Difficulty: Medium
Correct Answer: 11550
Explanation:
Introduction / Context:
This is a standard election question involving percentages and vote margins. It evaluates the ability to translate information about winning margins into totals and then compute the votes for each candidate.
Given Data / Assumptions:
Concept / Approach:
Let total votes be V. Then the winner gets 70 percent of V and the loser gets 30 percent of V since together they must account for 100 percent of the votes. The margin of victory equals difference between 70 percent of V and 30 percent of V, which is 40 percent of V. Setting this equal to 15,400 allows us to find V and then the loser votes.
Step-by-Step Solution:
Let total votes polled = V.Winner's votes = 0.70 * V.Loser's votes = 0.30 * V.Margin = winner - loser = (0.70V - 0.30V) = 0.40V.Given margin = 15,400, so 0.40V = 15400.Thus V = 15400 / 0.40 = 15400 * (10 / 4) = 15400 * 2.5 = 38,500.Loser's votes = 0.30 * 38,500 = 11,550.
Verification / Alternative check:
Winner's votes = 0.70 * 38,500 = 26,950. Difference between winner and loser votes = 26,950 - 11,550 = 15,400, which matches the margin given. This confirms that 11,550 is correct for the losing candidate.
Why Other Options Are Wrong:
38,500 is the total votes, not the loser votes. Other options such as 26,950 or 13,550 are incorrect because they either correspond to the winner's votes or to arbitrary figures that do not satisfy the margin condition.
Common Pitfalls:
People sometimes treat 70 percent directly as the margin or forget that the loser also has a share of the total. Another common mistake is to take the margin as 30 percent instead of 40 percent of the total. Always compute the difference between the two percentage shares to find the margin portion.
Final Answer:
The losing candidate received 11,550 votes.
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