[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
If A={x| x^3 > 8}, B={x| 1 < x^3 < 64}, C={x| x^3 &
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- Max@Math Revolution
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$$A = \left\{ {\,\left. {x\,\,} \right|\,\,\,{x^3} > {2^3}\,} \right\}$$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
$$B = \left\{ {\,\left. {x\,\,} \right|\,\,\,1 < {x^3} < {4^3}\,} \right\}$$
$$C = \left\{ {\,\left. {x\,\,} \right|\,\,\,{x^3} < {3^3}\,} \right\}$$
$$? = A \cap B \cap C = \left\{ {\,\left. {x\,\,} \right|\,\,\,{2^3} < {x^3} < {3^3}\,} \right\}\,\,\,\,\,\, \Rightarrow \,\,\,\,\left( E \right)$$
This solution follows the notations and rationale taught in the GMATH method.
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Fabio.
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- Max@Math Revolution
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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.
Answer: E
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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