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# M18-18

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Math Expert
Joined: 02 Sep 2009
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M18-18  [#permalink]

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16 Sep 2014, 00:03
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Difficulty:

65% (hard)

Question Stats:

56% (01:18) correct 44% (01:16) wrong based on 255 sessions

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If 25% of the company's employees contribute at least 4% of their salary to the Charity Fund, what percent of the company's employees contribute at least 5% of their salary to the Charity Fund?

(1) 20% of the company's employees contribute at least 4% but less than 5% of their salary to the Charity Fund

(2) 95% of the company's employees contribute less than 5% of their salary to the Charity Fund

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M18-18  [#permalink]

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16 Sep 2014, 00:03
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4
Official Solution:

If 25% of the company's employees contribute at least 4% of their salary to the Charity Fund, what percent of the company's employees contribute at least 5% of their salary to the Charity Fund?

Say:

X% contribute less than 4%;

Y% contribute at least 4% but less than 5%;

Z% contribute at least 5%.

Note that these groups don't have intersections and $$X+Y+Z=100$$.

Given: $$Y+Z=25\%$$. Question: $$Z=$$?

(1) 20% of the company's employees contribute at least 4% but less than 5% of their salary to the Charity Fund. Given: $$Y=20\%$$. Hence, $$Y+Z=20+Z=25\%$$, which gives $$Z=5\%$$. Sufficient.

(2) 95% of the company's employees contribute less than 5% of their salary to the Charity Fund. Given: $$X+Y=95\%$$. Hence, $$X+Y+Z=95+Z=100\%$$, which gives $$Z=5\%$$. Sufficient.

Answer: D
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Re: M18-18  [#permalink]

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17 Feb 2015, 10:47
Bunuel

Requesting you to clarify my doubt. In this question are we not assuming that every employee is making a donation.

lets assume there are 100 people. Then we know that 25 of them contribute >=4%...

From 2 we know that 95% contribute <=5%...

Can we not consider a possibility that the 25 employees contribute more than 4 and less than 5 are part of the 95% who contribute less than 5%.. In this possibility we will come to conclusion that 5% of the people are not making any contribution..
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Re: M18-18  [#permalink]

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18 Feb 2015, 03:14
2
qw1981 wrote:
Bunuel

Requesting you to clarify my doubt. In this question are we not assuming that every employee is making a donation.

lets assume there are 100 people. Then we know that 25 of them contribute >=4%...

From 2 we know that 95% contribute <=5%...

Can we not consider a possibility that the 25 employees contribute more than 4 and less than 5 are part of the 95% who contribute less than 5%.. In this possibility we will come to conclusion that 5% of the people are not making any contribution..

X% of the employees who contribute less than 4 include those employees who did not contribute at all (contribute 0<4).

Check other discussions of this question:
if-25-of-the-company-s-employees-contribute-at-least-4-of-their-191729.html
if-25-of-the-company-s-employees-contribute-at-least-4-of-108484.html

Hope it helps.
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Re M18-18  [#permalink]

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30 Dec 2015, 06:30
I think this is a poor-quality question and I don't agree with the explanation. what about the ones that don't contribute at all ?
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Re: M18-18  [#permalink]

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30 Dec 2015, 08:22
deospaima wrote:
I think this is a poor-quality question and I don't agree with the explanation. what about the ones that don't contribute at all ?

Please read the post just above yours:

X% of the employees who contribute less than 4 include those employees who did not contribute at all (contribute 0<4).

You just did not understand question/solution.
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Re M18-18  [#permalink]

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18 Apr 2018, 13:24
I think this is a high-quality question and I agree with explanation. I do agree that this is a good quality question, but it takes a little time to understand the flaw in the thought process which made me reject choice B. All thanks to Bunuel! Thanks man!
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Re: M18-18  [#permalink]

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26 Jul 2018, 07:21
How can one assume that there are no intersections?
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Re: M18-18  [#permalink]

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15 Aug 2018, 00:45
20Hobbit wrote:
How can one assume that there are no intersections?

Selection of sets (X, Y & Z) have been done in such a way that there is no intersection. Please read carefully.

X% contribute less than 4%;

Y% contribute at least 4% but less than 5%;

Z% contribute at least 5%.

X+Y+Z=100.
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Re: M18-18 &nbs [#permalink] 15 Aug 2018, 00:45
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# M18-18

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