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17 Feb 2023, 00:52
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D
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Difficulty:
95%
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Question Stats:
50% (02:20) correct
50%
(02:32)
wrong
based on 258
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In a university, every student is either a French major or a Spanish major but not both. Is the ratio of French majors to Spanish majors greater for the women than for the whole university ?
(1) The ratio of the number of French majors to the number of Spanish majors is greater for the whole university than for the men.
(2) Fewer than half of the French majors but more than half of the Spanish majors are men.
(1) The ratio of the number of French majors to the number of Spanish majors is greater for the whole university than for the men.
(2) Fewer than half of the French majors but more than half of the Spanish majors are men.
22 Feb 2023, 22:45
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Bunuel
\(s=\) Spanish Major
\(f=\) French Major
\(s_w=\) Spanish Major women
\(f_m=\) French major men
An university consists of \(m + w\). So we need to find whether \(\frac{f_w}{s_w}> \frac{f_w + f_m}{s_w +s_m}\)
\(= f_w*s_w + f_w*s_m > s_w*f_w + s_w * f_m\)
\(=f_w*s_m > s_w * f_m\)
(1) The ratio of the number of French majors to the number of Spanish majors is greater for the whole university than for the men.
\(\frac{f_w + f_m}{s_w +s_m} > \frac{f_m}{s_m}\)
\(= f_w *s_m +f_m*s_m >f_m*s_w+f_m*s_m\)
\(=f_w*s_m > f_m*s_w \)
Exactly what we wanted to find.
SUFF.
(2) Fewer than half of the French majors but more than half of the Spanish majors are men.
From this we can certainly deduce that :
\(\frac{f_m}{s_m}<\frac{f_w}{s_w}\)
\(=f_w*s_m > f_m*s_w \)
Exactly what we wanted to find.
SUFF.
Ans D
Hope it's clear.
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01 Oct 2025, 23:00
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