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Previous Year Question (PYQs)

A hand-held gaming device takes $X$ and $Y$ as two input values. These values get updated as $X=XY/2$ and $Y=Y+1$ at each iteration and the game stops when $X$ is greater than or equal to $N$. For $X=2$, $Y=4$ and $N=3000$, what would be the final value of $X$ when the game stops?




Solution

Given initial values:

$X=2,\quad Y=4$

Rule:

$X=\frac{XY}{2}$ and $Y=Y+1$

Now update step by step:

First iteration:

$X=\frac{2\times 4}{2}=4,\quad Y=5$

Second iteration:

$X=\frac{4\times 5}{2}=10,\quad Y=6$

Third iteration:

$X=\frac{10\times 6}{2}=30,\quad Y=7$

Fourth iteration:

$X=\frac{30\times 7}{2}=105,\quad Y=8$

Fifth iteration:

$X=\frac{105\times 8}{2}=420,\quad Y=9$

Sixth iteration:

$X=\frac{420\times 9}{2}=1890,\quad Y=10$

Seventh iteration:

$X=\frac{1890\times 10}{2}=9450$

Now $X=9450$, which is greater than $3000$.

So, the game stops.

Therefore, the final value of $X$ is $9450$.


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