Bunuel wrote:
[[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.
[[−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) =
-11This means the ABSOLUTE VALUE of
[[−pi]] +
[[−√37]] = |
-11| =
11Now 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 ... -questionsE) [[√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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