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# m05 q12

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30 Nov 2008, 21:15
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4% of population of country L has military experience and supports a war against Country G. If 20% of those who support the war have no military experience what percentage of the country's population actually supports war against G?

(A) 5%
(B) 7.5%
(C) 10%
(D) 12.5%
(E) 15%

[Reveal] Spoiler:
[spoiler=OA]A

Source: GMAT Club Tests - hardest GMAT questions

The solution is quite simple. If 20% of the supporters of war have no military experience, then 80% do. So, 4% of total population must be 80% of war supporters. Therefore, 100% of war supporters is 5% of the total population.

Can someone please explain how they got to 5%. The explaination lost me. Thanks...[/spoiler]

REVISED VERSION OF THIS QUESTION IS HERE: m05-q12-73440.html#p1207940

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01 Dec 2008, 22:07
bertlacy wrote:
Can someone please explain how they got to 5%. The explaination lost me. Thanks...

4% of population of country L has military experience and supports a war against Country G. If 20% of those who support the war have no military experience what percentage of the country's population actually supports war against G?

(C) 2008 GMAT Club - m05#12

5%
7.5%
10%
12.5%
15%
The solution is quite simple. If 20% of the supporters of war have no military experience, then 80% do. So, 4% of total population must be 80% of war supporters. Therefore, 100% of war supporters is 5% of the total population.

total (x) = people support war (y) + people do not support war (z) = y + z

people who support the war (y) = people with military experience + people with no military experience

y = 4% of x + 20% of y
y = 0.04x + 0.2y
y - 0.2y = 0.04x
0.8y = 0.04x
y = 4x/80
y = 0.05x

so y is 5% of x.
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26 Mar 2010, 06:46
bertlacy wrote:
4% of population of country L has military experience and supports a war against Country G. If 20% of those who support the war have no military experience what percentage of the country's population actually supports war against G?
(A) 5%
(B) 7.5%
(C) 10%
(D) 12.5%
(E) 15%
[Reveal] Spoiler: OA
A

Source: GMAT Club Tests - hardest GMAT questions

The solution is quite simple. If 20% of the supporters of war have no military experience, then 80% do. So, 4% of total population must be 80% of war supporters. Therefore, 100% of war supporters is 5% of the total population.

Can someone please explain how they got to 5%. The explaination lost me. Thanks...

Given 4% of total population support war and also has military training.
Let x be the country's population actually supports war against G
Also,
80% of x = Have military experience
from both
.8x = 4%
x = 5%
hence A.

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26 Mar 2010, 18:39
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Suppose total population is 100 and country's population that supports the war is X.

X = 4 + 0.2X
=> 0.8X = 4 => X = 5 (out of 100) that is 5%

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07 Apr 2010, 10:08
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Let total population = 100; x = no of those supporting war with no military expr
Statement says: 0.2(x+4) = x
0.2x + 0.8 = x
x = 1
supporters of war = 1+4 = 5
Percentage = 5/100 = 5%
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11 Sep 2010, 00:59
tried the same question today but had an issue with it:
let M=population with military experience
m = population without military experience
S
= population that supports military action
s = population against military action

where y ==> No military expr AND No support
population without military expr. = x + y
population that supports = 4 + x
20% of support = 0.2(4 +x)

"If 20% of those who support the war have no military experience what percentage of the country's population actually supports war against G?"

i think it should be 0.2(4+x) = (x+y) ?
or rather, how would the question be if it where to mean "0.2(4+x) = (x+y)"
but NOT "0.2(4+x) = x"

Thanks.
Attachments

military action.docx [10.05 KiB]

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30 Mar 2011, 05:45
Total y people - 0.04y have ME and Support War

Let x # of people support war

So 0.2x don't have ME but 0.8x have ME and support war

0.04y = 0.8x

=> x/y = 0.04/0.8 = 4/80 = 1/20 * 100 = 5%

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30 Mar 2011, 10:30
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Dealing with percents, let's assume the population is 100.
Attachments

Venn - Military.JPG [ 9.29 KiB | Viewed 5968 times ]

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30 Mar 2011, 11:29
bertlacy wrote:
4% of population of country L has military experience and supports a war against Country G. If 20% of those who support the war have no military experience what percentage of the country's population actually supports war against G?

(A) 5%
(B) 7.5%
(C) 10%
(D) 12.5%
(E) 15%

[Reveal] Spoiler: OA
A

Source: GMAT Club Tests - hardest GMAT questions

The solution is quite simple. If 20% of the supporters of war have no military experience, then 80% do. So, 4% of total population must be 80% of war supporters. Therefore, 100% of war supporters is 5% of the total population.

Can someone please explain how they got to 5%. The explaination lost me. Thanks...

The question never says one who has military Exp only support WAR.

can some one clarify me..where i m wrong..
here is my Sol ;

100% = 4% of population of L has military experience + 96%of population of L has no military experience

total population who supports War = 20% of those who support the war have no military experience + 80 % of those who support the war have military experience
=20% of 96% + 80% of 4%
=19.2% + 3.2%
=22.4%

so, by solving in this way i m arriving at an option beyond the answer given.
can someone give me a explanation where i m wrong....
thank you ..
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30 Mar 2011, 12:18
"100% = 4% of population of L has military experience + 96%of population of L has no military experience"
This is not accurate. 4% of the population has military experience and supports the war. 20% of the total supporters have military experience. Let X represent the total supporters.
4 + 0.2X = X. Solve fo X. X = 5.
See the double matrix table above.

321kumarsushant wrote:
bertlacy wrote:
4% of population of country L has military experience and supports a war against Country G. If 20% of those who support the war have no military experience what percentage of the country's population actually supports war against G?

(A) 5%
(B) 7.5%
(C) 10%
(D) 12.5%
(E) 15%

[Reveal] Spoiler: OA
A

Source: GMAT Club Tests - hardest GMAT questions

The solution is quite simple. If 20% of the supporters of war have no military experience, then 80% do. So, 4% of total population must be 80% of war supporters. Therefore, 100% of war supporters is 5% of the total population.

Can someone please explain how they got to 5%. The explaination lost me. Thanks...

The question never says one who has military Exp only support WAR.

can some one clarify me..where i m wrong..
here is my Sol ;

100% = 4% of population of L has military experience + 96%of population of L has no military experience

total population who supports War = 20% of those who support the war have no military experience + 80 % of those who support the war have military experience
=20% of 96% + 80% of 4%
=19.2% + 3.2%
=22.4%

so, by solving in this way i m arriving at an option beyond the answer given.
can someone give me a explanation where i m wrong....
thank you ..

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30 Mar 2011, 13:00
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bertlacy wrote:
4% of population of country L has military experience and supports a war against Country G. If 20% of those who support the war have no military experience what percentage of the country's population actually supports war against G?

(A) 5%
(B) 7.5%
(C) 10%
(D) 12.5%
(E) 15%

[Reveal] Spoiler: OA
A

Source: GMAT Club Tests - hardest GMAT questions

The solution is quite simple. If 20% of the supporters of war have no military experience, then 80% do. So, 4% of total population must be 80% of war supporters. Therefore, 100% of war supporters is 5% of the total population.

Can someone please explain how they got to 5%. The explaination lost me. Thanks...

When I first read this problem, I immediately thought of a Venn diagram...although it may not help directly solve the problem, it is useful for getting a visual of the problem. I in turn used a mental Venn diagram to help me solve the problem. Hopefully you can as well.

Attachment:

GMAT_Club_Question_of_the_Day_03-30-2011.jpg [ 49.41 KiB | Viewed 5890 times ]

As you can see in the diagram, indicated with the colors:
• Red = No support/Military Experience
• Blue = Support/No Military Experience
• Purple = Support/Military Experience
• Gray = No support/No Military Experience

Now, the question informs us that 4% of the total country population support and have military experience. This is the portion indicated in purple. This is the overlap between the red and blue circles. Next, the question informs us that 20% of those who support the war have no military experience. This is the portion of the blue circle excluding the purple overlapping portion (recall the purple portion is for those that support the war AND have military experience). So, with that, that must mean, if the blue portion excluding the purple portion = 20%, then the purple portion = 80%. Recall the question states that the purple portion (the percentage of the population that both supports the war and has military experience) is 4% of the total population. This allows us to set up the following equation and simply cross multiple and divide.

$${\frac{4%}{x}=\frac{80%}{20%} = \frac{4%}{x}=\frac{.8}{.2} = \frac{4*.2}{.8} = 1}$$

So, this lets us know that the portion of the blue circle (support/no experience) excluding the purple portion represents 1% of the overall population. Therefore, we can say that the overall support of the war is:

4% + 1% = 5%

Hope this helps.

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31 Mar 2011, 05:33
total population = people who support war + people who do not support war
X Y Z

people who support the war = 4P/100

people who do not support the war and dont have military experience = (20/100)Y

=> 4P/100 = (80/100)Y =>Y = 5% of population

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04 Jan 2012, 22:18
I think the clue is just to read the question properly...
It will come to you if u read the lines and whateever is written inbetween the lines well...

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04 Apr 2012, 15:45
If the wording of this question was better I could have easily solved this question but the wording was so darn confusing I did not know how to solve it. I tried numerous methods but the last part of the question was extremely confusing. What is the source for this question?

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04 Apr 2012, 18:18
A . very easy. Just take total population = 100 and u r done

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04 Apr 2012, 21:40
A it is

0.04* Population = .8 * Supportars of war

solve and get .05 * Population = Supportars of war

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17 Apr 2012, 08:55
4% of population of country L has military experience and supports a war against Country G. If 20% of those who support the war have no military experience what percentage of the country’s population actually supports war against G?

(A) 5%
(B) 7.5%
(C) 10%
(D) 12.5%
(E) 15%

Easy way to tackle the problem

sol: if we take the total population as 100 then the 4% of population has military exp and support war so i.e 4 people come under this category

then 20% of those who support the war have no military exp so this is indirectly showing that 80% have military exp and support war i.e 4 people

so for 80% we have 4 then for 100% can be calculated as fallows

100*4/80 = by cancelling 100 and 80 we get 5*4/4 then if we cancel 4/4 we are left with 5 which is our answer. i.e A.

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17 Apr 2012, 09:03
100% = 4% of population of L has military experience + 96%of population of L has no military experience"
This is not accurate. 4% of the population has military experience and supports the war. 20% of the total supporters have military experience. Let X represent the total supporters.
4 + 0.2X = X. Solve fo X. X = 5.
See the double matrix table above.

321kumarsushant wrote:
bertlacy wrote:
4% of population of country L has military experience and supports a war against Country G. If 20% of those who support the war have no military experience what percentage of the country's population actually supports war against G?

(A) 5%
(B) 7.5%
(C) 10%
(D) 12.5%
(E) 15%

[Reveal] Spoiler: OA

Source: GMAT Club Tests - hardest GMAT questions

The solution is quite simple. If 20% of the supporters of war have no military experience, then 80% do. So, 4% of total population must be 80% of war supporters. Therefore, 100% of war supporters is 5% of the total population.

Can someone please explain how they got to 5%. The explaination lost me. Thanks...

The question never says one who has military Exp only support WAR.

can some one clarify me..where i m wrong..
here is my Sol ;

100% = 4% of population of L has military experience + 96%of population of L has no military experience

total population who supports War = 20% of those who support the war have no military experience + 80 % of those who support the war have military experience
=20% of 96% + 80% of 4%
=19.2% + 3.2%
=22.4%

so, by solving in this way i m arriving at an option beyond the answer given.
can someone give me a explanation where i m wrong....
thank you ..

As the question is not stating that all people are supporting the war except 4%, there u gone wrong

from 100 people if 4 people have military exp and support war then it is not that remaining 96 % support and don't have military exp if we take x as total people who support war then .2x don't have military exp and these people support war so the remaining .8x have military exp and support war so if we solve for x we get ans as 5 i.e A.

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04 Apr 2013, 05:06
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Expert's post
bertlacy wrote:
4% of population of country L has military experience and supports a war against Country G. If 20% of those who support the war have no military experience what percentage of the country's population actually supports war against G?

(A) 5%
(B) 7.5%
(C) 10%
(D) 12.5%
(E) 15%

[Reveal] Spoiler: OA
A

Source: GMAT Club Tests - hardest GMAT questions

The solution is quite simple. If 20% of the supporters of war have no military experience, then 80% do. So, 4% of total population must be 80% of war supporters. Therefore, 100% of war supporters is 5% of the total population.

Can someone please explain how they got to 5%. The explaination lost me. Thanks...

BELOW IS REVISED VERSION OF THIS QUESTION:
4% of the population of a certain country owns both a car and a boat. If 20% of those who own a boat, do not own a car, what percentage of the country's population owns a boat?

A. 5%
B. 7.5%
C. 10%
D. 12.5%
E. 15%

Say total population of the country is 100. Then # of people who owns both a car and a boat is 0.04*100=4.

Now, since 20% of those who own a boat, do not own a car, then 80% of those who own a boat, do own a car, so own both a car and a boat. So, we have that if # of people who owns a boat is B, then # of people who owns both a car and a boat is 0.8B. On the other hand we know that # of people who owns both a car and a boat is 4, hence 0.8B=4 --> B=5. Which means that 5% of the population owns a boat.

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04 Apr 2013, 06:16
Military experience - ME
Support War against G - SWG

As per Q, ME intersection SWG = 4%

Also, 20% of SWG don't have ME => 80% of SWG have ME

Hence, 80% eqv to 4% sp 20% is eqv to 1%

Now Net SWG = 4%+1% = 5%

Hence A.

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Re: m05 q12   [#permalink] 04 Apr 2013, 06:16

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