In a particular card game, the minimum score a player can achieve in a single game is $20$ , and the maximum score possible in a single game is $52$ . If a player plays three games and scores a total of $141$ points, calculate the least number of points that the player could have scored in one of the games.

35

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37

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38

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Solution

The correct option is C $37$
Assume, he scored $x$ in one game which is minimum than the other game scores.
In first game he scored, $x$
In second game, he scored, $x + y$
In third game, he scored, $x + z$
Where, $x, y, z \in N$

$20 \leq x \leq 52$ ...{i}
$20 \leq x + y \leq 52$ ...{ii}
$20 \leq x + z \leq 52$ ...{iii}

Adding {ii} and {iii}, we get
$40 \leq 2 x + y + z \leq 104$
$\Rightarrow 2 x + y + z \leq 104$ ...{iv}

It is given that,
$3 x + y + z = 141$ ...{v}

From {iv} and {v}, we get
$x \geq 37$
Therefore, the minimum score achieved is $37$ .

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