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Free GMAT Multi-Source Reasoning Practice Question

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Thornfield Apiary keeps bees at two sites, a Meadow site and a Ridge site. After the season the beekeeper wrote: our average hive produced 54 pounds of honey this year. The Meadow hives averaged 60 pounds and the Ridge hives averaged 40 pounds, so 54 is right where I'd expect the apiary's average to land, about midway. These three figures, the Meadow site mean of 60 pounds, the Ridge site mean of 40 pounds, and the claimed apiary mean of 54 pounds, are the only per-hive averages recorded for the season. The cooperative that buys Thornfield's honey wants a verified per-hive average across the whole apiary to set a bulk price.

Suppose that, with every site's per-hive mean unchanged, the Meadow site had held 45 hives rather than its actual number, while Ridge held its actual number of hives. Using the method the sources describe, what would the apiary-wide per-hive average then have been?

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Answer & Explanation

Correct answer

D

The methodology note supplies the rule: the apiary-wide per-hive average is total honey ÷ total hives, where a site's total honey is its hive count × its per-hive mean. The stem alters only Meadow's count to 45 and otherwise holds the season fixed, so you must read the other figures off the cards. The per-hive means come only from the study summary: Meadow 60 lb, Ridge 40 lb. Ridge's actual hive count is not in the stem and cannot be reconstructed from the study summary, which records no counts; it comes only from the results table, which lists Ridge at 15 hives.

Rebuild the totals from these per-site figures: Meadow contributes 45 × 60 = 2,700 lb across 45 hives, and Ridge contributes 15 × 40 = 600 lb across 15 hives, so total honey is 2,700 + 600 = 3,300 lb across 45 + 15 = 60 hives, giving 3,300 ÷ 60 = 55 pounds. Adding more high-yield Meadow hives pulls the apiary average above the actual 54 toward Meadow's 60.

The 50-pound choice is the canonical trap, the unweighted midpoint (60 + 40) ÷ 2, which the note explicitly forbids and which holds only with equal hive counts. 45 swaps the weights, 52 anchors on the actual 54 instead of recomputing, and 60 simply reports Meadow's mean.