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Bunuel
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[[x]] is equal to the lesser of the two integer values closest to non- 15 Apr 2015, 04:21
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E
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44% (02:04) correct 56% (01:59) wrong based on 825 sessions

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[[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) \([[\sqrt{143}]]\)
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[[x]] is equal to the lesser of the two integer values closest to non- Updated on: 04 Jul 2020, 06:50
Originally posted by BrentGMATPrepNow on 26 Aug 2016, 08:13.
Last edited by BrentGMATPrepNow on 04 Jul 2020, 06:50, edited 1 time in total.
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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.

[[−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
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[[x]] is equal to the lesser of the two integer values closest to non- 15 Apr 2015, 08:24
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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.

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
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[[x]] is equal to the lesser of the two integer values closest to non- 15 Apr 2015, 14:58
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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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[[x]] is equal to the lesser of the two integer values closest to non- 23 Aug 2016, 09:25
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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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[[x]] is equal to the lesser of the two integer values closest to non- 27 Jan 2020, 21:20
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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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[[x]] is equal to the lesser of the two integer values closest to non- 14 Jan 2025, 03:36
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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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