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An army’s recruitment process included n rounds of selection tasks. For the first a rounds, the rejection percentage was 60 percent per round. For the next b rounds, the rejection percentage was 50 percent per round and for the remaining rounds, the selection percentage was 70 percent per round. If there were 100000 people who applied for the army and 1400 were finally selected, what was the value of n?
  • a)
    4
  • b)
    5
  • c)
    6
  • d)
    8
  • e)
    10
Correct answer is option 'C'. Can you explain this answer?
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Verified Answer
An army’s recruitment process included n rounds of selection tas...
Given:
  • Total number of applicants = 100000
  • Total people selected = 1400
  • Total number of rounds = n
  • Rejection percentage of each round for the first a rounds = 60%
    • Selection percentage of each round for the first n rounds = 40%
  • Rejection percentage of each round for the next b rounds = 50%
    • Selection percentage of each round for the next b rounds = 50%
  • Selection percentage of each round for the remaining rounds(let’s say c rounds) = 70%
To Find: Value of n?
  • n = a + b + c
    • So, we need to find the values of either all of a, b or c or the value of sum of a , b and c.
Approach:
  1. As we know the number of applicants, the selection percentage of each round and the number of people finally selected, we would need to devise an expression for people finally selected in terms of a, b and c.
  2. So, number of people who cleared the 1st round = Total number of applicants  x selection percentage of first round
    • Similarly, people who cleared the first 2 rounds = Total number of applicants x selection percentage of first
      round x selection percentage of second round
    • So, people who cleared the first a rounds = Total number of applicants x selection percentage of first round  x selection percentage of second round x  ...selection percentage of a round
    • As the selection percentage of each of the first a rounds is the same, we can write, people who cleared the first a rounds = Total number of applicants  x (selection percentage of each round till the a rounds)a
  3. Similarly, number of people who cleared the next b rounds as well= Total number of applicants x  (selection percentage of each round till a rounds)a x selection percentage of each round till the next b rounds)b
  4. So, number of people who cleared the last c rounds as well= Total number of applicants x  (selection percentage of each round till a rounds)a x (selection percentage of each round till next b rounds)b x  (selection percentage of each round till the last c rounds)
    c
  5. (People who were finally selected) = (people who cleared all the rounds).
  6. Now, we will prime factorize the expression on both the sides and equate the exponents of the individual prime factors to find the values of a, b and c.
Working out:
1. Total number of applicants = 100000
2. Number of people who were selected = (Number of people who cleared all the rounds). So, we can write
3. Comparing the powers of each prime factor on the two sides of the above equation:
  • Comparing powers of 7, we have c = 1
  • Comparing powers of 5, we have 5 – a –c = 2. As c = 1, we have a = 2
  • Comparing powers of 2, we have 5 + a – b – c = 3.
    • As c = 1 and a = 2, we have b = 3
4.  So, n = a+ b+ c = 2 + 3+1 = 6
Answer: C
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Most Upvoted Answer
An army’s recruitment process included n rounds of selection tas...
Given:
- Number of rounds of selection tasks: n
- Rejection percentage for the first a rounds: 60%
- Rejection percentage for the next b rounds: 50%
- Selection percentage for the remaining rounds: 70%
- Total number of applicants: 100000
- Number of people finally selected: 1400

To find: The value of n

Approach:
We can use the concept of percentages to calculate the number of applicants who were rejected in each of the rounds and the number of applicants who were selected in the end.

1. Calculate the number of applicants who were rejected in the first a rounds:
- In each round, 60% of the applicants were rejected.
- So, the number of applicants who were rejected in each of the first a rounds = 0.6 * (total number of applicants) = 0.6 * 100000 = 60000
- Therefore, the number of applicants who were not rejected in the first a rounds = (total number of applicants) - (number of applicants rejected in the first a rounds) = 100000 - (a * 60000)

2. Calculate the number of applicants who were rejected in the next b rounds:
- In each round, 50% of the applicants were rejected.
- So, the number of applicants who were rejected in each of the next b rounds = 0.5 * (number of applicants who were not rejected in the first a rounds) = 0.5 * (100000 - a * 60000) = 50000 - 0.3a * 10000

3. Calculate the number of applicants who were selected in the remaining rounds:
- In each round, 70% of the applicants were selected.
- So, the number of applicants who were selected in each of the remaining (n - a - b) rounds = 0.7 * (number of applicants who were not rejected in the first a rounds and next b rounds) = 0.7 * (100000 - a * 60000 - (50000 - 0.3a * 10000)) = 0.7 * (50000 + 0.7a * 10000)

4. Calculate the number of applicants who were finally selected:
- The number of applicants who were finally selected = (number of applicants who were selected in the remaining rounds) - (number of applicants who were rejected in the next b rounds) = 0.7 * (50000 + 0.7a * 10000) - (50000 - 0.3a * 10000) = 35000 + 0.4a * 1000

5. Equate the number of applicants who were finally selected to the given value of 1400 and solve for a:
- 35000 + 0.4a * 1000 = 1400
- 0.4a * 1000 = 12600
- 0.4a = 12.6
- a = 31.5
- As a has to be a whole number, we can round it up to 32.

6. Calculate the value of n:
- The total number of rounds = n
- Number of rounds in which 60% of the applicants were rejected = a
- Number of rounds in which 50% of the applicants
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An army’s recruitment process included n rounds of selection tasks. For the first a rounds, the rejection percentage was 60 percent per round. For the next b rounds, the rejection percentage was 50 percent per round and for the remaining rounds, the selection percentage was 70 percent per round. If there were 100000 people who applied for the army and 1400 were finally selected, what was the value of n?a)4b)5c)6d)8e)10Correct answer is option 'C'. Can you explain this answer?
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