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# M18-18

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Math Expert
Joined: 02 Sep 2009
Posts: 41634

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16 Sep 2014, 01:03
Expert's post
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Difficulty:

55% (hard)

Question Stats:

55% (01:15) correct 45% (01:09) wrong based on 146 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
[Reveal] Spoiler: OA

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Kudos [?]: 124124 [0], given: 12072

Math Expert
Joined: 02 Sep 2009
Posts: 41634

Kudos [?]: 124124 [0], given: 12072

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16 Sep 2014, 01:03
Expert's post
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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.

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Joined: 27 Jan 2013
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Location: United States
Concentration: Entrepreneurship, Marketing
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17 Feb 2015, 11:47
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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Math Expert
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18 Feb 2015, 04:14
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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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30 Dec 2015, 07:30
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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Math Expert
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30 Dec 2015, 09:22
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 ?

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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03 Aug 2017, 00:04
Bunuel wrote:
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.

so lets say we have at least 4% : so lets call it X

now we have at least four but less than 5% : so this is essentially from 4% to something less than 5%

now at least 5% is 5 and above. So let me try and draw a line

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M18-18   [#permalink] 03 Aug 2017, 00:04
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# M18-18

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