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# What will the ratio of birds to fish in a certain pet store be after t

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Math Expert
Joined: 02 Sep 2009
Posts: 46035
What will the ratio of birds to fish in a certain pet store be after t [#permalink]

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18 Apr 2017, 05:11
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Difficulty:

75% (hard)

Question Stats:

46% (01:15) correct 54% (01:32) wrong based on 116 sessions

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What will the ratio of birds to fish in a certain pet store be after the store buys seven additional fish?

(1) Before the purchase, the pet store has birds and fish, respectively, in a 6 to 7 ratio.
(2) The resultant ratio of birds to fish in the pet store would be the same if, instead of buying seven fish, the pet store sold four birds.

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Intern
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Posts: 21
Location: Israel
Concentration: Economics, Technology
WE: Engineering (Telecommunications)
Re: What will the ratio of birds to fish in a certain pet store be after t [#permalink]

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18 Apr 2017, 06:43
We need the ratio: b/(f+7).
1. We have b/f = 6x/7x. Since we need 6x/(7x+7) and we don't know what is x, this is clearly insufficient.
2. According to this statement: b/(f+7)=(b-4)/f. After some manipulation somehow I got: b/(f+7)= 4/7. So apperantly this is sufficient. I'm really not sure it's correct.
Anyway, the answer is B.

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Director
Joined: 21 Mar 2016
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Re: What will the ratio of birds to fish in a certain pet store be after t [#permalink]

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19 Apr 2017, 08:10
can u plz explain the manipulation..
Senior Manager
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Re: What will the ratio of birds to fish in a certain pet store be after t [#permalink]

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19 Apr 2017, 11:40
kolodits wrote:
We need the ratio: b/(f+7).
1. We have b/f = 6x/7x. Since we need 6x/(7x+7) and we don't know what is x, this is clearly insufficient.
2. According to this statement: b/(f+7)=(b-4)/f. After some manipulation somehow I got: b/(f+7)= 4/7. So apperantly this is sufficient. I'm really not sure it's correct.
Anyway, the answer is B.

Sent from my Redmi 4 using GMAT Club Forum mobile app

how did you get the ratio b/(f+7)= 4/7 ?
Can you explain?
Intern
Joined: 05 Sep 2016
Posts: 21
Location: Israel
Concentration: Economics, Technology
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Re: What will the ratio of birds to fish in a certain pet store be after t [#permalink]

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19 Apr 2017, 12:24
3
goforgmat wrote:
kolodits wrote:
We need the ratio: b/(f+7).
1. We have b/f = 6x/7x. Since we need 6x/(7x+7) and we don't know what is x, this is clearly insufficient.
2. According to this statement: b/(f+7)=(b-4)/f. After some manipulation somehow I got: b/(f+7)= 4/7. So apperantly this is sufficient. I'm really not sure it's correct.
Anyway, the answer is B.

Sent from my Redmi 4 using GMAT Club Forum mobile app

how did you get the ratio b/(f+7)= 4/7 ?
Can you explain?

Sorry about that. It's a little bit difficult to show all the maths using the cell app.
According to statement 2: $$\frac{b}{(f+7)}$$ = $$\frac{(b-4)}{f}$$
multiply by the denominator:$$b*f = (b-4)*(f+7)$$
$$b*f = b*f +7b - 4f -28$$
$$0 = 7b - 4f -28$$
$$7b = 4f + 28$$
$$\frac{7b}{(4f + 28)} = 1$$
Finally we have to divide by 7 and multiply by 4 to get:$$\frac{b}{(f+7)} = \frac{4}{7}$$
This is what we were looking for.
If we want to verify this (actually no match time for this during the exam) we can choose values which satisfy this ratio.
let's say b = 8 , f = 7 --> $$\frac{b}{(f+7)} = \frac{8}{(7+7)}= \frac{8}{14} = \frac{4}{7}$$
In addition:$$\frac{(b-4)}{f} = \frac{(8-4)}{7} = \frac{4}{7}$$
This works for values: b = 16, f = 21, since f+7 = 28, b-4 = 12, which fulfill the ratio we have found.

Hope this is clear.
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Re: What will the ratio of birds to fish in a certain pet store be after t [#permalink]

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11 Sep 2017, 07:29
1
Statement (2) provides
bf+7=b−4f
.

If we're clever, we can go straight to the answer without having to slog through this algebra. Notice that the difference between these two "after" ratios is four birds and seven fish. Furthermore, we are told that these two "after" ratios are equal. But adding to a ratio can only leave the ratio unchanged if what we added is the same ratio as what we added to. In other words, since we know that adding four birds and seven fish does not change the "after" ratio, the "after" ratio must itself be a
4
to
7
ratio of birds to fish. Statement (2) is sufficient, and the answer is B.
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Re: What will the ratio of birds to fish in a certain pet store be after t   [#permalink] 11 Sep 2017, 07:29
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# What will the ratio of birds to fish in a certain pet store be after t

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