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At the moment there are 54,210 tagged birds in a certain wildlife refu
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01 Jan 2026, 11:02
01 Jan 2026, 11:02
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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. $\(33 \frac{1}{3}\)$
D. $\(37 \frac{1}{2}\)$
E. 50
A. 25
B. 30
C. $\(33 \frac{1}{3}\)$
D. $\(37 \frac{1}{2}\)$
E. 50
- Part of the project: GRE Daily Quant Challenge - Topic-Wise 2025!!!
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Re: At the moment there are 54,210 tagged birds in a certain wildlife refu
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18 Jan 2026, 09:55
18 Jan 2026, 09:55
Expert Reply
1. Identify the Current Proportions
The problem divides the bird population into two groups:
- Tagged birds: $20 %$ of the total population.
- Untagged birds: $80 %$ of the total population (the remaining part).
2. Determine the Goal
We want half of all birds to be tagged, which means the Target Tagged Population is $50 %$.
3. Calculate the Required Increase
To get from $20 %$ tagged to $50 \%$ tagged, we need to tag an additional amount of the total population:
$$
\(50 %-20 \%=30 \% \text { of the total population }\)
$$
4. Find the Percentage of Untagged Birds
The question asks what percentage of the untagged birds ( $80 %$ of the total) must be tagged to reach that $30 %$ goal. We set up the ratio:
$$
\(\begin{gathered}
\text { Percentage }=\frac{\text { Amount to be tagged }}{\text { Current untagged population }} \\
\text { Percentage }=\frac{30 \%}{80 \%}=\frac{3}{8}
\end{gathered}\)
$$
5. Convert the Fraction to a Percentage
You may know from common fraction-to-percent conversions that:
- $\(\frac{1}{8}=12.5 %\)$
- $\(\frac{3}{8}=3 \times 12.5 %=\mathbf{3 7 . 5 %}\)$
In fraction form, $37.5 %$ is written as $\(37 \frac{1}{2}\) %$.
The problem divides the bird population into two groups:
- Tagged birds: $20 %$ of the total population.
- Untagged birds: $80 %$ of the total population (the remaining part).
2. Determine the Goal
We want half of all birds to be tagged, which means the Target Tagged Population is $50 %$.
3. Calculate the Required Increase
To get from $20 %$ tagged to $50 \%$ tagged, we need to tag an additional amount of the total population:
$$
\(50 %-20 \%=30 \% \text { of the total population }\)
$$
4. Find the Percentage of Untagged Birds
The question asks what percentage of the untagged birds ( $80 %$ of the total) must be tagged to reach that $30 %$ goal. We set up the ratio:
$$
\(\begin{gathered}
\text { Percentage }=\frac{\text { Amount to be tagged }}{\text { Current untagged population }} \\
\text { Percentage }=\frac{30 \%}{80 \%}=\frac{3}{8}
\end{gathered}\)
$$
5. Convert the Fraction to a Percentage
You may know from common fraction-to-percent conversions that:
- $\(\frac{1}{8}=12.5 %\)$
- $\(\frac{3}{8}=3 \times 12.5 %=\mathbf{3 7 . 5 %}\)$
In fraction form, $37.5 %$ is written as $\(37 \frac{1}{2}\) %$.
gmatclubot
Re: At the moment there are 54,210 tagged birds in a certain wildlife refu [#permalink]
18 Jan 2026, 09:55
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