[[x]] is equal to the lesser of the two integer values closest to non-

[[−pi]]
[[−pi]] = [[−3.14]] = -4, since -4 < -3.14 < -3, and -4 is the lesser of -4 and -3

[[−√37]]
Notice that √36 = 6 and √49 = 7, so √37 = 6.something
So, [[−√37]] = [[−6.something]] = -7, since -7 < −6.something < -6, and -7 is the lesser of -7 and -6

So, [[−pi]] + [[−√37]] = (-4) + (-7) = -11
This means the ABSOLUTE VALUE of [[−pi]] + [[−√37]] = |-11| = 11

Now check the answer choices....

NOTE: this is one of those questions that require us to check/test each answer choice. In these situations, always check the answer choices from E to A, because the correct answer is typically closer to the bottom than to the top. For more on this strategy, see my article: https://www.gmatprepnow.com/articles/han ... -questions

E) [[√143]]
Notice that √121 = 11 and √144 = 12, so √143 = 11.something
So, [[√143]] = [[11.something]] = 11 [ since 11 < 11.something < 12, and 11 is the lesser of 11 and 12

Answer: E