Exactly 14% of the reporters for a certain wire service : GMAT Problem Solving (PS)
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# Exactly 14% of the reporters for a certain wire service

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Exactly 14% of the reporters for a certain wire service [#permalink]

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12 Jan 2011, 15:53
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Exactly 14% of the reporters for a certain wire service cover local politics in Country X. If 30% of the reporters who cover politics for the wire service do not cover local politics in Country X, what percent of the reporters for the wire service do not cover politics?

(A) 20%
(B) 42%
(C) 44%
(D) 80%
(E) 84%
[Reveal] Spoiler: OA

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12 Jan 2011, 16:07
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rxs0005 wrote:
Exactly 14% of the reporters for a certain wire service cover local politics in Country X. If 30% of the reporters who cover politics for the wire service do not cover local politics in Country X, what percent of the reporters for the wire service do not cover politics?
(A) 20%
(B) 42%
(C) 44%
(D) 80%
(E) 84%

Let's assume there are 100 reporters --> 14 reporters cover local politics.

Now, as 30% of the reporters who cover all politics do not cover local politics then the rest 70% of the reporters who cover politics do cover local politics, so if there are x reporters who cover politics then 70% of them equal to 14 (# of reporters who cover local politics): 0.7x=14 --> x=20, hence 20 reporters cover politics and the rest 100-20=80 reporters do not cover politics at all.

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12 Jan 2011, 19:02
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rxs0005 wrote:
Exactly 14% of the reporters for a certain wire service cover
local politics in Country X. If 30% of the reporters who cover
politics for the wire service do not cover local politics in
Country X, what percent of the reporters for the wire service
do not cover politics?

(A) 20%
(B) 42%
(C) 44%
(D) 80%
(E) 84%

The wording does try to confuse you. Another method would be to take one sentence at a time and analyze its information. e.g.

Exactly 14% of the reporters for a certain wire service cover local politics in Country X

$$(14/100) * R = R_{LocPol}$$

If 30% of the reporters who cover politics for the wire service do not cover local politics in Country X
(This means 30% politics reporters cover non-local politics)

$$(30/100) * R_{Pol} = R_{NonLocPol)$$

what percent of the reporters for the wire service do not cover politics?

We know, $$R_{LocPol} + R_{NonLocPol} = R_{Pol}$$

So, $$(\frac{14}{100})*R + (\frac{30}{100})*R_{Pol} = R_{Pol}$$ (Using left hand sides of equations above)
We get $$R_{Pol} = (\frac{20}{100})*R$$
So, 80% reporters do not cover Politics.
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04 Jun 2011, 02:07
VeritasPrepKarishma wrote:
rxs0005 wrote:
Exactly 14% of the reporters for a certain wire service cover
local politics in Country X. If 30% of the reporters who cover
politics for the wire service do not cover local politics in
Country X, what percent of the reporters for the wire service
do not cover politics?

(A) 20%
(B) 42%
(C) 44%
(D) 80%
(E) 84%

The wording does try to confuse you. Another method would be to take one sentence at a time and analyze its information. e.g.

Exactly 14% of the reporters for a certain wire service cover local politics in Country X

$$(14/100) * R = R_{LocPol}$$

If 30% of the reporters who cover politics for the wire service do not cover local politics in Country X
(This means 30% politics reporters cover non-local politics)

$$(30/100) * R_{Pol} = R_{NonLocPol)$$

what percent of the reporters for the wire service do not cover politics?

We know, $$R_{LocPol} + R_{NonLocPol} = R_{Pol}$$

So, $$(\frac{14}{100})*R + (\frac{30}{100})*R_{Pol} = R_{Pol}$$ (Using left hand sides of equations above)
We get $$R_{Pol} = (\frac{20}{100})*R$$
So, 80% reporters do not cover Politics.

AWESOME! WOW!
Thanks, Karishma! Actually, I was stuck in this problem's solution for a long time. Hooooooooffffffff! Feeling relieved after going through your explanation!
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04 Jun 2011, 19:14
Let total reporters = R and # of reporters who cover local politics = R

So we need to find 1 - R/N

Now 0.14R = Cover local politics in country X

And 0.30N don't cover local politics in country X

=> 0.70N cover cover local politics in country X

=> 0.70N = 0.14R

=> N/R = 1/5

=> 1 - N/R = 4/5

So percent of the reporters for the wire service do not cover politics = 4/5 * 100 = 80%

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04 Jun 2011, 22:20
Consider there are x reporters in wire service.

14% cover local politics i.e. = 0.14x

Consider there are 100 reporters covering politics; of which non-local politics = 30

0.14x + 30 = 100
x = 500 total reporters

# of reporters do not cover politics = 500-100 = 400

so # of reports do not cover politics / # of total reporters = 400/500 = 80%
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Reporters.JPG [ 13.26 KiB | Viewed 4450 times ]

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11 Jun 2011, 15:21
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Let Total reporters = 100

Out of these 100 suppose 'x' cover politics
So 100-x do not cover politics

Now out of the ones who cover politics 70% cover local politics and 30% do not cover local politics
So number that covers local politics = 0.7x

0.7x = 14
so x = 20

So out of 100 there are 20 reporters that cover politics
so 80% do not cover politics
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12 Jun 2011, 23:49
0.7x = 14 gives x = 20

thus !politics = 100-20 = 80
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10 Sep 2011, 00:01
The answer is 80%. A similar problem, although relatively simpler, if some of you want to work out, is available here: motorists-13233.html#p973017
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29 Dec 2011, 10:57
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All Reporters (assume 100) = Cover Politics (assume x) + Do not Cover Politics (100 -x)

Cover Politics = Cover Local Politics (14% of all reporters or 70% of reporters covering politics) + Do not Cover Local Politics (30% of reporters covering politics, 30% of x)

So 14% of all reporters = 70% of x
14 = 70% of x
x = 20
Do not cover Politics = 100 -20 = 80…percentage 80%
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Politics Reporter.JPG [ 18.26 KiB | Viewed 3200 times ]

Last edited by RSG on 30 Dec 2011, 09:40, edited 2 times in total.
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30 Dec 2011, 02:19
using attached matrix:
we have to find the y.
.3x=X-14
So, X=20
Therefore, Y=80
80%
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politics.jpg [ 16.41 KiB | Viewed 3220 times ]

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13 Aug 2012, 10:48
BDSunDevil wrote:
using attached matrix:
we have to find the y.
.3x=X-14
So, X=20
Therefore, Y=80
80%

Thanks every one, for the explanation. I used the same table as BDsunDevil used only difference being i put "14" in the slot "total local politics" rather than in slot "Both politics and local politics" whic is not explicitly mentioned but is derived (14-0=14). It would have been better if "0" was logged under non politics tab in the table, just for better clarity.

Please correct me if I'M wrong.

Initially, I was also confused about this line "Exactly 14% of the reporters for a certain wire service cover local politics in Country X." . I took 14% to be the total local politics and completely ignored the fact that there can't be any local politics under non politics column.
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politics.jpg [ 20.71 KiB | Viewed 2719 times ]

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