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A retailer sells only radios and clocks

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A retailer sells only radios and clocks [#permalink] New post 18 Sep 2013, 14:50
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Difficulty:

  45% (medium)

Question Stats:

67% (02:07) correct 33% (01:38) wrong based on 48 sessions
A retailer sells only radios and clocks. If she currently has 44 total items in inventory, how many of them are radios?

(1) The retailer has more than 28 radios in inventory

(2) The retailer has less than twice as many radios as clocks in inventory.
[Reveal] Spoiler: OA
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Re: A retailer sells only radios and clocks [#permalink] New post 18 Sep 2013, 14:59
Expert's post
A retailer sells only radios and clocks. If she currently has 44 total items in inventory, how many of them are radios?

R + C = 44.

(1) The retailer has more than 28 radios in inventory --> R > 28. Not sufficient.

(2) The retailer has less than twice as many radios as clocks in inventory --> R < 2C --> . Not sufficient.

(1)+(2) Since from the stem we know that C = 44 - R, then from (2) we get that R < 2(44 - R) --> R < 88/3=~29.something. So, we have that 28 < R < 29.something, which means that R = 29. Sufficient.

Answer: C.
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Re: A retailer sells only radios and clocks [#permalink] New post 15 Oct 2013, 12:18
Hi Bunuel,
Please correct me if I am wrong.
As per my understanding, the second statement equation becomes C<2R
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Re: A retailer sells only radios and clocks [#permalink] New post 15 Oct 2013, 12:39
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aniketrathi wrote:
Hi Bunuel,
Please correct me if I am wrong.
As per my understanding, the second statement equation becomes C<2R


No.

Consider this: say we are told that "the retailer has twice as many radios as clocks in inventory", then we would have R=2C (twice as many radios as clocks).

But we are told that "the retailer has less than twice as many radios as clocks in inventory", so it should be R<2C.

Hope it's clear.
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Re: A retailer sells only radios and clocks   [#permalink] 15 Oct 2013, 12:39
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