yogasuhas wrote:
Please explain the 3rd question, i dont have Manhattan book to look out for solution.
Question #3: Which of the following expressions is equal to the approximate number of women who would have to enlist in the Army to make the fraction of Army personnel who are women equal the fraction of Air Force personnel who are women?
(Assume that the number of men in the Army and the number of men and women in the Air Force remain unchanged from what is shown in the tables above.)
Let's first determine
the fraction of Air Force personnel who are women.
Since the question asks us to find the APPROXIMATE number, we need not be super precise.
So, from the bottom chart, we can see that the Air Force has about 270,000 men and about 70,000 women
So, TOTAL number of people in the Air Force ≈ 270,000 + 70,000 ≈ 340,000
The FRACTION of women in the Air Force ≈
70,000/340,000From the bottom chart, we can see that the Army PRESENTLY has about 480,000 men and about 80,000 women
So, TOTAL number of people in the Army ≈ 480,000 + 80,000 ≈ 560,000
Let x = number of women that need to be added to the Army
So, 80,000 + x = the NEW population of women in the Army
And 560,000 + x = the NEW total population of people in the Army.
We want to fraction of women in the Army to EQUAL the fraction of women in the Air Force
We can write: (80,000 + x)/(560,000 + x) =
70,000/340,000Cross multiply to get: 340,000(80,000 + x) = 70,000(560,000 + x)
Expand: 340,000(80,000) + 340,000x = 70,000(560,000) + 70,000x
Rearrange: 340,000x - 70,000x = 70,000(560,000) - 340,000(80,000)
Simplify left side: 270,000x = 70,000(560,000) - 340,000(80,000)
Divide both sides by 270,000 to get: x = (70,000*560,000 - 340,000*80,000)/270,000
IMPORTANT: The problem with this question is that there are MANY DIFFERENT ways to determine the value of x.
The MGRE book notes that ONE POSSIBLE SOLUTION is to just compare the ratios of men to women in the Air Force and in the Army.
In my solution, I compared the women to the TOTAL POPULATION in the Air Force and in the Army.
If we evaluate my approximate solution, we get: x = 44,444
If we evaluate answer choice E, we get 40,104
In fact, if we evaluate all 5 answer choices we get:
A) x = 19.5
B) x = 22,298
C) x = 39,414
D) x = 70,888
E) x = 40,104
As we can see, answer choice C and E are very close in value. They're also quite close to my approximation.
Given all of this, I'd have to say that this is a faulty question, since it relies on the test-taker following
one very specific solution strategy.
Cheers,
Brent
_________________
Brent Hanneson - founder of Greenlight Test Prep