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Ratios

by eitijan » Wed May 11, 2016 9:50 am
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.

Not able to approach this question.

OA D
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by 800_or_bust » Wed May 11, 2016 11:41 am
eitijan wrote: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.

Not able to approach this question.

OA D
(1) Since the ratio of FT to PT is less for Division Y than for the company as a whole, then the ratio of FT to PT must be greater for Division X than the company as a whole. Remember, these are the only two divisions and each employee is an employee of only one division. Therefore, the overall company ratio must lie in between the ratios for each of the divisions. In other words, the target question could have simply been restated as "is the ratio of the number of full-time employees to the number of part-time employees less for Division Y than for Company Z?" (1) answers this question affirmatively, and therefore is sufficient.

(2) We're told that more than half the full-time employees of Company Z are employees of Division X, and more than half the part-time employees of Company Z are employees of Division Y. Again, since the employees can only work for one division or the other, this also implies that less than half the part-time employees of Company Z are employees of Division X and less than half the full-time employees of Company Z are employees of Division Y.

If more than half the total full-time employees, but less than half the total part-time employees, work for Division X, it logically follows that the ratio FT:PT for Division X must be greater than the corresponding ratio for Company Z as a whole. So this statement is also sufficient to answer the target question.
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by GMATGuruNY » Wed May 11, 2016 12:56 pm
eitijan wrote: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.
To make the situation easier to see, test an EASY CASE.
Let:
Total number of full-time employees at Company Z = 10.
Total number of part-time employees at Company Z = 10.
Resulting ratio:
(full-time at Z)/(part-time at Z) = 10/10 = 1.

Question stem, rephrased:
Is (full-time in X)/(part-time in X) > 1?

Statement 1:
Here, (full-time in Y)/(part-time in Y) < 1.

Test a SMALL ratio for Y.
Case 1: full-time in Y = 1, part-time in Y = 9
In this case:
Full-time in X = 10-1 = 9.
Part-time in X = 10-9 = 1.
Resulting ratio:
(full time in X)/(part-time in X) = 9/1 = 9.
Since the resulting ratio is greater than 1, the answer to the question stem is YES.

Test a LARGE ratio for Y.
Case 1: full-time in Y = 8, part-time in Y = 9
In this case:
Full-time in X = 10-8 = 2.
Part-time in X = 10-9 = 1.
Resulting ratio:
(full time in X)/(part-time in X) = 2/1 = 2.
Since the resulting ratio is greater than 1, the answer to the question stem is YES.

Since the answer is YES in both cases, SUFFICIENT.

Statement 2:
Here:
Full-time in X > 5.
Part-time in Y > 5.

Test a SMALL VALUE FOR X and a LARGE VALUE FOR Y.
Case 3: full-time in X = 6, part-time in Y = 9, implying that part-time in X = 10-9 = 1
Resulting ratio:
(full time in X)/(part-time in X) = 6/1 = 6.
Since the resulting ratio is greater than 1, the answer to the question stem is YES.

Test a LARGE VALUE FOR X and a SMALL VALUE FOR Y.
Case 3: full-time in X = 9, part-time in Y = 6, implying that part-time in X = 10-6 = 4
Resulting ratio:
(full time in X)/(part-time in X) = 9/4.
Since the resulting ratio is greater than 1, the answer to the question stem is YES.

Since the answer is YES in both cases, SUFFICIENT.

The correct answer is D
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