Sorry i didn't mention qs number...i am talking about the 3rd one

Typo in Option E, corrected.

Manhattan 5lb Book
Page 1151. Question No 15

Regards,

I can't find out the solution in ManhaTTAN 5LB. can u plz tell me where i found it

page 1150 questions 13-15

Hope this helps

Please explain the 3rd question, i dont have Manhattan book to look out for solution.

Hope this helps

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 ≈ 70,000/340,000

From 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) = 70,000/340,000
Cross 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

Please explain Q. 1. After calculations I got Option C has the highest %

With any calculation from the first chart, you can see that the sum of every branch (men+women) Army has the highest total amount of personnel.

Women in the category (the second we are looking for) is 11 thousand more so must be the highest %.

Ask for further assistance.

regards

Oh, I assumed there were asking in terms on gender, relative to men which category has the highest % of women but I think its within women itself.

Question #2: If a man whose spouse is also military personnel or retired military were to be selected at random, what would the probability be that he was NOT in the Air Force?

(A) 72%
(B) 58%
(C) 42%
(D) 24%
(E) 13%

Number of AIR FORCE men whose spouse is also military personnel or retired military = 20,760

TOTAL number of men whose spouse is also military personnel or retired military = 15,058 + 8638 + 20,760 + 4719 = 49,175

P(selected man is NOT in the air force) = 1 - P(selected man IS in the air force)
= 1 - 20,760/49,175
= 1 - 0.422
= 0.578
= 57.8%

Answer: B

Cheers,
Brent

Good explanation! Number 1 and 2 are easy

If somebody could please elaborate on the solution of the third part?

Sorry, what does that mean ?? do you need an explanation of the third question ??

Above Brent made it.

Regards

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