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# If 22 < < 23, which of the following could be the value of x

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Retired Moderator
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If 22 < < 23, which of the following could be the value of x [#permalink]  25 Aug 2018, 15:21
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Question Stats:

74% (01:22) correct 24% (01:02) wrong based on 28 sessions
If $$2^2 < \frac{x}{2^6-2^4}< 2^3$$, which of the following could be the value of x?
Indicate all such values.

A. 24
B. 64
C. 80
D. 128
E. 232
F. 256
[Reveal] Spoiler: OA

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Moderator
Joined: 07 Jan 2018
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Kudos [?]: 785 [0], given: 88

Re: If 22 < < 23, which of the following could be the value of x [#permalink]  26 Aug 2018, 02:13
$$2^2 < \frac{x}{2^4(2^2-1)}<2^3$$
multiplying the given inequality with 2^4 we get,
$$2^6 < x/3 < 2^7$$
multiplying the given inequality with 3 we get,

$$192 < x < 384$$
option E and F satisfy the inequality.
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Intern
Joined: 10 Aug 2018
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Kudos [?]: 8 [0], given: 2

Re: If 22 < < 23, which of the following could be the value of x [#permalink]  31 Aug 2018, 21:16
solving the inequality we get
4< x/48 < 8
Multiply each side by 48 which gives
192 < x <384
hence E,F
Re: If 22 < < 23, which of the following could be the value of x   [#permalink] 31 Aug 2018, 21:16
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