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A pet shop runs a sale on goldfish and platys. If one customer buys 1

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A pet shop runs a sale on goldfish and platys. If one customer buys 1 [#permalink]

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New post 31 Jan 2011, 22:22
00:00
A
B
C
D
E

Difficulty:

  45% (medium)

Question Stats:

64% (02:38) correct 36% (02:00) wrong based on 25 sessions

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A pet shop runs a sale on goldfish and platys. If one customer buys 13 goldfish and 12 platys for $5.60, and another buys 14 goldfish and 21 platys for $8.05, what is the ratio of the price of goldfish to platys?

A) 0.8
B) 0.75
C) 8/9
D) 5/7
E) 6/8
[Reveal] Spoiler: OA

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Re: A pet shop runs a sale on goldfish and platys. If one customer buys 1 [#permalink]

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New post 01 Feb 2011, 00:26
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Hi bhandariavi,

I tried this method and it worked....

I went by the answer choices.

took answer choice A) 0.8

Assumed x to be 8p and y to be 10p and substituted in 13x + 12y=5.6 and got the anwer as 224p=5.6 since 224 is a multiple of 56 there exists a common number p which should make the ratio to be true ( which is 1/40 in this case) and hence Option A.

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Location: India
Concentration: Leadership, Strategy
Schools: Haas '18, Kelley '18
GMAT 1: 650 Q44 V37
GMAT 2: 710 Q48 V40
GMAT 3: 750 Q51 V40
GPA: 3.5
WE: Education (Education)
Re: A pet shop runs a sale on goldfish and platys. If one customer buys 1 [#permalink]

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New post 01 Feb 2011, 19:09
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The approach of plugging in the numbers is a fine approach. But, in this case, the answer was the first option and thus, by plugging in a number in the ration given, we arrived at the answer quickly!
However, what if the correct ratio was option D or C?

In any case, the algebraic solution isn't that complex if you realize a key concept:
The number 7 can be factored out of the second equation!

Here's the working:

13x + 12y = 5.60 <<<<< Equation 1
14x + 21y = 8.05 <<<<< Equation 2

2x + 3y = 1.15 [Factor Out 7 from equation 2] <<<<< Equation 3

8x + 12y = 4.6 [Multiply Equation 3 with 4]

5x = 1.0 [Equation 1 - Equation 2]

x = 0.2

3y = 1.15 - 0.4 = 0.75 [Substitute for x in Equation 1]

y = 0.25

x/y = 0.2/0.25 = 20/25 = 4/5 = 0.8 [Answer A]

The whole thing must have taken me about 45 s :D
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Re: A pet shop runs a sale on goldfish and platys. If one customer buys 1 [#permalink]

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New post 01 Feb 2011, 20:02
thanks AmrithS. Thanks to mcmoorthy as well.
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Re: A pet shop runs a sale on goldfish and platys. If one customer buys 1 [#permalink]

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New post 17 Oct 2017, 07:08
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Re: A pet shop runs a sale on goldfish and platys. If one customer buys 1   [#permalink] 17 Oct 2017, 07:08
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