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# QOTD #4 Number of Military Personnel by Gender and Branch

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QOTD #4 Number of Military Personnel by Gender and Branch [#permalink]  07 Jul 2016, 17:53
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Expert's post
00:00

Question Stats:

33% (07:59) correct 66% (05:20) wrong based on 6 sessions

Which military branch has the greatest percentage of women who are single and have children under the age of 18?

(A) Army
(B) Navy
(C) Air Force
(D) Marines
(E) It cannot be determined from the information given.

[Reveal] Spoiler: OA
A

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%

[Reveal] Spoiler: OA
B

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.)

A. $$\frac{(482000 -268000)}{(75000 - 64000)}$$
B. $$\frac{(482000*64000 -268000*75000)}{482000}$$
C. $$\frac{(482000*75000 -268000*64000)}{482000}$$
D. $$\frac{482000*75000}{268000}$$$$-64000$$
E. $$\frac{482000*64000}{268000}$$$$-75000$$

[Reveal] Spoiler: OA
E

[Reveal] Spoiler: Img
Attachment:

test.jpg [ 182.23 KiB | Viewed 7616 times ]

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Last edited by Carcass on 06 Oct 2017, 02:54, edited 4 times in total.
Edited the question
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Re: QOTD #4 Number of Military Personnel by Gender and Branch [#permalink]  25 Aug 2016, 23:03
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There is a problem with options, the correct answer should be option B with denominatior as 268000 and not 482000.
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Re: QOTD #4 Number of Military Personnel by Gender and Branch [#permalink]  26 Aug 2016, 02:11
Expert's post
which one do you refer to ?? 1 through 3 ............

Thank you
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Re: QOTD #4 Number of Military Personnel by Gender and Branch [#permalink]  26 Aug 2016, 04:44
Sorry i didn't mention qs number...i am talking about the 3rd one
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Re: QOTD #4 Number of Military Personnel by Gender and Branch [#permalink]  26 Aug 2016, 05:26
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Sonalika42 wrote:
There is a problem with options, the correct answer should be option B with denominatior as 268000 and not 482000.

Typo in Option E, corrected.

Manhattan 5lb Book
Page 1151. Question No 15

Regards,
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Re: QOTD #4 Number of Military Personnel by Gender and Branch [#permalink]  27 Jan 2017, 09:26
I can't find out the solution in ManhaTTAN 5LB. can u plz tell me where i found it
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Re: QOTD #4 Number of Military Personnel by Gender and Branch [#permalink]  27 Jan 2017, 12:10
Expert's post
ridwanmd wrote:
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
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Re: QOTD #4 Number of Military Personnel by Gender and Branch [#permalink]  10 Aug 2017, 09:45
Please explain the 3rd question, i dont have Manhattan book to look out for solution.
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Re: QOTD #4 Number of Military Personnel by Gender and Branch [#permalink]  11 Aug 2017, 06:36
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yogasuhas wrote:
Please explain the 3rd question, i dont have Manhattan book to look out for solution.

Quote:
In order to solve this problem, make the two ratios equal. The ratio in question is Women/Total, but Women/Men is simpler and works also, because Total depends only on Women and Men):

$$\frac{resulting # of women in army}{resulting # of men in army}$$ = $$\frac{# of women in air force}{# of men in air force}$$

There are two ways to find the number of women and men in the Army and Air Force. Either sum the exact number of
women and men in each marital status for each branch of the service in question, or read an approximate number from
the second bar chart, Number of Military Personnel by Gender and Branch.

Since the problem says to approximate and gives numbers in the answer choices that can serve as guidelines,
approximation from the bar chart will be good enough.

The important thing is to focus on the structure of the math. Since adding women to the Army will change the number
of women in the Army, use a variable to represent the additional women. Let x represent the number of women who
would have to enlist in the Army in order to make the ratios equal
$$\frac{current # of women in army + x}{# of men in army}$$ = $$\frac{# of women in air force}{# of men in air force}$$

From the bar chart, look up the approximate numbers:
Army AF
# of women 75,000 60,000
# of men 475,000 270,000

The next step is to plug these approximate numbers into the equation and solve for x.

$$\frac{75,000 + x}{475,000}$$ = $$\frac{60,000}{270,000}$$

Looking at the answer choices, structurally, the answer must be (D) or (E), and the numbers in (E) are a better fit to the numbers approximated from the chart.

Hope this helps
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Re: QOTD #4 Number of Military Personnel by Gender and Branch [#permalink]  11 Aug 2017, 07:19
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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 ≈ 70,000/340,000

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 B 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
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Re: QOTD #4 Number of Military Personnel by Gender and Branch [#permalink]  10 Sep 2018, 13:30
Please explain Q. 1. After calculations I got Option C has the highest %
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Re: QOTD #4 Number of Military Personnel by Gender and Branch [#permalink]  11 Sep 2018, 15:10
Expert's post
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 %.

regards
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Re: QOTD #4 Number of Military Personnel by Gender and Branch [#permalink]  11 Sep 2018, 17:05
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Carcass wrote:
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 %.

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.
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Re: QOTD #4 Number of Military Personnel by Gender and Branch [#permalink]  16 Feb 2019, 09:43
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sandy wrote:

Which military branch has the greatest percentage of women who are single and have children under the age of 18?

(A) Army
(B) Navy
(C) Air Force
(D) Marines
(E) It cannot be determined from the information given.

[Reveal] Spoiler: OA
A

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%

[Reveal] Spoiler: OA
B

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.)

A. $$\frac{(482000 -268000)}{(75000 - 64000)}$$
B. $$\frac{(482000*64000 -268000*75000)}{482000}$$
C. $$\frac{(482000*75000 -268000*64000)}{482000}$$
D. $$\frac{482000*75000}{268000}$$$$-64000$$
E. $$\frac{482000*64000}{268000}$$$$-75000$$

[Reveal] Spoiler: OA
E

[Reveal] Spoiler: Img
Attachment:
test.jpg

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%

Cheers,
Brent
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