MATH

medium • PYQ Reworded

Question

Read carefully, then pick the best option.

Let

b_{i}>1

for

i=1,2, \ldots, 101

. Suppose

\log _{e} b_{1}, \log _{e} b_{2}, \ldots, \log _{e} b_{101}

are in Arithmetic Progression (A.P.) with the common difference

\log _{e} 2

. Suppose

a_{1}, a_{2}, \ldots, a_{101}

are in A.P. such that

a_{1}=b_{1}

and

a_{51}=b_{51}

. If

t=b_{1}+b_{2}+\cdots+b_{51}

and

s=a_{1}+a_{2}+\cdots+a_{51}

, then

s>t

and

a_{101}>b_{101}

s>t

and

a_{101}<b_{101}

s<t

and

a_{101}>b_{101}

s<t

and

a_{101}<b_{101}

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