Nitin was counting down from 32. Sumit was co | vedclass

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Question

(D) Nitin's sequence (counting down from $32$): $32, 31, 30, 29, 28, 27, 26, 25, 24, 23, 22, 21, 20, 19, 18, 17, 16, 15, 14, 13, 12, 11, 10, 9, 8, 7,

Vedclass · Accepted Answer

They will not call out the same number

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(D) Nitin's sequence (counting down from $32$): $32, 31, 30, 29, 28, 27, 26, 25, 24, 23, 22, 21, 20, 19, 18, 17, 16, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1$.Sumit's sequence (counting odd numbers upwards from $1$): $1, 3, 5, 7, 9, 11, 13, 15, 17, 19, 21, 23, 25, 27, 29, 31$.Let $n$ be the step number (starting from $1$).Nitin's $n$-th number is $N_n = 32 - (n - 1) = 33 - n$.Sumit's $n$-th number is $S_n = 2n - 1$.Setting $N_n = S_n$,we get $33 - n = 2n - 1$.$34 = 3n$,which gives $n = 34/3 = 11.33$.Since $n$ must be an integer,they will never call out the same number at the same time.

Nitin was counting down from $32$. Sumit was counting upwards starting from $1$ and he was calling out only the odd numbers. What common number will they call out at the same time if they were calling out at the same speed?

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