When x is subtracted from each of 27, 43, 36 and 60, the numbers so obtained,…
2022
When x is subtracted from each of 27, 43, 36 and 60, the numbers so obtained, in this order, are in proportion. What is the mean proportional between (x + 1) and (2x - 3)?
- A.
2√22
- B.
√42
- C.
5√15
- D.
5√6
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Correct answer: D
Since the four obtained numbers are in proportion, (27 - x)/(43 - x) = (36 - x)/(60 - x). Cross-multiplying gives (27 - x)(60 - x) = (43 - x)(36 - x), so x = 9. Then x + 1 = 10 and 2x - 3 = 15. The mean proportional is √(10 × 15) = √150 = 5√6.