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Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.  If A={x| x^3>8}, B={x| 1<x^3<64}, C={x| x^3<27}, which inequality repr

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Math Revolution GMAT Instructor V
Joined: 16 Aug 2015
Posts: 7999
GMAT 1: 760 Q51 V42 GPA: 3.82
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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[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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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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GMATH Teacher P
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Joined: 12 Oct 2010
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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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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.

Regards,
Fabio.
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Math Revolution GMAT Instructor V
Joined: 16 Aug 2015
Posts: 7999
GMAT 1: 760 Q51 V42 GPA: 3.82
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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=>

$$A∩B∩C$$ 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.
_________________ 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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