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The mother of four daughters: Tanya, Kamya, Saumya and Ananya, had given them a certain sum of money to make purchases of their own choices. Each of them bought a certain number of items. When their mother questioned them on the quantity of purchases made by them, their replies were as follows:
1. The sum of all items put together that we have purchased is less than 18.
2. The product of the number of items purchased by us is same as the amount you had given to us.
3. Further Tanya had purchased the least quantity followed by Kamya, Saumya and Ananya in that order.
The mother thought for a while on the quantity purchased by her daughters, but could not get the solution. She then asked her daughters whether any one of them had purchased only a single quantity to which the daughters replied and then the mother knew the number of items purchased by each one of them.
 
Q. How many items were purchased by Ananya?
    Correct answer is '5'. Can you explain this answer?
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    The mother of four daughters: Tanya, Kamya, Saumya and Ananya, had giv...
    From the solution to the first question of the set, Ananya purchased 5 items.
    Answer: 5
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    The mother of four daughters: Tanya, Kamya, Saumya and Ananya, had giv...
    Solution:

    Understanding the problem
    In this problem, we need to determine the number of items purchased by each of the four daughters of a mother who had given them a certain sum of money to make purchases of their own choices. The three pieces of information that we have are:

    1. The sum of all items put together that we have purchased is less than 18.
    2. The product of the number of items purchased by us is same as the amount you had given to us.
    3. Further Tanya had purchased the least quantity followed by Kamya, Saumya and Ananya in that order.

    From the first piece of information, we know that the sum of the number of items purchased by all four daughters is less than 18. The second piece of information tells us that the product of the number of items purchased by all four daughters is equal to the amount given by the mother. The third piece of information tells us the order of the number of items purchased by the four daughters.

    Using this information, we need to determine the number of items purchased by each daughter.

    Approach to solving the problem
    We can solve this problem by first using the second piece of information to determine the possible values of the product of the number of items purchased by the four daughters. We can then use the third piece of information to determine the order of the number of items purchased by the daughters. Finally, we can use the first piece of information to eliminate the impossible combinations of the number of items purchased by the daughters.

    Step-by-step solution
    Let's follow the approach mentioned above to solve the problem:

    1. Determine the possible values of the product of the number of items purchased by the four daughters.
    Since the product of the number of items purchased by the four daughters is equal to the amount given by the mother, we can determine the possible values of this product by finding the factors of the amount given by the mother. Let's assume that the amount given by the mother is x.

    Factors of x = {1, x}
    Therefore, the possible values of the product of the number of items purchased by the four daughters are 1 and x.

    2. Determine the order of the number of items purchased by the daughters.
    From the third piece of information, we know that Tanya purchased the least number of items followed by Kamya, Saumya, and Ananya in that order. Let's assume that the number of items purchased by Tanya, Kamya, Saumya, and Ananya are t, k, s, and a respectively.

    Therefore, we have:
    t < k="" />< s="" />< />

    3. Eliminate the impossible combinations of the number of items purchased by the daughters.
    From the first piece of information, we know that the sum of the number of items purchased by all four daughters is less than 18.

    Therefore, we have:
    t + k + s + a < />

    We can use these three conditions to eliminate the impossible combinations of the number of items purchased by the daughters.

    Let's consider the possible values of the product of the number of items purchased by the four daughters and the order in which they purchased the items.

    Case 1: The product of the number of items purchased by the four daughters is 1.

    Since the product of the number of items purchased by the four daughters is 1, we have:

    t × k × s × a = 1

    From the third piece of information, we know that T
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    The mother of four daughters: Tanya, Kamya, Saumya and Ananya, had given them a certain sum of money to make purchases of their own choices. Each of them bought a certain number of items. When their mother questioned them on the quantity of purchases made by them, their replies were as follows:1. The sum of all items put together that we have purchased is less than 18.2. The product of the number of items purchased by us is same as the amount you had given to us.3. Further Tanya had purchased the least quantity followed by Kamya, Saumya and Ananya in that order.The mother thought for a while on the quantity purchased by her daughters, but could not get the solution. She then asked her daughters whether any one of them had purchased only a single quantity to which the daughters replied and then the mother knew the number of items purchased by each one of them.Q.The amount in Rs. given to these daughters by their mother was.... Correct answer is '5'. Can you explain this answer?

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    The mother of four daughters: Tanya, Kamya, Saumya and Ananya, had given them a certain sum of money to make purchases of their own choices. Each of them bought a certain number of items. When their mother questioned them on the quantity of purchases made by them, their replies were as follows:1. The sum of all items put together that we have purchased is less than 18.2. The product of the number of items purchased by us is same as the amount you had given to us.3. Further Tanya had purchased the least quantity followed by Kamya, Saumya and Ananya in that order.The mother thought for a while on the quantity purchased by her daughters, but could not get the solution. She then asked her daughters whether any one of them had purchased only a single quantity to which the daughters replied and then the mother knew the number of items purchased by each one of them.Q.How many items were purchased by Ananya?Correct answer is '5'. Can you explain this answer?
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    The mother of four daughters: Tanya, Kamya, Saumya and Ananya, had given them a certain sum of money to make purchases of their own choices. Each of them bought a certain number of items. When their mother questioned them on the quantity of purchases made by them, their replies were as follows:1. The sum of all items put together that we have purchased is less than 18.2. The product of the number of items purchased by us is same as the amount you had given to us.3. Further Tanya had purchased the least quantity followed by Kamya, Saumya and Ananya in that order.The mother thought for a while on the quantity purchased by her daughters, but could not get the solution. She then asked her daughters whether any one of them had purchased only a single quantity to which the daughters replied and then the mother knew the number of items purchased by each one of them.Q.How many items were purchased by Ananya?Correct answer is '5'. 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 The mother of four daughters: Tanya, Kamya, Saumya and Ananya, had given them a certain sum of money to make purchases of their own choices. Each of them bought a certain number of items. When their mother questioned them on the quantity of purchases made by them, their replies were as follows:1. The sum of all items put together that we have purchased is less than 18.2. The product of the number of items purchased by us is same as the amount you had given to us.3. Further Tanya had purchased the least quantity followed by Kamya, Saumya and Ananya in that order.The mother thought for a while on the quantity purchased by her daughters, but could not get the solution. She then asked her daughters whether any one of them had purchased only a single quantity to which the daughters replied and then the mother knew the number of items purchased by each one of them.Q.How many items were purchased by Ananya?Correct answer is '5'. Can you explain this answer? covers all topics & solutions for CAT 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The mother of four daughters: Tanya, Kamya, Saumya and Ananya, had given them a certain sum of money to make purchases of their own choices. Each of them bought a certain number of items. When their mother questioned them on the quantity of purchases made by them, their replies were as follows:1. The sum of all items put together that we have purchased is less than 18.2. The product of the number of items purchased by us is same as the amount you had given to us.3. Further Tanya had purchased the least quantity followed by Kamya, Saumya and Ananya in that order.The mother thought for a while on the quantity purchased by her daughters, but could not get the solution. She then asked her daughters whether any one of them had purchased only a single quantity to which the daughters replied and then the mother knew the number of items purchased by each one of them.Q.How many items were purchased by Ananya?Correct answer is '5'. Can you explain this answer?.
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