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If all of the students at FDR High School take either French or Spanis

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Bunuel
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If all of the students at FDR High School take either French or Spanis [#permalink] New post   27 Mar 2017, 04:42
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64% (02:22) correct 36% (02:17) wrong based on 100 sessions
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If all of the students at FDR High School take either French or Spanish as a foreign language, how many female students took Spanish?

(1) Of the 400 students, females account for 60% of the student body and three-fourths of the total number of French students.
(2) Of the 400 students, twice as many females as males take Spanish, and three-fourths of the 160 French students are female.
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Re: If all of the students at FDR High School take either French or Spanis [#permalink] New post   27 Mar 2017, 11:38
Bunuel wrote:
If all of the students at FDR High School take either French or Spanish as a foreign language, how many female students took Spanish?

(1) Of the 400 students, females account for 60% of the student body and three-fourths of the total number of French students.
(2) Of the 400 students, twice as many females as males take Spanish, and three-fourths of the 160 French students are female.


Option 1 will give you total french and spanish students but not the number of girls who took spanish.
Option 2 is sufficient

Ans is B
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Re: If all of the students at FDR High School take either French or Spanis [#permalink] New post   28 Mar 2017, 00:14
stat 1 : no info about total number of french students

stat 2 : 3/4 of the 160 french students are female.. so 1/4 are male.
also 240 speak spanish.. hence number of females speaking spanish can be deduced,,

ans B
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Re: If all of the students at FDR High School take either French or Spanis [#permalink] New post   27 Apr 2023, 10:31
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Bunuel wrote:
If all of the students at FDR High School take either French or Spanish as a foreign language, how many female students took Spanish?

(1) Of the 400 students, females account for 60% of the student body and three-fourths of the total number of French students.
(2) Of the 400 students, twice as many females as males take Spanish, and three-fourths of the 160 French students are female.

Solution:
Pre Analysis:
  • Let us assume a 2*2 grid
Attachment:
French.png
French.png [ 5.04 KiB | Viewed 705 times ]


Statement 1: Of the 400 students, females account for 60% of the student body and three-fourths of the total number of French students
  • Total number of females \(= 60\% \times 400 = 240\)
    • Thus, total number of males \(= 400 - 240 = 160\)
  • Let us assume total number of French students be \(x\)
    • Female french students \(=\frac{3}{4}\times x=\frac{3x}{4}\)
    • Male french students \(=x-\frac{3x}{4}=\frac{x}{4}\)
Attachment:
French1.png
French1.png [ 7.87 KiB | Viewed 702 times ]

  • No way to get the answer

Statement 2: Of the 400 students, twice as many females as males take Spanish, and three-fourths of the 160 French students are female
  • Let male spanish \(=x\)
    • So, female spanish \(=2x\)
  • Total french students \(=160\)
    • So, total spanish students \(=400-160=240\)
Attachment:
French2.png
French2.png [ 6.69 KiB | Viewed 696 times ]

  • We can write \(x+2x=240\) and get the value of \(x\) and \(2x\)

Hence the right answer is Option B
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Re: If all of the students at FDR High School take either French or Spanis [#permalink]
27 Apr 2023, 10:31
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Bunuel
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