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Inequalities Involving Modulus Function

For [ |a+1|<3...

Question

For ${\begin{matrix} | a + 1 | < 3 | b - 1 | < 10 \end{matrix}$ , if $x$ and $y$ are the greatest and the least integers respectively, satisfying $x < a + b < y$ , then $x + y$ is

0

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26

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13

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- 13

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Solution

The correct option is A $0$
$- 3 < a + 1 < 3 \Rightarrow - 4 < a < 2 . . . (1) - 10 < b - 1 < 10 \Rightarrow - 9 < b < 11 . . . (2)$

From eqns. $(1)$ and $(2)$ ,
$- 4 - 9 < a + b < 2 + 11 \Rightarrow - 13 < a + b < 13$
$∴ x = - 13$ and $y = 13$

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