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Bunuel
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[[-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
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Bunuel
[[x]] is equal to the lesser of the two integer values closest to non-integer x. What is the absolute value of \([[-\pi]] + [[-\sqrt{37}]]\) ?

(A) [[9.4]]

(B) [[4 pi]]

(C) \([[\sqrt{99}]]\)

(D) \([[\sqrt{120}]]\)

(E) \([[\sqrt{143}]]\)

Kudos for a correct solution.


"[[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.


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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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\([[-\pi]]\) = Lesser of the two integer values closest to non-integer x

\([[-\pi]]\) = \([[-3.14]]\), two closest integers are -3 and -4
Smallest value = -4
=> \([[-\pi]]\) = -4

\([[-\sqrt{37}]]\) ~
[[-6.Something]]
Two closest integers are -6 and -7
Smallest value = -7
=> \([[-\sqrt{37}]]\) = -7

Absolute Value of \([[-\pi]] + [[-\sqrt{37}]]\) = |-4 + -7| = 11

(A) [[9.4]]
Two closest integers are 9 and 10
Smallest value = 9 ≠ 11

(B) [[4 pi]] = [[4 * 3.14]] = [[12.56]]
Two closest integers are 12 and 13
Smallest value = 12 ≠ 11

(C) \([[\sqrt{99}]]\) ~ [[9.9]] ( as \(\sqrt{100}\) = 10 )
Two closest integers are 9 and 10
Smallest value = 9 ≠ 11

(D) \([[\sqrt{120}]]\) ~ [[10.9]] ( as \(\sqrt{121}\) = 11 )
Two closest integers are 10 and 11
Smallest value = 10 ≠ 11

(E) \([[\sqrt{143}]]\) ~ [[11.9]] ( as \(\sqrt{144}\) = 12 )
Two closest integers are 11 and 12
Smallest value = 11

So, Answer will be E
Hope it helps!

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