At College P, one fourth of the students are seniors and one fifth

Question

At College P, one − fourth of the students are seniors and one– fifth of the seniors major in business. If two– fifths of all students at the college major in business, the business majors who are not seniors are what fraction of all business majors?

A. 1/20
B. 1/8
C. 7/20
D. 7/15
E. 7/8

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Feb2024 · Answer

Let the Total number of Students be X.

Of this X,  one − fourth of the students are seniors . Thus, number of Seniors = X/4

Again, of this one − fourth senior students,  one– fifth of the seniors major in business . Thus, seniors with majors in business = 1/5 * X/4 = X/20

Now,  two– fifths of all students at the college major in business . So, total number of students (including seniors) with business majors= 2/5 * X = 2X/5.
 Remember that this "2X/5" includes Seniors.

Thus, number of non-senior with business majors = 2X/5 - X/20 = 7X/20

Since the question asks the ratio of "non-senior with business majors" to "total number of students (including seniors) with business majors",
our answer is= (7X/20) / (2X/5) = 7/8

Dereno · Answer

Let the total number of students at the college P be 20.

1/4*(20) = 5 seniors.

1/5*(seniors ) = business major = 1/5*(5) = 1

2/5*(20) major in Business = 8

Out of the 8 who major in Business, 1 accounts for Senior. And 7 accounts for Non Senior.

Fraction of Non senior who major in Business =  7/8 .

Option E

RDM42 · Answer

At College P, one − fourth of the students are seniors and one– fifth of the seniors major in business. If two– fifths of all students at the college major in business, the business majors who are not seniors are what fraction of all business majors?

Let, total students= 100 
Seniors = 1/4* 100=25 
Seniors majored in business= 1/5 *25=5 
Total students majored in business= 2/5 *100=40 
Business Majors who are not seniors= 40-5=35

Required fraction = 35/40=7/8

Answer: E

ManifestDreamMBA · Answer

Let total students be 20
Seniors = 20*1/4 = 5
Seniors major in business = 5*1/5 = 1

Total major in business = 20*2/5 = 8

Students major in business but not seniors = 8-1=7

Business majors who are not seniors are what fraction of all business majors = 7/8

rohitz98 · Answer

Taking total students as 100
If 1/4th are seniors then seniors = 25 and 1/5th are seniors who are major in business => 5 
If 2/5th of students are major in business = 40
Hence not seniors who are not major in business are 35/40 =  7/8 Option E

bumpbot · Answer

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At College P, one fourth of the students are seniors and one fifth

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