Problem Solving

at a certain college there are twice as many english majors as history majors and three times as many english majors as mathematics majors. what is the ration of the number of history majors to mathematics majors?

a) 6: 1
b) 3: 2
c) 2: 3
d) 1: 5
e) 1: 6

OAB

Please explain i got [/spoiler]c[spoiler]

IMO B.

This question is basically trying to confuse & consume time if you don't interpret the data properly.

We can either choose to select numbers or use variables. I prefer chosing numbers because using variables can sometimes get confusing especially when running against time.

The question says there are twice english majors as history majors & then goes on to say there are three times english majors as mathematics majors.

English majors are common in the comparison, we have to keep that as our reference & chose numbers for history & mathematics majors.

Lets assume there are 30 English majors. From the info provided in the question, history majors will be 15 & mathematics majors will be 10. From this ratio of the number of history majors to mathematics majors ==> 15/10 ==> 3 : 2
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We can use the variables, lets assume H, E & M as the variables for History, English & Mathematics.

2H = E & 3M = E ==> H = E/2 & M = E/3.

So, H/M ==> (E/2)/(E/3) ==> 3 : 2

Hope this helps.

Lets assume number of histoy major = x
therefore, English major would be 2x

Math Major = 1/3rd of english major = 2x/3

history major: Math major = x/(2x/3) = x * (3/2x)
= 3:2

B