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DS Question

by MI3 » Sun Jul 03, 2011 9:21 pm
Q. Each employee of Company Z is an employee of either Division X or Division Y, but not both. If each division has some part-time employees, is the ratio of the number of full-time employees to the number of part-time employees greater for Division X than for Company Z?
(1) The ratio of the number of full-time employees to the number of part-time employees is less for Division Y than for Company Z.
(2) More than half the full-time employees of Company Z are employees of Division X, and more than half of the part-time employees of Company Z are employees of Division Y.

IMO B, am I correct?
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Source: — Data Sufficiency |
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by Geva@EconomistGMAT » Sun Jul 03, 2011 9:59 pm
MI3 wrote:Q. Each employee of Company Z is an employee of either Division X or Division Y, but not both. If each division has some part-time employees, is the ratio of the number of full-time employees to the number of part-time employees greater for Division X than for Company Z?
(1) The ratio of the number of full-time employees to the number of part-time employees is less for Division Y than for Company Z.
(2) More than half the full-time employees of Company Z are employees of Division X, and more than half of the part-time employees of Company Z are employees of Division Y.

IMO B, am I correct?
Stat. (1) is also sufficient. The ratio for the entire company Z is a weighted average of the ratios of the two divisions. As such, if the ratio of division Y is smaller than the overall ratio, then the ratio for division X must be greater than the overall ratio to "compensate", which means that it is also greater than the ratio in division Y.

Stat. (2) is indeed sufficient. Think of the ratios as a fraction of Full/part.

When comparing these two fractions, stat. (2) basically tells you that the fraction for X has a greater numerator than the fraction for Y, and a smaller denominator than the fraction for Y - which means that the overall fraction for division X is greater than the fraction for Y.

Thus, both statements define the answer to the question "is the ratio for X greater than for Y" to be "yes", and thus sufficient.
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