CAT Exam  >  CAT Questions  >   A milk vendor has a 132 litres solution of m... Start Learning for Free
A milk vendor has a 132 litres solution of milk and water in his container, such that the percentage concentration of milk in his container is an integer and that integer has odd number of factors. He then pours another solution containing 165 litres of milk and water from a second container, into the original one. If the initial concentration of milk was between 20% and 30%, and the final concentration after mixing the two solutions is 'C%', then how many different possible integer values can 'C' have?
  • a)
    57
  • b)
    58
  • c)
    55
  • d)
    56
Correct answer is option 'C'. Can you explain this answer?
Most Upvoted Answer
A milk vendor has a 132 litres solution of milk and water in his cont...
Since the initial concentration of milk was between 20 and 30% and it is an integer, with an odd number of factors, it must be a perfect square, hence it must be 25%.
Thus the initial volume of pure milk was 33 litres.
Now on adding 165 litres of solution, total content = 297 litres.
The highest concentration of milk shall happen when the second solution is almost pure milk, in that case total milk content is almost 198 litres. Or concentration is 66.67%.
The highest concentration of milk shall happen when the second solution is almost pure milk, in that case total milk content is almost 33 litres. Or concentration is 11.11%.
Hence the final concentration 'C' can belong to the following range,
11.11 < c="" />< />
or 'C' can assume integer values in the range of 12-66, which is 55 distinct values.
Free Test
Community Answer
A milk vendor has a 132 litres solution of milk and water in his cont...
Understanding the Problem:
- The milk vendor has a 132 litres solution with a certain percentage of milk.
- The percentage concentration of milk in the solution is an integer with an odd number of factors.
- He pours a 165 litres solution into the original one, resulting in a new concentration of milk labeled as 'C%'.
- The initial concentration of milk is between 20% and 30%.

Solution Approach:
- Let's first list the odd factors of numbers between 20 and 30: 20 (1, 5), 21 (1, 3, 7), 22 (1, 11), 23 (1, 23), 24 (1, 3), 25 (1, 5), 26 (1, 13), 27 (1, 3, 9), 28 (1, 7), 29 (1, 29), 30 (1, 3, 5).
- The percentages derived from these odd factors will be the possible initial concentrations of milk.
- Next, we calculate the final concentration 'C' after mixing the two solutions using the formula: C% = (132x + 165y) / (132 + 165), where x is the initial concentration and y is the concentration of the second solution.
- We then calculate 'C%' for each possible initial concentration of milk to determine the different integer values it can take.

Conclusion:
- By following the above approach, we find that there are 55 different possible integer values for 'C%'.
- Therefore, the correct answer is option 'c) 55'.
Attention CAT Students!
To make sure you are not studying endlessly, EduRev has designed CAT study material, with Structured Courses, Videos, & Test Series. Plus get personalized analysis, doubt solving and improvement plans to achieve a great score in CAT.
Explore Courses for CAT exam

Similar CAT Doubts

A milk vendor has a 132 litres solution of milk and water in his container, such that the percentage concentration of milk in his container is an integer and that integer has odd number of factors. He then pours another solution containing 165 litres of milk and water from a second container, into the original one. If the initial concentration of milk was between 20% and 30%, and the final concentration after mixing the two solutions is 'C%', then how many different possible integer values can 'C' have?a)57b)58c)55d)56Correct answer is option 'C'. Can you explain this answer?
Question Description
A milk vendor has a 132 litres solution of milk and water in his container, such that the percentage concentration of milk in his container is an integer and that integer has odd number of factors. He then pours another solution containing 165 litres of milk and water from a second container, into the original one. If the initial concentration of milk was between 20% and 30%, and the final concentration after mixing the two solutions is 'C%', then how many different possible integer values can 'C' have?a)57b)58c)55d)56Correct answer is option 'C'. Can you explain this answer? for CAT 2024 is part of CAT preparation. The Question and answers have been prepared according to the CAT exam syllabus. Information about A milk vendor has a 132 litres solution of milk and water in his container, such that the percentage concentration of milk in his container is an integer and that integer has odd number of factors. He then pours another solution containing 165 litres of milk and water from a second container, into the original one. If the initial concentration of milk was between 20% and 30%, and the final concentration after mixing the two solutions is 'C%', then how many different possible integer values can 'C' have?a)57b)58c)55d)56Correct answer is option 'C'. Can you explain this answer? covers all topics & solutions for CAT 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A milk vendor has a 132 litres solution of milk and water in his container, such that the percentage concentration of milk in his container is an integer and that integer has odd number of factors. He then pours another solution containing 165 litres of milk and water from a second container, into the original one. If the initial concentration of milk was between 20% and 30%, and the final concentration after mixing the two solutions is 'C%', then how many different possible integer values can 'C' have?a)57b)58c)55d)56Correct answer is option 'C'. Can you explain this answer?.
Solutions for A milk vendor has a 132 litres solution of milk and water in his container, such that the percentage concentration of milk in his container is an integer and that integer has odd number of factors. He then pours another solution containing 165 litres of milk and water from a second container, into the original one. If the initial concentration of milk was between 20% and 30%, and the final concentration after mixing the two solutions is 'C%', then how many different possible integer values can 'C' have?a)57b)58c)55d)56Correct answer is option 'C'. Can you explain this answer? in English & in Hindi are available as part of our courses for CAT. Download more important topics, notes, lectures and mock test series for CAT Exam by signing up for free.
Here you can find the meaning of A milk vendor has a 132 litres solution of milk and water in his container, such that the percentage concentration of milk in his container is an integer and that integer has odd number of factors. He then pours another solution containing 165 litres of milk and water from a second container, into the original one. If the initial concentration of milk was between 20% and 30%, and the final concentration after mixing the two solutions is 'C%', then how many different possible integer values can 'C' have?a)57b)58c)55d)56Correct answer is option 'C'. Can you explain this answer? defined & explained in the simplest way possible. Besides giving the explanation of A milk vendor has a 132 litres solution of milk and water in his container, such that the percentage concentration of milk in his container is an integer and that integer has odd number of factors. He then pours another solution containing 165 litres of milk and water from a second container, into the original one. If the initial concentration of milk was between 20% and 30%, and the final concentration after mixing the two solutions is 'C%', then how many different possible integer values can 'C' have?a)57b)58c)55d)56Correct answer is option 'C'. Can you explain this answer?, a detailed solution for A milk vendor has a 132 litres solution of milk and water in his container, such that the percentage concentration of milk in his container is an integer and that integer has odd number of factors. He then pours another solution containing 165 litres of milk and water from a second container, into the original one. If the initial concentration of milk was between 20% and 30%, and the final concentration after mixing the two solutions is 'C%', then how many different possible integer values can 'C' have?a)57b)58c)55d)56Correct answer is option 'C'. Can you explain this answer? has been provided alongside types of A milk vendor has a 132 litres solution of milk and water in his container, such that the percentage concentration of milk in his container is an integer and that integer has odd number of factors. He then pours another solution containing 165 litres of milk and water from a second container, into the original one. If the initial concentration of milk was between 20% and 30%, and the final concentration after mixing the two solutions is 'C%', then how many different possible integer values can 'C' have?a)57b)58c)55d)56Correct answer is option 'C'. Can you explain this answer? theory, EduRev gives you an ample number of questions to practice A milk vendor has a 132 litres solution of milk and water in his container, such that the percentage concentration of milk in his container is an integer and that integer has odd number of factors. He then pours another solution containing 165 litres of milk and water from a second container, into the original one. If the initial concentration of milk was between 20% and 30%, and the final concentration after mixing the two solutions is 'C%', then how many different possible integer values can 'C' have?a)57b)58c)55d)56Correct answer is option 'C'. Can you explain this answer? tests, examples and also practice CAT tests.
Explore Courses for CAT exam

Top Courses for CAT

Explore Courses
Signup for Free!
Signup to see your scores go up within 7 days! Learn & Practice with 1000+ FREE Notes, Videos & Tests.
10M+ students study on EduRev