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If p, q and r are positive integers such that pq=231 and qr=63 then the smallest possible value of p+q+r is?
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If p, q and r are positive integers such that pq=231 and qr=63 then th...
Solution:
Given:
- pq = 231
- qr = 63
- p, q, r are positive integers
To find:
- The smallest possible value of pqr
Approach:
- Firstly, we need to factorize 231 and 63 to get the values of p, q and r.
- Then, we need to find the product of p, q and r to get the smallest possible value of pqr.
Factorizing 231:
- 231 can be factorized as 231 = 3 × 7 × 11.
- Therefore, p, q and r can take the values of 3, 7 and 11 in some order.
Factorizing 63:
- 63 can be factorized as 63 = 3 × 3 × 7.
- Therefore, p, q and r can take the values of 3, 7 and 3 in some order.
Product of p, q and r:
- The possible values of p, q and r are:
- p = 3, q = 7, r = 11
- p = 3, q = 11, r = 7
- p = 7, q = 3, r = 3
- p = 11, q = 3, r = 7
- The product of p, q and r for each of the above cases is:
- 3 × 7 × 11 = 231
- 3 × 11 × 7 = 231
- 7 × 3 × 3 = 63
- 11 × 3 × 7 = 231
- Therefore, the smallest possible value of pqr is 63.
Answer:
- The smallest possible value of pqr is 63.
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If p, q and r are positive integers such that pq=231 and qr=63 then the smallest possible value of p+q+r is?
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If p, q and r are positive integers such that pq=231 and qr=63 then the smallest possible value of p+q+r is? for CAT 2024 is part of CAT preparation. The Question and answers have been prepared according to the CAT exam syllabus. Information about If p, q and r are positive integers such that pq=231 and qr=63 then the smallest possible value of p+q+r is? covers all topics & solutions for CAT 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If p, q and r are positive integers such that pq=231 and qr=63 then the smallest possible value of p+q+r is?.
If p, q and r are positive integers such that pq=231 and qr=63 then the smallest possible value of p+q+r is? for CAT 2024 is part of CAT preparation. The Question and answers have been prepared according to the CAT exam syllabus. Information about If p, q and r are positive integers such that pq=231 and qr=63 then the smallest possible value of p+q+r is? covers all topics & solutions for CAT 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If p, q and r are positive integers such that pq=231 and qr=63 then the smallest possible value of p+q+r is?.
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