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# A retailer sells only radios and clocks. If she currently has 44 total

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Joined: 06 Sep 2013
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A retailer sells only radios and clocks. If she currently has 44 total  [#permalink]

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18 Sep 2013, 15:50
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Difficulty:

55% (hard)

Question Stats:

67% (01:58) correct 33% (02:01) wrong based on 210 sessions

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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.
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Joined: 02 Sep 2009
Posts: 58335
Re: A retailer sells only radios and clocks. If she currently has 44 total  [#permalink]

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18 Sep 2013, 15:59
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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.

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Re: A retailer sells only radios and clocks. If she currently has 44 total  [#permalink]

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15 Oct 2013, 13:18
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. If she currently has 44 total  [#permalink]

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15 Oct 2013, 13:39
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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. If she currently has 44 total  [#permalink]

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05 Apr 2016, 18:25
1. r>28 - not sufficient.
2. r<2C - not sufficient.

1+2
r=29 - yes
r=30 - no

r=29
sufficient. C
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Re: A retailer sells only radios and clocks. If she currently has 44 total  [#permalink]

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24 Nov 2018, 17:06
Hi All,

We're told that a retailer sells only radios and clocks and she currently has 44 total items in inventory. We're asked how many of those items are radios. This question can be solved by TESTing VALUES.

1) The retailer has MORE than 28 radios in inventory.

With 44 total items, and MORE than 28 radios, the number of radios could be any integer from 29 to 44, inclusive.
Fact 1 is INSUFFICIENT

2) The retailer has LESS than TWICE as many radios as clocks in inventory.

Just as in Fact 1, there are a number of different possibilities.
IF....
Radios = 28, Clocks = 16, then the answer to the question is 28
Radios = 27, Clocks = 17, then the answer to the question is 27
Fact 2 is INSUFFICIENT

Combined, we know...
-The retailer has MORE than 28 radios in inventory.
-The retailer has LESS than TWICE as many radios as clocks in inventory.

Fact 1 gives us a minimum number of radios, while Fact 2 gives us a maximum number of radios....
IF....
Radios = 29, Clocks = 15, then the answer to the question is 29
Radios = 30, Clocks = 14, then the number of radios is MORE than twice the number of clocks, so this option is NOT possible (and neither are any options that include more than 30 radios). Thus, there's only one possible outcome that fits everything we were told: 29 radios and 15 clocks.
Combined, SUFFICIENT

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Re: A retailer sells only radios and clocks. If she currently has 44 total  [#permalink]

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06 Jan 2019, 08:46
Top Contributor
jlgdr wrote:
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.

Given: A retailer sells only radios and clocks, and she currently has 44 total items in inventory.

Target question: How many radios are there in the inventory

Statement 1: The retailer has more than 28 radios in inventory
There are several scenarios that satisfy statement 1. Here are three:
Case a: There are 29 radios and 15 clocks. In this case, the answer to the target question is there are 29 radios
Case b: There are 30 radios and 14 clocks. In this case, the answer to the target question is there are 30 radios
Case c: There are 31 radios and 13 clocks. In this case, the answer to the target question is there are 31 radios
Since we cannot answer the target question with certainty, statement 1 is NOT SUFFICIENT

Statement 2: The retailer has less than twice as many radios as clocks in inventory.
There are several scenarios that satisfy statement 2. Here are three:
Case a: There are 29 radios and 15 clocks. In this case, the answer to the target question is there are 29 radios
Case b: There are 28 radios and 16 clocks. In this case, the answer to the target question is there are 28 radios
Case c: There are 27 radios and 17 clocks. In this case, the answer to the target question is there are 27 radios
Since we cannot answer the target question with certainty, statement 2 is NOT SUFFICIENT

Statements 1 and 2 combined
Statement 1 tells us that the number of radios can be 29, 30, 31, 32, . . . . 44
Statement 2 tells us that the number of radios can be 29, 28, 27, 26, . . . . 0
Since BOTH statements are true, the only scenario that satisfies BOTH statements is when there are 29 radios
So, the answer to the target question MUST be there are 29 radios
Since we can answer the target question with certainty, the combined statements are SUFFICIENT

Cheers,
Brent
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Re: A retailer sells only radios and clocks. If she currently has 44 total  [#permalink]

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20 Apr 2019, 09:33
If you divide 44 by 3 you get, 14 Remainder 2
Consider it like a ratio, if R was equal 2C it would be R = 28, C = 14, but we know from (1) R>28 so let's add 1 from the remainder to each. Now R = 29 and C = 15. This also satisfies (2) that R must be <2C i.e. 29 < 30.
Basically, we can't add the remainder 2 to only R or C since it would break the constraints.
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Re: A retailer sells only radios and clocks. If she currently has 44 total  [#permalink]

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20 Apr 2019, 18:54
Bunuel wrote:
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.

Hi!

I thought it was 2R<C.

I somehow always get the wording wrong. Is there a way to avoid this kind of a mistake?
Re: A retailer sells only radios and clocks. If she currently has 44 total   [#permalink] 20 Apr 2019, 18:54
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