[[−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: http://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
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pi=3.14
-pi=-3.14
Lesser of the 2 integers closest to -3.14 is -4

\(\sqrt{37}\)=6.1 (approx)
Lesser of the 2 integers closest to -6.1 is -7

-4 + -7 = -11
|-11|=11

Option E:
\(\sqrt{143}\)= Little less than 12 or 11.9
Lesser of the 2 integers closest to 11.9 is 11

Answer: E

[[-3.14]] = -4 (lesser of the two{-3 and -4}= -4)
[[-(Sqroot37)]] = -7 (lesser of the two{-6 and -7}= -7)
Adding both -4-7 = -11 ;Absolute value = 11

E = [[(Sqroot143)]] = 11 (lesser of the two{11 and 12}= 11

Thus answer E

"[[x]] is equal to the lesser of the two integer values closest to non-integer x " can be interpreted as floor(x) or round-down of x.
i.e if \(x= 3.9, [[x]] = 3\) and if\(x=-3.1, [[x]] = -4\)
so \([[-\pi]] + [[-\sqrt{37}]]\) = \([[-3.14] + [[-6.something]]\) = \(-4 + -7\) = \(-11\)

And absolute value is 11. Only E has the value when rounded down equals to 11.


+1 for kudos

The value of the function is the value of integer that is left to x.
When [x] = [-pi] = [-3.14] = -4
When [x] = [-sqrt(37)] = [-6.1] = -7
[-pi]+[-sqrt(37)] = -4 -7 = -11
|-11| = 11 = required value

A. [[9.4]] = 9

(B) [[4 pi]] = 12

(C) [[99]] = 10

(D) [[120]] = 10

(E) [[√143]] = 11

E is correct
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