Of the 800 employees of company X,70% have been with the company for last 10 years.if y of those long term members were to retire and no other employee changes were to occur,what value of y would reduce the percent of longterm employees in the company to 60%?

A.200
B.160
C.112
D.80
E.56

The key here is to remember is that when a certain number DO retire, that will make the ABSOLUTE number of total employees less--that is what is throwing you. So take each of the answer choices and subtract them from the original number , 560 long-term employees (that is 70% of the original 800). Aha--but whatever number you choose, remember that the total number of employees will be reduced as well--whatever long term employees are left will NOT be out of the original 800, but out of whatever is left! Try that and see which answer choice gives you 60% of what number is left.

the first step of the problem, of course, is to calculate 70% of 800, which is 560.

after you do this, the algebra isn't really that bad. you just have to realize that the number of employees who retire (call this x) must be subtracted from BOTH the 800 and the 560.

after you take away x employees:
total # employees = 800 - x
# of long-term employees = 560 - x

so, set up a proportion: (560 - x) / (800 - x) = 3 / 5
(note that 3/5 is the reduced version of the 60% percentage)

cross-multiply to solve: 2800 - 5x = 2400 - 3x
400 = 2x
200 = x

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as the poster above has said, though, it's much easier just to PLUG IN THE ANSWER CHOICES.

try the middle choice first, as is always advisable in these sorts of problems:
new # of employees = 800 - 112 = 688
new # of long-term employees = 560 - 112 = 448
% = 448/668. this is almost 2/3, so it's too big.
this means you didn't take away enough employees.
therefore, we're down to choices (a) and (b).

try (a):
new # of employees = 800 - 200 = 600
new # of long-term employees = 560 - 200 = 360
% = 360/600 = 60%
bingo.