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A company selected 250 zipcodes in Northeastern, Florida, Ar

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A company selected 250 zipcodes in Northeastern, Florida, Ar  [#permalink]

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New post 26 Aug 2014, 08:17
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  45% (medium)

Question Stats:

75% (03:14) correct 25% (03:21) wrong based on 104 sessions

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A company selected 250 zip codes in Northeastern, Florida, Arizona and California in order to mail a product catalog. The number of Northeastern zip codes was twice Florida's, and four times Arizona's, and 4/3 California's. 150,000 catalogues were mailed to California and 25% resulted in product orders. What is the ratio of the number of orders to the number of California's zip codes?

a) 500
b) 750
c) 1,000
d) 1,250
e) 1,500
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A company selected 250 zipcodes in Northeastern, Florida, Ar  [#permalink]

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New post 26 Aug 2014, 14:28
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So we get N=2F , N=4/3C and N=4A
through those relations we can put an equation with only Californian zips as variable
4/3C + 1/3C + C + 2/3C=250 therefore C=75
then the ratio would be equal to 150000/4/75 =500

hope it helps :p
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Re: A company selected 250 zipcodes in Northeastern, Florida, Ar  [#permalink]

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New post 26 Aug 2014, 22:34
pbarrocas wrote:
A company selected 250 zip codes in Northeastern, Florida, Arizona and California in order to mail a product catalog. The number of Northeastern zip codes was twice Florida's, and four times Arizona's, and 4/3 California's. 150,000 catalogues were mailed to California and 25% resulted in product orders. What is the ratio of the number of orders to the number of California's zip codes?

a) 500
b) 750
c) 1,000
d) 1,250
e) 1,500


Let's put everything in number of Northeastern zip codes since all those relations are given.

Since N = 2F, no of Florida zip codes (F) will be N/2.
Since N = 4A, no of Arizona zip codes (A) will be N/4
Since N = (4/3)C, no of California zip codes (C) will be 3N/4

N + N/2 + N/4 + 3N/4 = 5N/2 = 250
N = 100
C = 3N/4 = 75

No of orders is 25% of 150,000 = 37,500

So required ratio = 37,500/75 = 500
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Re: A company selected 250 zipcodes in Northeastern, Florida, Ar  [#permalink]

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New post 21 Sep 2014, 11:58
VeritasPrepKarishma wrote:
pbarrocas wrote:
A company selected 250 zip codes in Northeastern, Florida, Arizona and California in order to mail a product catalog. The number of Northeastern zip codes was twice Florida's, and four times Arizona's, and 4/3 California's. 150,000 catalogues were mailed to California and 25% resulted in product orders. What is the ratio of the number of orders to the number of California's zip codes?

a) 500
b) 750
c) 1,000
d) 1,250
e) 1,500


Let's put everything in number of Northeastern zip codes since all those relations are given.

Since N = 2F, no of Florida zip codes (F) will be N/2.
Since N = 4A, no of Arizona zip codes (A) will be N/4
Since N = (4/3)C, no of California zip codes (C) will be 3N/4

N + N/2 + N/4 + 3N/4 = 5N/2 = 250
N = 100
C = 3N/4 = 75

No of orders is 25% of 150,000 = 37,500

So required ratio = 37,500/75 = 500

Hi Karishma,
I tried doing it in a similar way but somehow I'm not getting the correct numbers.
I wanted to translate everything to California zip codes, so we basically have:
N=2F=4A=(4/3)C -> C( 4/3 + 4/6 + 4/12) = 250 -> C*(16+8+4)/12 = 250
And I'm getting a different result than what you're getting for C.
Where am I going wrong here?
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Re: A company selected 250 zipcodes in Northeastern, Florida, Ar  [#permalink]

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New post 22 Sep 2014, 21:25
ronr34 wrote:
Hi Karishma,
I tried doing it in a similar way but somehow I'm not getting the correct numbers.
I wanted to translate everything to California zip codes, so we basically have:
N=2F=4A=(4/3)C -> C( 4/3 + 4/6 + 4/12) = 250 -> C*(16+8+4)/12 = 250
And I'm getting a different result than what you're getting for C.
Where am I going wrong here?



You have got everything in terms of C but forgotten to add C.

N + F + A + C = 250
C( 4/3 + 4/6 + 4/12) + C = 250
C = 75
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Re: A company selected 250 zipcodes in Northeastern, Florida, Ar  [#permalink]

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New post 25 Aug 2018, 11:14
Express everything in terms of northeastern zip codes.

Let N be the number of zip codes. N + N/2 + N/4 + 3N/4 = 250 which implies that N = 75

25% of 150,000 = 37,500

Therefore the correct answer is A [37,500/75]
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Re: A company selected 250 zipcodes in Northeastern, Florida, Ar  [#permalink]

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New post 02 Sep 2018, 08:51
pbarrocas wrote:
A company selected 250 zip codes in Northeastern, Florida, Arizona and California in order to mail a product catalog. The number of Northeastern zip codes was twice Florida's, and four times Arizona's, and 4/3 California's. 150,000 catalogues were mailed to California and 25% resulted in product orders. What is the ratio of the number of orders to the number of California's zip codes?

a) 500
b) 750
c) 1,000
d) 1,250
e) 1,500


OA:A

Number of Northeastern Zipcodes =\(2\)*Number of Florida Zipcodes =\(4\)*Number of Arizona Zipcodes=\(\frac{4}{3}\)*Number of California Zipcodes

Number of Northeastern Zipcodes + Number of Florida Zipcodes + Number of Arizona Zipcodes + Number of California Zipcodes \(= 250\)

\(\frac{4}{3}\) Number of California Zipcodes+\(\frac{2}{3}\) Number of California Zipcodes+\(\frac{1}{3}\) Number of California Zipcodes+ Number of California Zipcodes \(= 250\)

\(\frac{4+2+1+3}{3}\)Number of California Zipcodes \(= 250\)

Number of California Zipcodes\(= 250* \frac{3}{10} = 75\)

Number of Orders \(=\frac{25}{100}*150,000\)

Ratio of the number of orders to the number of California's zip codes \(=\frac{ \frac{25}{100}*150,000}{75}= 500\)
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