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A nursery has 363, 429 and 693 plants respectively of 3 distinct varieties. It is desired to place these plants in straight rows of plants of 1 variety only so that the number of rows required is the minimum. What is the size of each row and how many rows would be required?
 
  • a)
    33 and 45
  • b)
    37 and 48
  • c)
    41 and 56
  • d)
    45 and 55
Correct answer is option 'A'. Can you explain this answer?
Most Upvoted Answer
A nursery has 363, 429 and 693 plants respectively of 3 distinct varie...
Solution:

To find the size of each row and the number of rows required, we need to find the HCF (highest common factor) of the given numbers.

1. Find the prime factors of the given numbers:
- 363 = 3 x 11 x 11
- 429 = 3 x 11 x 13
- 693 = 3 x 3 x 7 x 11

2. Identify the common factors of the given numbers:
- The common factor is 3 x 11 = 33

3. Divide each number by the common factor:
- 363 ÷ 33 = 11
- 429 ÷ 33 = 13
- 693 ÷ 33 = 21

The size of each row is 33 plants and the number of rows required are 11, 13, and 21 for the three varieties respectively.

Therefore, the correct answer is option A: 33 and 45.
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Community Answer
A nursery has 363, 429 and 693 plants respectively of 3 distinct varie...
The size of each row would be the HCF of 363, 429 and 693. Difference between 363 and 429 =66.
Factors of 66 are 66, 33, 22, 11, 6, 3, 2, 1.
66 need not to be checked as it is even and 363 is odd. 33 divides 363, hence would automatically divide
429 and also divides 693. Hence, 33 is the correct answer for the size of each row.
For how many rows would be required we need to follow the following process:
Minimum number of rows required = 363/33 + 429/33 + 693/33 = 11 + 13 + 21 = 45 rows.
Therefore, the correct answer is A
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A nursery has 363, 429 and 693 plants respectively of 3 distinct varieties. It is desired to place these plants in straight rows of plants of 1 variety only so that the number of rows required is the minimum. What is the size of each row and how many rows would be required?a)33 and 45b)37 and 48c)41 and 56d)45 and 55Correct answer is option 'A'. Can you explain this answer?
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A nursery has 363, 429 and 693 plants respectively of 3 distinct varieties. It is desired to place these plants in straight rows of plants of 1 variety only so that the number of rows required is the minimum. What is the size of each row and how many rows would be required?a)33 and 45b)37 and 48c)41 and 56d)45 and 55Correct answer is option 'A'. Can you explain this answer? for UPSC 2024 is part of UPSC preparation. The Question and answers have been prepared according to the UPSC exam syllabus. Information about A nursery has 363, 429 and 693 plants respectively of 3 distinct varieties. It is desired to place these plants in straight rows of plants of 1 variety only so that the number of rows required is the minimum. What is the size of each row and how many rows would be required?a)33 and 45b)37 and 48c)41 and 56d)45 and 55Correct answer is option 'A'. Can you explain this answer? covers all topics & solutions for UPSC 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A nursery has 363, 429 and 693 plants respectively of 3 distinct varieties. It is desired to place these plants in straight rows of plants of 1 variety only so that the number of rows required is the minimum. What is the size of each row and how many rows would be required?a)33 and 45b)37 and 48c)41 and 56d)45 and 55Correct answer is option 'A'. Can you explain this answer?.
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