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Three friends - Annie, Bobby and Carole like to play with numbers. Annie picks a random natural number x, triples it and gives the result to Bobby. Each time Bobby gets a number from Annie; he adds 75 to the number and gives the result to Carole. Each time Carole gets a number from Bobby, she doubles the number and subtracts 50 from it and gives the result to Annie. Annie again triples it and gives the result to Bobby and this process continues. The first person to receive a 5-digit number (from other) is declared the winner. If Bobby wins the game, what is remainder when the least possible value of x is divided by 13?
  • a)
    7
  • b)
    8
  • c)
    9
  • d)
    10
Correct answer is option 'C'. Can you explain this answer?
Most Upvoted Answer
Three friends - Annie, Bobby and Carole like to play with numbers. An...
Bobby wins the game.
⇒ Bobby received a 5-digit number. 108x + 2100 > 9999 ⇒ x = 74 Remainder when 74 is divided by 13 = 9 Hence, option 3.
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Community Answer
Three friends - Annie, Bobby and Carole like to play with numbers. An...
To find the remainder when the least possible value of x is divided by 13, we need to understand the pattern of numbers that are generated by Annie, Bobby, and Carole.

Let's start by analyzing the operations performed by each person:

1. Annie: Triples the number and gives the result to Bobby.
- Operation: 3x
- Result given to Bobby: 3x

2. Bobby: Adds 75 to the number and gives the result to Carole.
- Operation: 3x + 75
- Result given to Carole: 3x + 75

3. Carole: Doubles the number and subtracts 50 from it and gives the result to Annie.
- Operation: 2(3x + 75) - 50 = 6x + 150 - 50 = 6x + 100
- Result given to Annie: 6x + 100

The process continues with Annie receiving the result from Carole and performing the triple operation.

From the above analysis, we can see that the numbers generated by Carole are of the form 6x + 100. Let's find the condition for Bobby to receive a 5-digit number from Carole.

5-digit numbers range from 10000 to 99999. So, we can set up the following inequality:

10000 ≤ 6x + 100 ≤ 99999

Simplifying the inequality:

10000 - 100 ≤ 6x ≤ 99999 - 100

9900 ≤ 6x ≤ 99899

Dividing both sides by 6:

1650 ≤ x ≤ 16649

Since x is a natural number, the least possible value of x is 1650.

Now, we need to find the remainder when 1650 is divided by 13.

1650 ÷ 13 = 126 remainder 12

Therefore, the remainder when the least possible value of x is divided by 13 is 12.

Hence, the correct answer is option 'C' (9).
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Three friends - Annie, Bobby and Carole like to play with numbers. Annie picks a random natural number x, triples it and gives the result to Bobby. Each time Bobby gets a number from Annie; he adds 75 to the number and gives the result to Carole. Each time Carole gets a number from Bobby, she doubles the number and subtracts 50 from it and gives the result to Annie. Annie again triples it and gives the result to Bobby and this process continues. The first person to receive a 5-digit number (from other) is declared the winner. If Bobby wins the game, what is remainder when the least possible value of x is divided by 13?a)7b)8c)9d)10Correct answer is option 'C'. Can you explain this answer?
Question Description
Three friends - Annie, Bobby and Carole like to play with numbers. Annie picks a random natural number x, triples it and gives the result to Bobby. Each time Bobby gets a number from Annie; he adds 75 to the number and gives the result to Carole. Each time Carole gets a number from Bobby, she doubles the number and subtracts 50 from it and gives the result to Annie. Annie again triples it and gives the result to Bobby and this process continues. The first person to receive a 5-digit number (from other) is declared the winner. If Bobby wins the game, what is remainder when the least possible value of x is divided by 13?a)7b)8c)9d)10Correct answer is option 'C'. Can you explain this answer? for NEET 2024 is part of NEET preparation. The Question and answers have been prepared according to the NEET exam syllabus. Information about Three friends - Annie, Bobby and Carole like to play with numbers. Annie picks a random natural number x, triples it and gives the result to Bobby. Each time Bobby gets a number from Annie; he adds 75 to the number and gives the result to Carole. Each time Carole gets a number from Bobby, she doubles the number and subtracts 50 from it and gives the result to Annie. Annie again triples it and gives the result to Bobby and this process continues. The first person to receive a 5-digit number (from other) is declared the winner. If Bobby wins the game, what is remainder when the least possible value of x is divided by 13?a)7b)8c)9d)10Correct answer is option 'C'. Can you explain this answer? covers all topics & solutions for NEET 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Three friends - Annie, Bobby and Carole like to play with numbers. Annie picks a random natural number x, triples it and gives the result to Bobby. Each time Bobby gets a number from Annie; he adds 75 to the number and gives the result to Carole. Each time Carole gets a number from Bobby, she doubles the number and subtracts 50 from it and gives the result to Annie. Annie again triples it and gives the result to Bobby and this process continues. The first person to receive a 5-digit number (from other) is declared the winner. If Bobby wins the game, what is remainder when the least possible value of x is divided by 13?a)7b)8c)9d)10Correct answer is option 'C'. Can you explain this answer?.
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