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BTG Practice question - good one

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by rohu27 » Mon Feb 14, 2011 3:57 am
At the moment there are 54,210 tagged birds in a certain wildlife refuge. If exactly 20 percent of all birds in the refuge are tagged, what percent of the untagged birds must be tagged so that half of all birds in the refuge are tagged?

a) 25
b) 30
c) 33 1/3
d) 37 1/2
e) 50


[spoiler]OA: D[/spoiler]
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by garuhape » Mon Feb 14, 2011 4:23 am
At the moment you have 20% tagged and therefore 80% untagged. Now you want to know how many % of the untagged you have to tag.

Therefore the equation is:

20% + x%*80%=50% or just 20+x*80=50

x*80=30

x=30/80

Then you have to multiply 80 and 30 by 1.25 to get the number in percent

x=30*1.25/80*1.25=37.5/100
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by GMATGuruNY » Mon Feb 14, 2011 4:44 am
rohu27 wrote:At the moment there are 54,210 tagged birds in a certain wildlife refuge. If exactly 20 percent of all birds in the refuge are tagged, what percent of the untagged birds must be tagged so that half of all birds in the refuge are tagged?

a) 25
b) 30
c) 33 1/3
d) 37 1/2
e) 50


[spoiler]OA: D[/spoiler]
Ignore the number of birds given.
Plug in birds = 100.
Tagged = 20.
Since 1/2*100 = 50, 50-20 = 30 more birds need to be tagged.
100-20 = 80 untagged.
Percent that need to be tagged = 30/80 * 100 = 37.5.

The correct answer is D.
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by ankur.agrawal » Mon Feb 14, 2011 9:39 am
GMATGuruNY wrote:
rohu27 wrote:At the moment there are 54,210 tagged birds in a certain wildlife refuge. If exactly 20 percent of all birds in the refuge are tagged, what percent of the untagged birds must be tagged so that half of all birds in the refuge are tagged?

a) 25
b) 30
c) 33 1/3
d) 37 1/2
e) 50


[spoiler]OA: D[/spoiler]
Ignore the number of birds given.
Plug in birds = 100.
Tagged = 20.
Since 1/2*100 = 50, 50-20 = 30 more birds need to be tagged.
100-20 = 80 untagged.
Percent that need to be tagged = 30/80 * 100 = 37.5.

The correct answer is D.
How can one be so sure of removing the number of birds given. I mean to say- Does this strategy works with specific type of % questions / does it works with all % questions?
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by GMATGuruNY » Mon Feb 14, 2011 11:13 am
ankur.agrawal wrote:
GMATGuruNY wrote:
rohu27 wrote:At the moment there are 54,210 tagged birds in a certain wildlife refuge. If exactly 20 percent of all birds in the refuge are tagged, what percent of the untagged birds must be tagged so that half of all birds in the refuge are tagged?

a) 25
b) 30
c) 33 1/3
d) 37 1/2
e) 50


[spoiler]OA: D[/spoiler]
Ignore the number of birds given.
Plug in birds = 100.
Tagged = 20.
Since 1/2*100 = 50, 50-20 = 30 more birds need to be tagged.
100-20 = 80 untagged.
Percent that need to be tagged = 30/80 * 100 = 37.5.

The correct answer is D.
How can one be so sure of removing the number of birds given. I mean to say- Does this strategy works with specific type of % questions / does it works with all % questions?
We can plug in for the original value under the following conditions:

-- the answers are percentages
-- the original value is unknown or there are no fixed values in the problem other than the original value

Why can we plug in our own number? Because a percentage represents only the relationship between two values, and that relationship will be the same no matter how many total elements there are. In the problem above, the ratio of tagged birds to untagged birds will be the same no matter how many total birds there are.
Last edited by GMATGuruNY on Mon Feb 14, 2011 6:47 pm, edited 1 time in total.
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by rohu27 » Mon Feb 14, 2011 6:25 pm
thanks Mitch. It indeed is a great takeway from this problem. This problem is another case to put in smart work.
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