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If A={x| x^3 > 8}, B={x| 1 < x^3 < 64}, C={x| x^3 &

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If A={x| x^3 > 8}, B={x| 1 < x^3 < 64}, C={x| x^3 &

by Max@Math Revolution » Mon Oct 15, 2018 12:03 am

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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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by fskilnik@GMATH » Mon Oct 15, 2018 4:34 am
Max@Math Revolution 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)
English-speakers :: https://www.gmath.net
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by Max@Math Revolution » Tue Oct 16, 2018 11:29 pm
=>

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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