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[x] is the greatest integer less than or equal x, what is the value of

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[x] is the greatest integer less than or equal x, what is the value of  [#permalink]

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New post 06 Nov 2018, 01:48
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[Math Revolution GMAT math practice question]

\([x]\) is the greatest integer less than or equal \(x\), what is the value of \([√30]+[√40]+[√50]?\)

\(A. 12\)
\(B. 15\)
\(C. 16\)
\(D. 18\)
\(E. 20\)

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[x] is the greatest integer less than or equal x, what is the value of  [#permalink]

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New post 06 Nov 2018, 03:11
1
MathRevolution wrote:
[Math Revolution GMAT math practice question]

\([x]\) is the greatest integer less than or equal \(x\), what is the value of \([√30]+[√40]+[√50]?\)

\(A. 12\)
\(B. 15\)
\(C. 16\)
\(D. 18\)
\(E. 20\)


\([√30]+[√40]+[√50]\)

\([√30]\) is between perfect squares \(25\) and \(36\). Square root of \([√30]\) is between \(5\) and \(6\).

Given \([x]\) is the greatest integer less than or equal \(x\).

Therefore \([√30] = 5\)

\([√40]\) is between perfect squares \(36\) and \(49\). Square root of \([√40]\) is between \(6\) and \(7\).

Therefore \([√40] = 6\)

\([√50]\) is between perfect squares \(49\) and \(64\). Square root of \([√50]\) is between \(7\) and \(8\).

Therefore \([√50] = 7\)

Hence \([√30]+[√40]+[√50] = 5 + 6 + 7 = 18\)

Answer D
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Re: [x] is the greatest integer less than or equal x, what is the value of  [#permalink]

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New post 06 Nov 2018, 06:50
Top Contributor
MathRevolution wrote:
[Math Revolution GMAT math practice question]

\([x]\) is the greatest integer less than or equal \(x\), what is the value of \([√30]+[√40]+[√50]?\)

\(A. 12\)
\(B. 15\)
\(C. 16\)
\(D. 18\)
\(E. 20\)

GIVEN: [x] is the greatest integer less than or equal x
For example, [3.2] = 3, since 3 is the greatest integer that is less than (or equal) to 3.2
Likewise, [8.7] = 8, since 8 is the greatest integer that is less than (or equal to) 8.7

Now onto the question....
√25 = 5
√36 = 6
√49= 7
√64 = 8

Since √30 is BETWEEN √25 (aka 5) and √36 (aka 6), we know that √30 = 5.something
So, [√30] = 5

Since √40 is BETWEEN √36 (aka 6) and √49 (aka 6), we know that √40 = 6.something
So, [√40] = 6

Since √50 is BETWEEN √49 (aka 7) and √64 (aka 8), we know that √50 = 7.something
So, [√50] = 7

So, [√30]+[√40]+[√50] = 5 + 6 + 7 = 18

Answer: D

Cheers,
Brent
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Math Revolution GMAT Instructor
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Re: [x] is the greatest integer less than or equal x, what is the value of  [#permalink]

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New post 08 Nov 2018, 01:44
=>

Since\(5 = √25 < √30 < √36 = 6\), we have \([√30] = 5\).
Since \(6 = √36 < √40 < √49 = 7\), we have \([√40] = 6\)
Since \(7 = √49 < √50 < √64 = 8\), we have \([√50] = 7\)
Thus \([√30]+[√40]+[√50] = 18.\)

Therefore, D is the answer.
Answer: D
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Re: [x] is the greatest integer less than or equal x, what is the value of   [#permalink] 08 Nov 2018, 01:44
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