CAT Question > A milk vendor has a 132 litres solution of m...

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?

Nipun Tuteja
Sep 24, 2022 |

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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?

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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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 2022 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 2022 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?.

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 2022 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 2022 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?.

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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 or 'C' can assume integer values in the range of 12-66, which is 55 distinct values.