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Is there an easy way to solve this GRE math question? |
After 5 males leave an office, there are twice as many females as there are males. Then, 3 females leave the office and there are twice as many males as there are females.
Which is greater?
a) The number of people left in the office after the 5 males leave.
b) 4 people.
Is there an easy way to solve this question? The answer is a because there are 6 people left in the office. WHY?
This question is most simply solved using simultaneous equations:
Let m be the number of males, f be the number of females:
f = 2(m-5)… after 5 males leave, there are twice as many females
2(f – 3) = m-5
Of course the most thorough way to solve the question is to resolve this system of equaitons, so let’s do that:
use multiplication addition: we have (simplifying the two equations)
2m – f = 10
2f – m = 1… multiply the top one by two and add
4m – 2f = 20
2f – m = 1
3m = 21… now solve
m = 7
solving for f, we have:
f = 2(m-5) = 2(7 – 5) = 4
So, there are 4 women and 7 men. After 5 men leave, there are only 2 left, and 6 people total.
Alternatively, if you have this equation stuff down, you could just solve for m+f-5 using the set of equations to save yourself some steps
f = 2(m-5)
2(f – 3) = m-5… subtract the lower one from the top one
f – 2(f-3) = 2(m-5) – (m-5)
-f + 6 = m-5
6 = f + m – 5
However, if that confuses the crap out of you, I don’t recommend it.
