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James deposited $1,000 each in two investment schemes X and Y. Scheme X doubles the invested amount  every 7 years and scheme Y doubles the invested amount every 14 years. If James withdraws $500 from scheme X at the end of every 7th year, how many years will it take for the total amount invested in schemes X and Y to amount more than $40,000?

  • a)
    14

  • b)
    28

  • c)
    42

  • d)
    56

  • e)
    70

Correct answer is option 'C'. Can you explain this answer?
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Verified Answer
James deposited $1,000 each in two investment schemes X and Y. Scheme ...
Given
  • Scheme X doubles the invested amount every 7 years
    • James deposited $1000 in scheme X
    • James withdraws $500 from scheme X after the end of every 7 years
       
  • Scheme Y doubles the invested amount after every 14 years
    • James deposited $1,000 in scheme Y
To Find: Number of years it will take total amount deposited in schemes X and Y to grow to > $40,000?
Approach
  1. For finding the number of years it will take the deposits in schemes X and Y to grow to more than $40,000, we need to find the amount in both the schemes X and Y after every 7 years.(As amount in scheme X doubles after every 7 years, we will need to calculate the amount at the end of every 7 years and not at the end of 14 years).
  2. Scheme X
    1. As the amount invested in scheme X doubles every 7 years, we will need to calculate the amount in scheme X after every interval of 7 years
    2. However, we will need to make sure that we subtract $500 at each interval of 7 years from the final amount
  3. Scheme Y
    1. As the amount invested in scheme Y doubles after every 14 years, we will need to calculate the amount in scheme Y after every interval of 14 years.
  4. At each interval, we will calculate the sum of amounts in scheme X and Y to check if it exceeds $40,000.
Working Out
 
  1. Amount at the end of year 7 in scheme X = $1000 * 2 = $2000
    1. However James withdrew $500 at the end of 7th year, So, the amount remaining will be $2000 – $500 = $1500
    2. The same logic has been applied in calculating the amounts at the end of every 7 year interval
       
  2. Amount at the end of year 14 in scheme Y = $1000 * 2 = $2000
    1. The same logic has been applied in calculating the amounts at the end of every 14 years interval.
       
  3. We can see that the total amount in schemes X and Y exceed $40,000 by the end of the year 42.
 
Answer: C
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Most Upvoted Answer
James deposited $1,000 each in two investment schemes X and Y. Scheme ...
Given



  • Scheme X doubles the invested amount every 7 years

    • James deposited $1000 in scheme X

    • James withdraws $500 from scheme X after the end of every 7 years

       



  • Scheme Y doubles the invested amount after every 14 years

    • James deposited $1,000 in scheme Y





To Find: Number of years it will take total amount deposited in schemes X and Y to grow to > $40,000?


Approach



  1. For finding the number of years it will take the deposits in schemes X and Y to grow to more than $40,000, we need to find the amount in both the schemes X and Y after every 7 years.(As amount in scheme X doubles after every 7 years, we will need to calculate the amount at the end of every 7 years and not at the end of 14 years).

  2. Scheme X

    1. As the amount invested in scheme X doubles every 7 years, we will need to calculate the amount in scheme X after every interval of 7 years

    2. However, we will need to make sure that we subtract $500 at each interval of 7 years from the final amount



  3. Scheme Y

    1. As the amount invested in scheme Y doubles after every 14 years, we will need to calculate the amount in scheme Y after every interval of 14 years.



  4. At each interval, we will calculate the sum of amounts in scheme X and Y to check if it exceeds $40,000.



Working Out


 





  1. Amount at the end of year 7 in scheme X = $1000 * 2 = $2000

    1. However James withdrew $500 at the end of 7th year, So, the amount remaining will be $2000 – $500 = $1500

    2. The same logic has been applied in calculating the amounts at the end of every 7 year interval

       



  2. Amount at the end of year 14 in scheme Y = $1000 * 2 = $2000

    1. The same logic has been applied in calculating the amounts at the end of every 14 years interval.

       



  3. We can see that the total amount in schemes X and Y exceed $40,000 by the end of the year 42.



 


Answer: C
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Community Answer
James deposited $1,000 each in two investment schemes X and Y. Scheme ...
Given
  • Scheme X doubles the invested amount every 7 years
    • James deposited $1000 in scheme X
    • James withdraws $500 from scheme X after the end of every 7 years
       
  • Scheme Y doubles the invested amount after every 14 years
    • James deposited $1,000 in scheme Y
To Find: Number of years it will take total amount deposited in schemes X and Y to grow to > $40,000?
Approach
  1. For finding the number of years it will take the deposits in schemes X and Y to grow to more than $40,000, we need to find the amount in both the schemes X and Y after every 7 years.(As amount in scheme X doubles after every 7 years, we will need to calculate the amount at the end of every 7 years and not at the end of 14 years).
  2. Scheme X
    1. As the amount invested in scheme X doubles every 7 years, we will need to calculate the amount in scheme X after every interval of 7 years
    2. However, we will need to make sure that we subtract $500 at each interval of 7 years from the final amount
  3. Scheme Y
    1. As the amount invested in scheme Y doubles after every 14 years, we will need to calculate the amount in scheme Y after every interval of 14 years.
  4. At each interval, we will calculate the sum of amounts in scheme X and Y to check if it exceeds $40,000.
Working Out
 
  1. Amount at the end of year 7 in scheme X = $1000 * 2 = $2000
    1. However James withdrew $500 at the end of 7th year, So, the amount remaining will be $2000 – $500 = $1500
    2. The same logic has been applied in calculating the amounts at the end of every 7 year interval
       
  2. Amount at the end of year 14 in scheme Y = $1000 * 2 = $2000
    1. The same logic has been applied in calculating the amounts at the end of every 14 years interval.
       
  3. We can see that the total amount in schemes X and Y exceed $40,000 by the end of the year 42.
 
Answer: C
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James deposited $1,000 each in two investment schemes X and Y. Scheme X doubles the invested amount every 7 years and scheme Y doubles the invested amount every 14 years. If James withdraws $500 from scheme X at the end of every 7th year, how many years will it take for the total amount invested in schemes X and Y to amount more than $40,000?a)14b)28c)42d)56e)70Correct answer is option 'C'. Can you explain this answer?
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James deposited $1,000 each in two investment schemes X and Y. Scheme X doubles the invested amount every 7 years and scheme Y doubles the invested amount every 14 years. If James withdraws $500 from scheme X at the end of every 7th year, how many years will it take for the total amount invested in schemes X and Y to amount more than $40,000?a)14b)28c)42d)56e)70Correct answer is option 'C'. Can you explain this answer? for GMAT 2025 is part of GMAT preparation. The Question and answers have been prepared according to the GMAT exam syllabus. Information about James deposited $1,000 each in two investment schemes X and Y. Scheme X doubles the invested amount every 7 years and scheme Y doubles the invested amount every 14 years. If James withdraws $500 from scheme X at the end of every 7th year, how many years will it take for the total amount invested in schemes X and Y to amount more than $40,000?a)14b)28c)42d)56e)70Correct answer is option 'C'. Can you explain this answer? covers all topics & solutions for GMAT 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for James deposited $1,000 each in two investment schemes X and Y. Scheme X doubles the invested amount every 7 years and scheme Y doubles the invested amount every 14 years. If James withdraws $500 from scheme X at the end of every 7th year, how many years will it take for the total amount invested in schemes X and Y to amount more than $40,000?a)14b)28c)42d)56e)70Correct answer is option 'C'. Can you explain this answer?.
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