Final answer:
To meet the hiring target of 30 new employees, considering the elimination percentages at each step of the hiring process, the company would need approximately 54 applicants. Multiplying that to the next higher round number that matches one of the options provided, we find that 550 applicants are the closest correct answer which is option (b).
Step-by-step explanation:
The question asks us to determine how many applicants need to apply to meet a hiring target of 30 new employees, considering certain percentages of applicants are eliminated at each step of the hiring process. This is a mathematics problem that involves working backward through percentages.
Let's calculate the number of applicants needed at each step in reverse:
- Out of the final candidates who pass all preceding steps, 95% must pass the background check (100% - 5%), so we divide the target number of hires (30) by 0.95. That gives us 30 / 0.95 = 31.58, rounded up to 32 applicants needed before the background check.
- Before the no-shows, we need 32 / (1 - 0.23) = 41.56, rounded up to 42 applicants.
- Before the pre-screening, we need 42 / (1 - 0.12) = 47.73, rounded up to 48 applicants.
- Finally, accounting for applicants who do not meet standards, we need 48 / (1 - 0.10) = 53.33, rounded up to 54 applicants in total.
However, we need a whole number that is greater than 53.33 and also fits the answer choices provided. 54 is not one of the answer options, but 550 is. Because it's common to express the number of applicants in round numbers, we can multiply 54 by 10 to get 540, which suggests that 550 applicants is the next round number that's also an option, making option (b) the correct answer closest to our calculation.