Last month, John rejected 0.5% of the products that he inspected and

X - fraction of products Jane inspected
(1 - X) - fraction of products John inspected

0.8(X) + 0.5(1-X) = 0.75
0.3X = 0.75 - 0.5
X = 0.25/0.3
X = 5/6

Therefore the answer is D: 5/6.

IMO D 5/6

Basically you have the formula
0.8x+0.6y=0.75T

x=products jane rejected
y=products John rejected
T=total

i.e 8x+5y=7.5T
Now you just need to try different number to see which one will fit here.
Put x=1/6T y=5/6T (1-1/6T)
you get 8(1/6)+5(5/6) = 33/6 < 7.5 does not match with 7.5
try x=5/6T y=1/6T
8(5/6)+5(1/6)=45/6=7.5 matches so thats your answer.
You can plugin other numbers but it wont give you the exact 7.5

I have seen many GMAT problem including DS where you have to plugin numbers.
consider kudos if you like the answer.

produced = 1000
Rejected = 7.5

John = 0.5x (1/6)
Jane = 0.8y (5/6)

0.005x+0.008y = 7.5
x+y = 1000

0.005x + 0.008(1000-x) = 7.5
-0.003x = 7.5-8


0.003x = 0.5
x = 166.67


So Jane inspected 5/6 of the total products

Lets be smarter...what if this is the last question and we are left with just 1 minute to do it....

We knw that total rejections were .75% that means Jane would have done the bulk of rejections given that his rejection rate is .80%. clearly the options A,B and C would thus be eliminated that are around 50% mark. Now choose 1 between D and E that would atleast raise your chances of getting the solution right by 50%.

No problems if you have loads of time. This can even work at that time as you have to choose and work between D and E only.

Hope this helps !!

I never thought about solving it that way. Good idea AKProdigy87. Thanks.

Yeah AKProdigy87 did it the exact way I did it. I'll give you kudos for that, homie.
_________________

5X+8Y=.75T

substitute 1,5=6(total)

5+40=45

I chose D until i assumed that Jane and John inspected all products produced last month. At my first attempt, i thought that we could not assume like that since it is not stated in the question.
We may assume that the total number of Jane and John inspected is X% of all products produced last month.
Is it the typical of GMAT question which requires to solve using the unclear assumption?

We can let the number of products inspected by John = a and the number inspected by Jane = b and create the equation:

0.005a + 0.008b = 0.0075(a + b)

50a + 80b = 75a + 75b

5b = 25a

b = 5a

Thus, Jane inspected b/(a + b) = 5a/6a = 5/6 of the products.

Answer: D
_________________

Last month, John rejected 0.5% of the products that he inspected and Jane rejected 0.8 percent of the products that she inspected. If total of 0.75 percent of the products produced last month were rejected, what fraction of the products did Jane inspect?

We could use alligation method

Aaverage = 0.75
john = 0.5
jane = 0.8
0.8 - \(0.75/0.75 - 0.5\) = \(John/ Jane\)
\(0.05/0.25\) = \(1/5\)
Jane rejected \(5/5+1 \)= \(5/6\)

D
_________________