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Question

The greatest integer less than or equal to (2+1)6 is?

A
196
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B
197
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C
198
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D
199
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Solution

The correct option is B 197
Let (2+1)6=I+F, Where I is an integer and 0< F<1.
f=21=12+10<21<10<f<1
Also I+F+f=(2+1)6+(21)6
= 2[6C0.23+6C2.22+6C4.2+6C6]
=2(8+60+30+1)=198
Hence, F+f=198I is an integer. But 0<F+f<2.
F+f=1, and thus, I=197

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