The sum of seven consecutive odd integer is $133$ . The least integer is

17

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19

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11

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13

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Solution

The correct option is D $13$
Let the seven consecutive odd integers be
$(2 x + 1), (2 x + 3), (2 x + 5), (2 x + 7), (2 x + 9), (2 x + 11), (2 x + 13)$
Then, $(2 x + 1) + (2 x + 3) + (2 x + 5) + (2 x + 7) + (2 x + 9) + (2 x + 11) + (2 x + 13) = 133$
$\Rightarrow 14 x + 49 = 133$
$\Rightarrow 14 x = 133 - 49 = 84$
$\Rightarrow x = \frac{84}{14} = 6$
Hence, the least odd integer is $= 2 x + 1 = 2 \times 6 + 1 = 13$ .

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