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

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, then what is the ratio of senior business majors to non senior business majors?

A. 1 : 3
B. 1 : 5
C. 1 : 7
D. 1 : 8
E. 7 : 8

A. 1 : 3
B. 1 : 5
C. 1 : 7
D. 1 : 8
E. 7 : 8

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GMATinsight · Answer

Let, Seniors = 20
i.e. Students = 4*Senior = 4*20 = 80
Seniors major in Business = (1/5)*20 = 4

Total Major in Business = (2/5)*80 = 32

Non-Senior Business Majors = 32-4 = 28

Ratio of Senior to non-senior in Business = 4:28 = 1:7

Answer: Option C

HarishD · Answer

Total = 100
Seniors = (1/4)*100 =25
Seniors with major in B = (1/5)*25 =5.................(a)

Total major in B = (2/5)*100 = 40

Non seniors major in B = 35...........................(b)

(a) / (b) = 5/35 =1/7 ,,,,,,,,,,,,,,,C

ans 1:7

Purnank · Answer

Take students as 20x
one-fourth of the students are seniors -> 5x from them one-fifth of the seniors major in business -> x
If two fifths of all students at the college major in business -> 8x
non senior business majors = 8x-x = 7x
ratio of senior business majors to non senior business majors  = \frac{x}{7x} = \frac{1}{7} 
  Answer C.

imeanup · Answer

Let the total number of students be  P .

$$
Seniors = \dfrac{1}{4} 	imes P, \

Non\_seniors = (1 - \dfrac{1}{4})	imes P = \dfrac{3}{4} 	imes P \

Seniors\_business\_major = \dfrac{1}{4} 	imes \dfrac{1}{5} 	imes P = \dfrac{1}{20} 	imes P \

Business\_major = \dfrac{2}{5} 	imes P \

Non\_senior\_with\_business\_major = \dfrac{2}{5}	imes P - \dfrac{1}{20} 	imes P = \dfrac{7}{20} 	imes P \

Required\_ratio = \dfrac{Senior\_business\_major}{Non\_senior\_business\_major} = \dfrac{\frac{1}{20}}{\frac{7}{20}} = \dfrac{1}{7}

$$

C

Nidzo · Answer

Using a 3x3 matrix.

Let the total students at College P =  100 .

One-fourth of the students are seniors  =  25 , and therefore non-seniors  100-25=75

\begin{tabular}{|l|l|l|l|}
\hline
~ & Business & non-Business & Total \ \hline
Senior & ~ & ~ & 25 \ \hline
non-Senior & ~ & ~ & 75 \ \hline
Total & ~ & ~ & 100 \ \hline
\end{tabular}

One-fifth of the seniors major in business  =  25*\frac{1}{5} = 5 , and therefore the number of senior non-business students  25-5=20

\begin{tabular}{|l|l|l|l|}
\hline
~ & Business & non-Business & Total \ \hline
Senior & 5 & 20 & 25 \ \hline
non-Senior & ~ & ~ & 75 \ \hline
Total & ~ & ~ & 100 \ \hline
\end{tabular}

Two fifths of all students at the college major in business  =  100*\frac{2}{5} = 40  and therefore the number of non-senior business majors is  40-5=35

\begin{tabular}{|l|l|l|l|}
\hline
~ & Business & non-Business & Total \ \hline
Senior & 5 & 20 & 25 \ \hline
non-Senior & 35 & ~ & 75 \ \hline
Total & 40 & ~ & 100 \ \hline
\end{tabular}

What is the ratio of senior business majors to non senior business majors:  \frac{5}{35} = \frac{1}{7}

ANSWER C

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

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

Prep Toolkit

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