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Bunuel
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At a certain university, there are s students, w of whom are female an 24 Nov 2016, 02:55
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E
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65% (hard)

Question Stats:

65% (02:51) correct 35% (03:07) wrong based on 446 sessions

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At a certain university, there are s students, w of whom are female and m of whom are male. The number of female physics students is denoted by \(p_w\) and is exactly 12% of the female enrollment. Similarly, the number of male physics students is denoted by \(p_m\) and is exactly 25% of the male enrollment. If the overall number of physics students is denoted by p, which of the following must be true?

A. \(p_w<p_m\)

B. \(w>0.06s\)

C. \(w<p<m\)

D. \(p_m=0.125s\)

E. \( 0.12s<p<0.25s \)
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E
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KarishmaB
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At a certain university, there are s students, w of whom are female an 24 Nov 2016, 06:05
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Bunuel
At a certain university, there are s students, w of whom are female and m of whom are male. The number of female physics students is denoted by \(p_w\) and is exactly 12% of the female enrollment. Similarly, the number of male physics students is denoted by \(p_m\) and is exactly 25% of the male enrollment. If the overall number of physics students is denoted by p, which of the following must be true?

A. \(p_w<p_m\)

B. w>0.06s

C. w<p<m

D. \(p_m=0.125s\)

E. 0.12s<p<0.25s
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The only challenging part of this question is the number of variables introduced.

Total no of students - s, Female - w, Male - m
12% of females (w) take physics. \(p_w\)
25% of males (m) take physics. \(p_m\)

No of students who have taken physics = p
Overall percentage of students taking physics = (p/s)*100

This reminds one of weighted average. 12% of females take physics. 25% of male take physics. What % of total have taken physics. The overall percentage will lie between 12 and 25. If all students were male, 25% of them would have taken physics. If all were female, 12% would have taken physics. But since they are a mix, the overall percentage will lie between 12 and 25.

Hence (E) is correct.

E. 0.12s<p<0.25s
.12 < p/s < 0.25
12/100 < p/s < 25/100
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Vinayak Shenoy
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At a certain university, there are s students, w of whom are female an 24 Nov 2016, 04:57
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Bunuel
At a certain university, there are s students, w of whom are female and m of whom are male. The number of female physics students is denoted by \(p_w\) and is exactly 12% of the female enrollment. Similarly, the number of male physics students is denoted by \(p_m\) and is exactly 25% of the male enrollment. If the overall number of physics students is denoted by p, which of the following must be true?

A. \(p_w<p_m\)

B. w>0.06s

C. w<p<m

D. \(p_m=0.125s\)

E. 0.12s<p<0.25s
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Concept tested is weighted average.
IMO E
if 12% of total girls and 25% of the total boys are enrolled in physics classes then the students in physics class will be between 0.12s<p<0.25s
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At a certain university, there are s students, w of whom are female an 05 Oct 2024, 21:41
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Bunuel
At a certain university, there are s students, w of whom are female and m of whom are male. The number of female physics students is denoted by \(p_w\) and is exactly 12% of the female enrollment. Similarly, the number of male physics students is denoted by \(p_m\) and is exactly 25% of the male enrollment. If the overall number of physics students is denoted by p, which of the following must be true?

A. \(p_w<p_m\)

B. \(w>0.06s\)

C. \(w<p<m\)

D. \(p_m=0.125s\)

E. \(0.12s\)
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Bunuel option E is incomplete. I checked from multiple devices.
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At a certain university, there are s students, w of whom are female an 06 Oct 2024, 00:40
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Adarsh_24
Bunuel
At a certain university, there are s students, w of whom are female and m of whom are male. The number of female physics students is denoted by \(p_w\) and is exactly 12% of the female enrollment. Similarly, the number of male physics students is denoted by \(p_m\) and is exactly 25% of the male enrollment. If the overall number of physics students is denoted by p, which of the following must be true?

A. \(p_w<p_m\)

B. \(w>0.06s\)

C. \(w<p<m\)

D. \(p_m=0.125s\)

E. \(0.12s\)
Bunuel option E is incomplete. I checked from multiple devices.
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Fixed the issue. Thank you.
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At a certain university, there are s students, w of whom are female an 06 Dec 2025, 13:08
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