Of 1400 college teachers surveyed, 42% said they considered research essential. How many teachers surveyed were women?
A) In survey 36% of men and 50% of women said they considered research essential
B) 288 men said they considered research essential
How can I solve this type of questions?
Thanks
OA A
This is a WEIGHTED AVERAGE/MIXTURE problem.
Statement 1:
Of all the men, the percentage who considered research essential = 36%.
Of all the women, the percentage who considered research essential = 50%.
Of all the teachers -- the MIXTURE -- the percentage who considered research essential = 42.
To determine the ratio of men to women, use ALLIGATION -- a very efficient way to handle mixture problems.
Step 1: Plot the 3 percentages on a number line, with the two percentages for the two subgroups (36% and 50%) on the ends and the percentage for all the teachers (42%) in the middle.
M(36%)---------42---------W(50%)
Step 2: Calculate the distances between the percentages.
M36%)----
6----42----
8----W(50%)
Step 3: Determine the ratio in the mixture.
The ratio of men to women is the RECIPROCAL of the distances in red.
M:W = 8:6 = 4:3.
Since there are 1400 teachers, and M:W = 4:3 = 400:300 = 800:600, W=600.
SUFFICIENT.
Statement 2:
No way to determine the number of women.
INSUFFICIENT.
The correct answer is
A.
Please note the following:
Almost NO MATH is needed here if we understand how WEIGHTED AVERAGES work.
Statement 1 indicates the percentage attributed to each INGREDIENT (the men and the women).
The question stem indicates the percentage attributed to the MIXTURE (all of the teachers).
If we know the percentage attributed to each ingredient and the percentage attributed to the mixture, we can ALWAYS determine the RATIO of the two ingredients (in this case, M:W).
Thus -- without doing any math -- we can see that statement 1 is SUFFICIENT to determine how many of the 1400 teachers are women.
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