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Question

If the A.M. between two numbers exceeds their G.M. by 12 and the G.M. exceeds their H.M. by 36/5, then the greater of the two numbers is .

A
72
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B
54
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C
18
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D
48
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Solution

The correct option is B 54
Let the A.M., G.M., and H.M. of the two numbers a and b (a > b) be represented by A, G, and H respectively.
A-G=12 and G-H=36/5
G2=AH=(G+12)(G365)G2=G236G5+12G432536G512G=432524G5=4325G=18A=30a+b=60G=18ab=18ab=324a=54 and b=6 as a>b

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