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If A={x| x^3>8}, B={x| 1<x^3<64}, C={x| x^3<27}, which inequality repr

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If A={x| x^3>8}, B={x| 1<x^3<64}, C={x| x^3<27}, which inequality repr  [#permalink]

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New post 15 Oct 2018, 01:26
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[Math Revolution GMAT math practice question]

If \(A={x| x^3>8}, B={x| 1<x^3<64}, C={x| x^3<27}\), which inequality represents \(A∩B∩C\)?

\(A. x^3<27\)
\(B. 1< x^3<64\)
\(C. x^3<64\)
\(D. 1<x^3<27\)
\(E. 8<x^3<27\)

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If A={x| x^3>8}, B={x| 1<x^3<64}, C={x| x^3<27}, which inequality repr  [#permalink]

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New post 15 Oct 2018, 02:10
MathRevolution wrote:
[Math Revolution GMAT math practice question]

If \(A={x| x^3>8}, B={x| 1<x^3<64}, C={x| x^3<27}\), which inequality represents \(A∩B∩C\)?

\(A. x^3<27\)
\(B. 1< x^3<64\)
\(C. x^3<64\)
\(D. 1<x^3<27\)
\(E. 8<x^3<27\)


a) \(A={x| x^3>8}\)
Range of A: (2,inf)
b) \(B={x| 1<x^3<64}\)
Range of B: (1, 4)
c) \(C={x| x^3<27}\)
Range of C: (-inf, 3)

Now, \(A∩B∩C\)= \(2<x<3\)
Or, \(8<x^3<27\)

Ans. (E)
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Re: If A={x| x^3>8}, B={x| 1<x^3<64}, C={x| x^3<27}, which inequality repr  [#permalink]

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New post 15 Oct 2018, 05:40
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MathRevolution wrote:
[Math Revolution GMAT math practice question]

If \(A={ x| x^3>8 }, B={ x| 1<x^3<64 }, C={ x| x^3<27 }\), which inequality represents \(A∩B∩C\)?

\(A. x^3<27\)
\(B. 1< x^3<64\)
\(C. x^3<64\)
\(D. 1<x^3<27\)
\(E. 8<x^3<27\)

\(A = \left\{ {\,\left. {x\,\,} \right|\,\,\,{x^3} > {2^3}\,} \right\}\)

\(B = \left\{ {\,\left. {x\,\,} \right|\,\,\,1 < {x^3} < {4^3}\,} \right\}\)

\(C = \left\{ {\,\left. {x\,\,} \right|\,\,\,{x^3} < {3^3}\,} \right\}\)

\(? = A \cap B \cap C = \left\{ {\,\left. {x\,\,} \right|\,\,\,{2^3} < {x^3} < {3^3}\,} \right\}\,\,\,\,\,\, \Rightarrow \,\,\,\,\left( E \right)\)


This solution follows the notations and rationale taught in the GMATH method.

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If A={x| x^3>8}, B={x| 1<x^3<64}, C={x| x^3<27}, which inequality repr  [#permalink]

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New post 17 Oct 2018, 00:39
=>

\(A∩B∩C\) is the set of all numbers that are in all three of the sets \(A, B\) and \(C\). So,
\(A∩B∩C\) = { \(x\) | \(x^3>8\) and \(1<x^3<64\) and \(x^3<27\)} = { \(x\) | \(8<x^3<27\)}

Therefore, the answer is E.
Answer: E
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If A={x| x^3>8}, B={x| 1<x^3<64}, C={x| x^3<27}, which inequality repr   [#permalink] 17 Oct 2018, 00:39
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