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A={x| x^2>9}, B={x| 1<x<16}, C={x| x^2<25}, what is the range of A∩B∩C

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Math Revolution GMAT Instructor
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A={x| x^2>9}, B={x| 1<x<16}, C={x| x^2<25}, what is the range of A∩B∩C  [#permalink]

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New post Updated on: 28 Oct 2017, 11:49
1
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A
B
C
D
E

Difficulty:

  95% (hard)

Question Stats:

41% (02:18) correct 59% (02:21) wrong based on 107 sessions

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A={x| x^2>9}, B={x| 1<x^2<16}, C={x| x^2<25}, what is the range of A∩B∩C?

A. |x|<4
B. 3<|x|<5
C. |x|<5
D. 1<|x|<4
E. 3<|x|<4

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Originally posted by MathRevolution on 12 Oct 2017, 00:49.
Last edited by MathRevolution on 28 Oct 2017, 11:49, edited 1 time in total.
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Re: A={x| x^2>9}, B={x| 1<x<16}, C={x| x^2<25}, what is the range of A∩B∩C  [#permalink]

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New post 12 Oct 2017, 01:54
A={x| x^2>9} - This set contains all positive numbers greater than x=3
B={x| 1<x<16} - This set contains all positive number from x=1.1 to x=15.9
C={x| x^2<25} - This set contains all positive numbers from x=-4.9 to x=4.9

If we have been asked to find the intersection of the three sets,
we need to find the common numbers which is 3<|x|<5(Option B)

P.S if x is an integer, then Option E is the correct answer.
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Re: A={x| x^2>9}, B={x| 1<x<16}, C={x| x^2<25}, what is the range of A∩B∩C  [#permalink]

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New post 16 Oct 2017, 06:14
A={x| x^2>9} = {x| |x|^2>9} = {x| |x|>3}.
B={x| 1<x^2<16}={x| 1<|x|^2<16}={x| 1<|x|<4},
C={x| x^2<25}={x| |x|^2<25}={x| |x|<5}.

A∩B∩C = { x | 3 < |x| < 4 }.

Therefore, the answer is E.
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Re: A={x| x^2>9}, B={x| 1<x<16}, C={x| x^2<25}, what is the range of A∩B∩C  [#permalink]

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New post 16 Oct 2017, 10:32
MathRevolution wrote:
A={x| x^2>9}, B={x| 1<x<16}, C={x| x^2<25}, what is the range of A∩B∩C?

A. |x|<4
B. 3<|x|<5
C. |x|<5
D. 1<|x|<4
E. 3<|x|<4


Please fix original post above. B should say 1<x^2<16, according to explanation above.
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Re: A={x| x^2>9}, B={x| 1<x<16}, C={x| x^2<25}, what is the range of A∩B∩C &nbs [#permalink] 16 Oct 2017, 10:32
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