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Data InsightsMulti-Source Reasoning

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 next season Thornfield expands the Ridge site to 35 hives while every site's per-hive mean stays at this season's level. Using the sources' method, what would the apiary-wide per-hive average then be?

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Answer & Explanation

Correct answer

E

The methodology note gives the rule: the apiary average is total honey ÷ total hives, with each site's total being its hive count × its per-hive mean. You must therefore gather three things from across the cards. The per-hive means come only from the study summary: Meadow 60 lb, Ridge 40 lb. Meadow's hive count comes only from the results table, which the stem does not change: 35 hives. The stem supplies the one altered figure, Ridge's new count of 35.

Now rebuild the totals: Meadow contributes 35 × 60 = 2,100 lb and Ridge contributes 35 × 40 = 1,400 lb, so total honey is 2,100 + 1,400 = 3,500 lb over 35 + 35 = 70 hives, and 3,500 ÷ 70 = 50 pounds. The key insight is that once the two sites have equal hive counts, the weighted average and the simple average of the site means coincide, both giving (60 + 40) ÷ 2 = 50. Equalizing the group sizes is exactly the condition under which the unweighted shortcut becomes correct.

Choice 54 is the load-bearing trap: it carries over this season's average as if growing Ridge changed nothing, when in fact adding lower-yielding Ridge hives pulls the average down from 54 to 50. 52 weights each mean by a honey total instead of by its now-equal hive count. 60 reports Meadow's mean. 46 misreads which site changed, swapping the weights.