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The total number of people in honor society
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12 Dec 2024, 00:45
12 Dec 2024, 00:45
Expert Reply
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Question Stats:
50% (02:07) correct
50% (03:24) wrong based on 2 sessions
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Melpomene High School has 400 students, and Thalia High School has 700 students. The following table shows the percentage breakdown for various groups in each school. .
GRE table analysis.jpg [ 175.18 KiB | Viewed 115 times ]
The total number of people in honor society at Melpomene High School, regardless of other activities, is approximately what percent higher than the total number of people in honor society at Thalia High School, regardless of other activities?
A. 2%
B. 8%
C. 19%
D. 29%
E. 56%
Attachment:
GRE table analysis.jpg [ 175.18 KiB | Viewed 115 times ]
The total number of people in honor society at Melpomene High School, regardless of other activities, is approximately what percent higher than the total number of people in honor society at Thalia High School, regardless of other activities?
A. 2%
B. 8%
C. 19%
D. 29%
E. 56%
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The total number of people in honor society
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22 Dec 2024, 04:16
22 Dec 2024, 04:16
Expert Reply
In this question, we need to find the two numbers, and then find how much bigger one is than the other.
At Melpomene, the four categories that include the honor society add up to $\(16 \%+26 \%+10 \%+4 \%$ $=56 \%$, and $56 \%$ of $400=(0.56) * 400=22\)4$ students.
At Thalia, the four categories that include the honor society add up to $\(2 \%+15 \%+8 \%+2 \%=27 \%$, and $27 \%$ of $700=(0.27) * 700=189\)$ students.
The question really is: 224 is what percent higher than 189 ? Estimate --- $\(10 \%\)$ of 189 is approximately 19. $\(189+19=208\)$, a $10 \%$ increase. $\(208+19=227\)$, a $\(20 \%\)$ increase, and that's just over 224 , so 224 should be very close to, maybe slight less than, a 20\% increase. This leads us to the answer of (C).
A more precise calculation:
$$
\(\begin{aligned}
& \text { percentage change }=\frac { end value-start value} { start value } \times 100 \% \\
& \text { percentage change }=\frac{224-189}{189} \times 100 \%=18.5185 \%=19 \% \\
& \text { Answer }=(\mathrm{C}) .
\end{aligned}\)
$$
At Melpomene, the four categories that include the honor society add up to $\(16 \%+26 \%+10 \%+4 \%$ $=56 \%$, and $56 \%$ of $400=(0.56) * 400=22\)4$ students.
At Thalia, the four categories that include the honor society add up to $\(2 \%+15 \%+8 \%+2 \%=27 \%$, and $27 \%$ of $700=(0.27) * 700=189\)$ students.
The question really is: 224 is what percent higher than 189 ? Estimate --- $\(10 \%\)$ of 189 is approximately 19. $\(189+19=208\)$, a $10 \%$ increase. $\(208+19=227\)$, a $\(20 \%\)$ increase, and that's just over 224 , so 224 should be very close to, maybe slight less than, a 20\% increase. This leads us to the answer of (C).
A more precise calculation:
$$
\(\begin{aligned}
& \text { percentage change }=\frac { end value-start value} { start value } \times 100 \% \\
& \text { percentage change }=\frac{224-189}{189} \times 100 \%=18.5185 \%=19 \% \\
& \text { Answer }=(\mathrm{C}) .
\end{aligned}\)
$$
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