and 32 add up to 100:
- Base 6 (Correct Answer):
- In base 6, the numbers 24 and 32 can be interpreted as:
- 24 in base 6 = 2*6 + 4 = 16 in decimal.
- 32 in base 6 = 3*6 + 2 = 20 in decimal.
- Adding these values: 16 + 20 = 36 in decimal.
- In base 6, the number 100 is represented as 6*6 + 0*6 + 0 = 36 in decimal.
Thus, when viewed through the lens of base 6, the teacher's statement holds true.
Conclusion
The teacher is using base 6 in his calculations, as it aligns with the total students being 100 when the respective values for boys and girls are considered.
The teacher mentioned that there were 100 students in the class, comprising 24 boys and 32 girls. To determine the base system used, we need to analyze the numbers.
Breaking Down the Numbers
- The total number of students is stated as 100.
- The number of boys is 24.
- The number of girls is 32.
Calculating the Total
When we add the number of boys and girls:
- 24 (boys) + 32 (girls) = 56.
Since the total students mentioned is 100, it indicates a discrepancy because 56 does not equal 100 in the decimal (base 10) system.
Exploring Base Systems
Now, we will explore the base system that would make 24 and 32 add up to 100:
- Base 6 (Correct Answer):
- In base 6, the numbers 24 and 32 can be interpreted as:
- 24 in base 6 = 2*6 + 4 = 16 in decimal.
- 32 in base 6 = 3*6 + 2 = 20 in decimal.
- Adding these values: 16 + 20 = 36 in decimal.
- In base 6, the number 100 is represented as 6*6 + 0*6 + 0 = 36 in decimal.
Thus, when viewed through the lens of base 6, the teacher's statement holds true.
Conclusion
The teacher is using base 6 in his calculations, as it aligns with the total students being 100 when the respective values for boys and girls are considered.
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Teacher said that there were 100 students in his class, 24 of whom were boys and 32 were girls. Which base system did the teacher use in this statement?a)9b)5c)6d)8Correct answer is option 'C'. Can you explain this answer? for Mechanical Engineering 2025 is part of Mechanical Engineering preparation. The Question and answers have been prepared according to the Mechanical Engineering exam syllabus. Information about Teacher said that there were 100 students in his class, 24 of whom were boys and 32 were girls. Which base system did the teacher use in this statement?a)9b)5c)6d)8Correct answer is option 'C'. Can you explain this answer? covers all topics & solutions for Mechanical Engineering 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Teacher said that there were 100 students in his class, 24 of whom were boys and 32 were girls. Which base system did the teacher use in this statement?a)9b)5c)6d)8Correct answer is option 'C'. Can you explain this answer?.
Teacher said that there were 100 students in his class, 24 of whom were boys and 32 were girls. Which base system did the teacher use in this statement?a)9b)5c)6d)8Correct answer is option 'C'. Can you explain this answer? for Mechanical Engineering 2025 is part of Mechanical Engineering preparation. The Question and answers have been prepared according to the Mechanical Engineering exam syllabus. Information about Teacher said that there were 100 students in his class, 24 of whom were boys and 32 were girls. Which base system did the teacher use in this statement?a)9b)5c)6d)8Correct answer is option 'C'. Can you explain this answer? covers all topics & solutions for Mechanical Engineering 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Teacher said that there were 100 students in his class, 24 of whom were boys and 32 were girls. Which base system did the teacher use in this statement?a)9b)5c)6d)8Correct answer is option 'C'. Can you explain this answer?.
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