Ratio & proportion

[GMAT]

At a certain college ther are twice as many English majors as history majors and three times as many English majors as mathematics majors. What is the ratio of the number of history majors to the number of mathematics majors

1 6 to 1
2 3 to 2
3 2 to 3
4 1 to 5
5 1 to 6


as per me it shud be 2 to 3

[RonPurewal]

At a certain college ther are twice as many English majors as history majors and three times as many English majors as mathematics majors. What is the ratio of the number of history majors to the number of mathematics majors

1 6 to 1
2 3 to 2
3 2 to 3
4 1 to 5
5 1 to 6


as per me it shud be 2 to 3

first:
please take the time to write out "should". it only takes an additional 0.3 seconds or so.

in order to combine ratios, you should multiply them so that the COMMON TERM has the SAME COEFFICIENT in both ratios.

here, we have:
history : english = 1 : 2
english : mathematics = 3 : 1
the common term is "english", but the coefficients don't match: one of them is 2, and the other is 3. therefore, multiply the first ratio by 3 on both sides, and multiply the second ratio by 2 on both sides.
therefore:
history : english = 3 : 6
english : mathematics = 6 : 2
you can then combine the ratios:
history : english : mathematics = 3 : 6 : 2
therefore, history : mathematics = 3 : 2.
ans = (b)

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you can also PICK NUMBERS on this problem.
there are twice as many english majors as history majors, so let's arbitrarily say that there are 60 english majors and 30 history majors.
there are 3 times as many english majors as math majors, and we've already decided that there are 60 english majors, so there must be 20 mathematics majors.
therefore, history : mathematics = 30 : 20 = 3 : 2.
ans = (b).