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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.
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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'.
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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?
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