awilhelm 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 of the full-time employees of company z are employees of division x, and more than 1/2 of the part-time employees of company z are employees of division y.

IMO [spoiler]A[/spoiler]

Second look and explanation to follow

sanju09 wrote:

awilhelm 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 of the full-time employees of company z are employees of division x, and more than 1/2 of the part-time employees of company z are employees of division y.

IMO [spoiler]A[/spoiler]

Second look and explanation to follow

Since, n (X ∩ Y) = 0, hence n (Z) = n (X) + n (Y) = n (X ∪ Y)

If n (X) = a + b and n (Y) = c + d, where

a is number of full-time employees in X,
b is number of part-time employees in X,
c is number of full-time employees in Y, and
d is number of part-time employees in Y, then

Is a/b > (a + c)/ (b + d)?

(1) It reads that c/d < (a + c)/ (b + d); please note that if a, b, c, and d are 4 positive integers such that, c/d < (a + c)/ (b + d), then it's a must that a/b > (a + c)/ (b + d). Sufficient

(2) It reads that a + b > ½ (a + b + c + d) and c + d > ½ (b + d). With this we can conclude that a + b > c + d > ½ (b + d). This is not enough to answer what's asked, I think. Insufficient

[spoiler]A[/spoiler]

[spoiler]But I'm still not happy with my explanation, not in a mood to give it a third look right now, getting tired may be. Anybody, please![/spoiler]

sanju09 wrote:

awilhelm 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 of the full-time employees of company z are employees of division x, and more than 1/2 of the part-time employees of company z are employees of division y.

IMO [spoiler]A[/spoiler]

Second look and explanation to follow

Sanju09 --- let me add my 2 cents

IMO -- D

statement (1)
if div. y has a lower ratio, then div. x must have a higher ratio.
so, sufficient.

statement (2)
FT and PT are mutually exclusive,
div. x has more FT employees, but fewer PT employees.

therefore, the ratios for div. x must be higher.

sufficient

Continuing from explation above

If

a is number of full-time employees in X,
b is number of part-time employees in X,
c is number of full-time employees in Y, and
d is number of part-time employees in Y, then

Is a/b > (a + c)/ (b + d)?

(1) It reads that c/d < (a + c)/ (b + d)

(2) a > c and d > b

a > c , dividing by b , a/b > c / b since d > b , therefore a/b > c/d

Still inconclusive so E

onedayi'll wrote:

sanju09 wrote:

awilhelm 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 of the full-time employees of company z are employees of division x, and more than 1/2 of the part-time employees of company z are employees of division y.

IMO [spoiler]A[/spoiler]

Second look and explanation to follow

Sanju09 --- let me add my 2 cents

IMO -- D

statement (1)
if div. y has a lower ratio, then div. x must have a higher ratio.
so, sufficient.

statement (2)
FT and PT are mutually exclusive,
div. x has more FT employees, but fewer PT employees.

therefore, the ratios for div. x must be higher.

sufficient

[spoiler]Thank you, I know D should be the answer. In fact my first post against this problem was made on Tue Jan 27, 2009 at 6:03 am and it read "IMO D" with an advice to revise Ratio and Proportions and no explanation. I, actually wanted members to comment on it, as I was quite new then. But it was lying unattended till the last time "Sat Feb 13, 2010 at 4:23 am" I visited it. This gave me a chance to add feather to my notoriety of toying with members (https://www.beatthegmat.com/probability-t52561.html) and I edited my old post to new, which went unnoticed in the absence of a subsequent post. The question has thus got the attention of persons other than me. A detailed explanation is yet to be seen, in fact.[/spoiler]