In an MBA selection process, the ratio of selected to unselected candidates was 11 : 2. If 40 fewer candidates had applied and 20 fewer had been selected, the ratio of selected to unselected would have become 10 : 1. How many candidates had originally applied?

Introduction / Context:
This problem involves working with ratios and a hypothetical change in the number of candidates. Initially, we know the ratio of selected to unselected candidates. After a hypothetical reduction in both total applicants and selected candidates, the ratio changes. The task is to find the original total number of applicants. These questions are common in exam settings and test skill with forming and solving algebraic equations from verbal ratio statements.

Given Data / Assumptions:

• Initial ratio of selected to unselected candidates = 11 : 2.
• In a hypothetical case, 40 fewer candidates applied and 20 fewer were selected.
• Under this hypothetical scenario, the new ratio of selected to unselected is 10 : 1.
• We need the original number of candidates who applied.

Concept / Approach:
Let the number of selected candidates initially be 11k and unselected candidates be 2k, so total applicants N = 13k. After the hypothetical change, the total applicants become N - 40 and the selected become 11k - 20. The unselected become (N - 40) - (11k - 20). The new ratio (selected : unselected) is 10 : 1, which gives an equation in k. Solving this equation gives k, and hence N = 13k.

Step-by-Step Solution:
Let initial selected candidates = 11k and unselected candidates = 2k.Total initial applicants N = 11k + 2k = 13k.In the hypothetical situation, total applicants become N - 40 = 13k - 40.Selected candidates become 11k - 20.Unselected candidates in the hypothetical case = (13k - 40) - (11k - 20) = 13k - 40 - 11k + 20 = 2k - 20.We are told that the new ratio of selected to unselected is 10 : 1.So (11k - 20) / (2k - 20) = 10 / 1.Cross multiply: 11k - 20 = 10 * (2k - 20).11k - 20 = 20k - 200.Bring like terms together: 20k - 11k = 200 - 20.9k = 180, so k = 20.Therefore, original total applicants N = 13k = 13 * 20 = 260.

Verification / Alternative check:
Original: selected = 11 * 20 = 220, unselected = 2 * 20 = 40, total = 260.Initial ratio selected : unselected = 220 : 40 = 11 : 2, which matches the given ratio.Hypothetical: total = 260 - 40 = 220, selected = 220 - 20 = 200.Unselected in the hypothetical case = 220 - 200 = 20.New ratio selected : unselected = 200 : 20 = 10 : 1, which matches the condition.

Why Other Options Are Wrong:
If we assume other totals like 220, 300 or 340, we do not get integer values of selected and unselected candidates that satisfy both ratio conditions simultaneously. Only N = 260 allows consistent integer values that satisfy both the original and the hypothetical ratio statements.

Common Pitfalls:
Common errors include mixing up the direction of the hypothetical changes or forgetting that unselected candidates in the second case must be computed as total minus selected. Some students also misinterpret the 40 fewer applicants as referring only to selected candidates. Carefully defining selected, unselected and total in both scenarios and forming an equation using the given ratios avoids such mistakes.

Final Answer:
The original number of candidates who applied for the process was 260.