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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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Math Revolution GMAT Instructor
Joined: 16 Aug 2015
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GMAT 1: 760 Q51 V42
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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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15 Oct 2018, 01:26
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25% (medium)

Question Stats:

78% (01:27) correct 22% (01:55) wrong based on 29 sessions

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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 $$A∩B∩C$$?

$$A. x^3<27$$
$$B. 1< x^3<64$$
$$C. x^3<64$$
$$D. 1<x^3<27$$
$$E. 8<x^3<27$$

_________________
MathRevolution: Finish GMAT Quant Section with 10 minutes to spare
The one-and-only World’s First Variable Approach for DS and IVY Approach for PS with ease, speed and accuracy.
"Only $79 for 1 month Online Course" "Free Resources-30 day online access & Diagnostic Test" "Unlimited Access to over 120 free video lessons - try it yourself" VP Status: Learning stage Joined: 01 Oct 2017 Posts: 1019 WE: Supply Chain Management (Energy and Utilities) If A={x| x^3>8}, B={x| 1<x^3<64}, C={x| x^3<27}, which inequality repr [#permalink] ### Show Tags 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) _________________ Regards, PKN Rise above the storm, you will find the sunshine GMATH Teacher Status: GMATH founder Joined: 12 Oct 2010 Posts: 935 Re: If A={x| x^3>8}, B={x| 1<x^3<64}, C={x| x^3<27}, which inequality repr [#permalink] ### Show Tags 15 Oct 2018, 05:40 1 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. _________________ Fabio Skilnik :: GMATH method creator (Math for the GMAT) Our high-level "quant" preparation starts here: https://gmath.net Math Revolution GMAT Instructor 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] ### Show Tags 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 _________________ MathRevolution: Finish GMAT Quant Section with 10 minutes to spare The one-and-only World’s First Variable Approach for DS and IVY Approach for PS with ease, speed and accuracy. "Only$79 for 1 month Online Course"
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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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