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16 Sep 2014, 01:03
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If 25% of a company's employees donate at least 4% of their salary to the Charity Fund, what percentage of the company's employees donate at least 5% of their salary to the Charity Fund?
(1) 20% of the company's employees donate at least 4% but less than 5% of their salary to the Charity Fund.
(2) 95% of the company's employees donate less than 5% of their salary to the Charity Fund.
(1) 20% of the company's employees donate at least 4% but less than 5% of their salary to the Charity Fund.
(2) 95% of the company's employees donate less than 5% of their salary to the Charity Fund.
16 Sep 2014, 01:03
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Official Solution:
If 25% of a company's employees donate at least 4% of their salary to the Charity Fund, what percentage of the company's employees donate at least 5% of their salary to the Charity Fund?
Let:
\(x\%\) donate less than 4%;
\(y\%\) donate at least 4% but less than 5%;
\(z\%\) donate at least 5%.
Observe that these groups do not intersect and \(x+y+z=100\).
Given: \(y+z = 25\%\). Question: \(z=\)?
(1) 20% of the company's employees donate at least 4% but less than 5% of their salary to the Charity Fund.
Given: \(y=20\%\). Therefore, \(y+z=20+z=25\%\), which results in \(z=5\%\). Sufficient.
(2) 95% of the company's employees donate less than 5% of their salary to the Charity Fund.
Given: \(x+y=95\%\). Therefore, \(x+y+z=95+z=100\%\), which results in \(z=5\%\). Sufficient.
Answer: D
If 25% of a company's employees donate at least 4% of their salary to the Charity Fund, what percentage of the company's employees donate at least 5% of their salary to the Charity Fund?
Let:
\(x\%\) donate less than 4%;
\(y\%\) donate at least 4% but less than 5%;
\(z\%\) donate at least 5%.
Observe that these groups do not intersect and \(x+y+z=100\).
Given: \(y+z = 25\%\). Question: \(z=\)?
(1) 20% of the company's employees donate at least 4% but less than 5% of their salary to the Charity Fund.
Given: \(y=20\%\). Therefore, \(y+z=20+z=25\%\), which results in \(z=5\%\). Sufficient.
(2) 95% of the company's employees donate less than 5% of their salary to the Charity Fund.
Given: \(x+y=95\%\). Therefore, \(x+y+z=95+z=100\%\), which results in \(z=5\%\). Sufficient.
Answer: D
18 Feb 2015, 04:14
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qw1981
X% of the employees who contribute less than 4 include those employees who did not contribute at all (contribute 0<4).
Check other discussion of this question:
https://gmatclub.com/forum/if-25-of-the ... 91729.html
Hope it helps.
