Blood banks will shortly start to screen all donors for NANB hepatitis

Question

Blood banks will shortly start to screen all donors for NANB hepatitis. Although the new screening tests are estimated to disqualify up to 5 percent of all prospective blood donors, they will still miss two-thirds of donors carrying NANB hepatitis. Therefore, about 10 percent of actual donors will still supply NANB-contaminated blood.

The argument above depends on which of the following assumptions?

(A) Donors carrying NANB hepatitis do not, in a large percentage of cases, carry other infections for which reliable screening tests are routinely performed.

(B) Donors carrying NANB hepatitis do not, in a large percentage of cases, develop the disease themselves at any point.

(C) The estimate of the number of donors who would be disqualified by tests for NANB hepatitis is an underestimate.

(D) The incidence of NANB hepatitis is lower among the potential blood donors than it is in the population at large.

(E) The donors who will still supply NANB-contaminated blood will donate blood at the average frequency for all donors

Anu26 · Accepted Answer

Meaning of the question :

Let there be 100 people(all prospective blood donors) -> so 5 people will be caught in the new test.

2/3 * (people carrying nanb) = missed

therefore 1/3 * (people carrying nanb) = those that were caught = 5

therefore, people carrying nanb = 5*3 = 15

missed people = 10 (15-5) -> this is 10% of the prospective donor and the conclusion that they will still supply contaminated blood

Conclusion : 10% of actual donors will still supply NANB-contaminated blood

Now if donors carrying nanb carry other infections for which tests are routinely performed -> then the number of people carrying

nanb (with other infection) will be caught and will be less in number.

Thus, 2/3 * (people carrying nanb) -> will be less -> those missed will be less -> then we cannot claim that 10% of the donors will

still supply contaminated blood.

KarishmaB · Answer

Screening for NANB will start.
5% of prospective donors will be disqualified. (So if 100 people come to donate, only 95 will be allowed after NANB screening because 5 will have NANB).
But only 1/3rd will be caught and 2/3rd will still be missed. So these 5 make up only 1/3rd of total who carry NANB. So another 10 will be there carrying NANB but they will be missed.

Conclusion: About 10 percent of actual donors will still supply NANB-contaminated blood.

10 out of 95 allowed donors will have NANB so that's 'about 10%'. Looks right. Now the gap is will all these 95 supply blood i.e. will all of them be allowed to supply blood? For our conclusion, we are assuming that all these 95 will supply blood. That NANB test was the only hurdle they needed to cross to become actual donors.

(A) Donors carrying NANB hepatitis do not, in a large percentage of cases, carry other infections for which reliable screening tests are routinely performed.

Correct. We are assuming that no other test will disqualify many NANB carriers. What if NANB carriers usually carry other infections too which are tested for too? Then of these 10, perhaps another 8 would be disqualified because of other associated infections. So negating this breaks our conclusion.

(B) Donors carrying NANB hepatitis do not, in a large percentage of cases, develop the disease themselves at any point.

Irrelevant.

(C) The estimate of the number of donors who would be disqualified by tests for NANB hepatitis is an underestimate.

The argument takes the 1/3rd number to be accurate.

(D) The incidence of NANB hepatitis is lower among the potential blood donors than it is in the population at large.

No such comparison in the argument.

(E) The donors who will still supply NANB-contaminated blood will donate blood at the average frequency for all donors

We are talking about the donor numbers only, not the units donated and frequency of donation by each donor.

Answer (A)

boeinz · Answer

Tough one.

My explanation:

If NANB carries other infections which can be tested true positive (or reliable as stated in Option A), then the chance of detecting NANB will be higher. However, Option A states that this is not the case. Hence the 2/3 of NANB will still be missed and this figure (2/3) has to be taken as accurate. Thus its a necessary assumption.

ykaiim · Answer

Hi,

I solved this question with a different approach. I hope you will find it useful:

The premises are all seemed peculiar to me. But, I used %age and Number to solve this.

Conclusion is on ACTUAL 10% donors, which is nowhere mentioned in the argument. So, we need to look for following as per CR Bible:
1. Options which have ACTUAL keyword.
2. Options involveing %age instead of numbers, as we are given %ages only. So, choice with numbers will be Incorrect.
3. There seems to logical gaps in the argument and the author mentioned strong words to indicate that his reasoning is air-tight, which points to a DEFENDER assumption case. So, look for negative answer choices, which involve some defending language.

subhashghosh · Answer

Answer - A) Donors carrying NANB hepatitis do not, in a large percentage of cases, carry other infections for which reliable screening tests are routinely performed

So they'll escape the screening here, and the other screenings also, hence the number of infected donors who did not get filtered out does not change.

Say there are 15% donors affected, so 2/3 * 15 escape, hence 10% remain, they don't get caught in any other test so the %age is constant.

sowragu · Answer

Derived 'A' through POE.

Understanding of the passage.
P1 - Screening is happening.
P2 - Able to restrict only 5% out of 15%
C1 - Still 10% of ppl r giving the contaminated blood.

Assumption made - Some issue is there bcos of transfering this contaminated blood, Hence screening is happening in all the blood donors.

B - Donors carrying NANB hepatitis do not, in a large percentage of cases, develop the disease themselves at any point.   The information provided is not creating any link between the premise and conclusion. Also, if its not going to have any effect or creating any disease then why the screening is happening. 
(C) The estimate of the number of donors who would be disqualified by tests for NANB hepatitis is an underestimate. -   The statement has been already stated in the main Argument. Only 1/3rd was being identified.  
(D) The incidence of NANB hepatitis is lower among the potential blood donors than it is in the population at large. -   Complete Out of scope. Blood Donor Vs Total Population 
(E) The donors who will still supply NANB-contaminated blood will donate blood at the average frequency for all donors   Again its a statement or an information which no way supports the argument. Its a mere inforation. What ever frequecny they are giving it doesnt support the Conclusion made

So Finally A. A is ok with the pre assumption made during reading the argument. We are only checking for NANB, what if any other contamination is there? Through POE and pre assumption i reached A.

A is better choice among the 5.

HardWorkBeatsAll · Answer

I initially replied (E) incorrectly. Here's the explanation of why it is (A) -

Great question. Thanks for posting.

Leo8 · Answer

" Although the new screening tests are estimated to disqualify up to 5 percent of all prospective blood donors, 
they will still miss two-thirds of donors carrying NANB hepatitis. "

Isn't the correct answer choice attacking the given premise. we are given that 2/3rd will be missed. How can we attack the given fact in the argument.

A. Donors carrying NANB hepatitis do not, in a large percentage of cases, carry other infections for which reliable screening tests are routinely performed.

if this is true, our premise doesn't stand.

I was actually hoping to see the link between donors and actual donors.

DAVEexamPAL · Answer

Leo8  it doesn't contradict our premise. We are asked which answer strengthens the premise that 2/3 of NANB donors will not be disqualified. One thing that is necessary for this is that those 2/3 won't be disqualified for any other reason - which is exactly what A tells us. 
Is this clear, or still confusing? Why do you think the premise doesn't stand?

DAVEexamPAL · Answer

Logically, we are given an assumption (the test will miss 2/3 of NANB donors) and a conclusion (2/3 of NANB donors, or 10% of all donors, will not be disqualified). But notice this assumes those infected won't be disqualified for any OTHER reason than NANB either - which is what A suggests.

By process of elimination:
A - Yes! this means if they aren't detected for NANb, they won't be detected for anything else. 
B - irrelevant
C - this contradicts the argument, it doesn't underline it 
D - not relevant: the stats we were given are about the potential donors, not the population at large
E - we don't know anything about the average frequency of donors, so this is just a distraction.

teaserbae · Answer

AjiteshArun 
I choose B.
I interpreted B as if the NANB hepatitis develop of its own then there might be increase in the number of donors having NANB hepatitis there by weakening the conclusion that only 10% will be left.

AjiteshArun · Answer

The conclusion is:

Therefore, about 10 percent of actual donors will still supply NANB-contaminated blood.

Option A :  Donors carrying NANB hepatitis do not, in a large percentage of cases, carry other infections for which reliable screening tests are routinely performed.

The argument says that because the NANB screening misses 2 out of every 3 people with NANB-contaminated blood, 10% of the donors will continue to supply NANB-contaminated blood. This conclusion does not take into account the possibility that there could be other ( reliable ) screening processes for other problems.

If we apply negation, we see that if people with NANB-contaminated blood  do  have other problems that reliable screening methods can detect, then the conclusion that 10% of donors will donate NANB-contaminated blood is weakened, as these people will get "screened out" by these other tests.

Option B :  Donors carrying NANB hepatitis do not, in a large percentage of cases, develop the disease themselves at any point.

This option basically says that for the conclusion to be true, donors with NANB-contaminated blood should never get the disease at any point in their lives.

I think the most important thing to remember here is that this is an  assumption  question, and not a general strengthen question. In assumption questions, we need to pick an option that, given the logic of the argument, the argument  needs  in order to get to its conclusion. This argument does not  need  donors with NANB-contaminated blood to be  free  or  not free  of the actual disease  at any point . Just the fact that these donors have NANB-contaminated  blood  is enough.

You might be looking at the possibility that NANB hepatitis is infectious. However, whether it is infectious or not is already "factored in". That is, option B does not involve a change in the nature of the disease from non-infectious to infectious.

hadimadi · Answer

AjiteshArun ,  KarishmaB

Hi,

let x be the number of potential donors, and N be the number of people who actually have NANB. 
We know that 2/3N won't be detected, and that 1/3N is contained in the 0.05x:

1/3N <= 0.05x

I put smaller and equal because:

We know the test is not 100% accurate, since 2/3N are not being detected. So when 5% of people are disqualified, it could be that at least some are falsely tested positive. So on top of the 1/3N who actually have the disease, we have some potential unknown amount of people who are false positives.

Now we can follow:

2/3N <= 0.1x

And now, even (A) won't work as an answer choice.

Where did I go wrong?

AjiteshArun · Answer

Hi  hadimadi ,

You seem to be mostly on the right track (just remember that we don't want to take  x  in both cases, because the second total does not involve all of  x , and the second total is not exactly 10% of something else), but false positives don't play an important role in the author's argument (in fact, he or she doesn't even mention false positives).

That said, it'd help if you could tell us why you think option A won't work. Until then, let's include the possibility of false positives, and then try to work with actual numbers.

\frac{1}{3}N_{prospective\:donors\:with\:NANB}+N_{prospective\:donors,\:false\:positives}\leq\frac{5}{100}N_{prospective\:donors}

If we start with 100 prospective donors, the test is estimated to reject up to 5. It's worth noting that 5 is the maximum number of prospective donors with NANB that the test is estimated to reject. This is the number the author seems to be using, so we'll also use it. Now, there are two important points to keep in mind here:

1.  We've been looking at  prospective  donors till now. If this is the only test, the number of  actual  donors is 95, not 100.
 2.  This is an assumption question. The process of solving this question will involve  understanding how the author reached his or her conclusion .

Point (2) is particularly important. Whatever else we do to solve the question,  the answer we choose must, at the end of the day, help us get to the author's conclusion .

So, how  did  the author reach the conclusion that "about 10 percent of actual donors will still supply NANB-contaminated blood"? Clearly, it's not by maximising the number of false positives. For example, if we assume that 4 out of the 5 rejected prospective donors were false positives, that would leave us with  \frac{1}{3}N_{prospective\:donors\:with\:NANB}=1 , which would mean that the number of prospective donors with NANB is 3 and the number of actual donors with NANB is just 2, which is not particularly close to "about 10 percent" of 95.

What the author has done here is assume that the number of false positives is very low. As far as the author is concerned, the number of false positives is 0 if we assume the total number of prospective donors to be 100. That means the test takes  ~ 5 prospective donors with NANB out, leaving 10 actual donors with NANB.  \frac{10}{95}  is  ~ 0.105, and we can now see how the author got to "about 10% of actual donors".

Finally, why is A correct? One weakness in the argument is that it does not take into account the possibility that there could be other ( reliable ) screening processes for other problems. If people with NANB-contaminated blood  do  have other problems that other reliable screening methods can detect, then the conclusion that about 10% of donors will donate NANB-contaminated blood is weakened, as these people will get "screened out" by these other tests.

KarishmaB · Answer

The highlighted part is not implied and there is no reason to assume it. A test gives false negatives is no reason to assume that it gives false positives too. For example, the Rapid Antigen test for covid - if it is positive, one has covid but it is negative, the result is uncertain.

Assuming total 100 potential donors, all we know is that the test misses out 2/3rd cases and only detects 1/3rd cases which will be about 5 of the potential donors. So rest 95 have about 10 cases among them. Note that these are approximates that the author has given.

To say that about 10 percent of actual donors will still supply NANB-contaminated blood, he has assumed that these 10 are not likely to be disqualified from donating blood because of other infections that they carry with NANB. 
What if most people with NANB have other related infections too and they are screened for regularly? Then most of the other 10 may be disqualified too. So to arrive at the conclusion that 10 percent people will still give NANB infected blood, he has assumed that no other such related infections are present & screened for.

Hence (A) works.

hadimadi · Answer

Hi AjiteshArun , the yellow part: Just because something is not mentioned in the argument explicitly it doesn't mean that one should still be aware of all cases - in many CR questions in fact the solution is hidden in some apparently small words (i.e., when there are 100 vehicles caught by a speed camera, it doesn't mean that we have 100 different drivers. Same way, if we have 5% disqualified, I can't just go and assume that all really have the diseases unless otherwise is being told in the question stem) the red part: This is an assumption you are making, and not the author himself anywhere in his argument, so we can't just take it as 'it is implicitly assumed', because exactly this could be faulty in his argument / the missing link which the answer choice could be looking for. However, to assume that false positives are non existent is necessary for this argument. But it is nowhere mentioned. Not even in an answer choice. Now, one could argue that there might be several necessary conditions for an assumption question to hold true, so it doesn't need to be mentioned anywhere. Alright, then let's not make any assumptions about the number of false positives, and just look at the question stem and answer choices (now we don't assume anything about how many false positives there are in the 5%): Not (A) and other premises from question stem -> Not Conclusion X=A large percentage of those who carry NANB carry other diseases that are reliably and routinely tested for (this is our not (A)) Y= 5% of potential donors are disqualified ( potentially including false positives) Z= Exactly 2/3 of people that carry the disease are in the 95% that become actual donors N=Total number of people actually carrying NANB E=Total potential donors X and Y and Z -> The percentage of actual donors carrying NANB is not around 10% From Y: N/3<=0.05E -> 2N/3<= 0.1E From Z: (2N/3)/(0.95E), this is the share of people carrying NANB in the a total of 0.95E Combining these findings, we get: (2N/3)/(0.95E) <= (0.1E)/(0.95E) = 0.1/0.95 = approx. 0.1 In total: The share of people carrying NANB of the 0.95E, where 0.95E=actual donors, is smaller than or equal to 10%. Let's name this finding F. Hence: F and X -> The percentage of actual donors carrying NANB is not around 10% Since X tells us that there are very likely fewer people carrying the disease, meaning N is smaller than what we assumed it to be. Now since F is equal to: (2N/3)/(0.95E)<=0.1x, and we know that we will have fewer than 2N/3 people who will actually become donors, we get: (Some number smaller than (2N/3)/(0.95E))< (2N/3)/(0.95E) <= 0.1x -> ((Some number smaller than (2N/3)/(0.95E)) < 0.1x But this is exactly our not (A). This now looks fine to me, at least I hope it is correct

Thanks for your tremendous help!!

AjiteshArun · Answer

Hi hadimadi , I'll try to address both your points. I agree, but my main point was that "false positives don't play an important role in the author's argument". We should look at the rest of my reply as an attempt to show that the author doesn't consider false positives to be an issue. This is not my assumption. It's the author's.

The tests either don't generate a significant number of false positives, or don't generate any false positives. To see this, imagine that you're the author, and the total number of prospective donors is 100. You need \left (\frac{2}{3}H\right ) to be "about 10%" of \left (100-d\right ) , where H is the number of prospective donors with NANB Hepatitis, and d is the number of disqualified prospective donors. At the same time, d , which is \left (\frac{1}{3}H+F\right ) , can be 5 at most ( F is the number of false positives). Try to make the numbers work. How large (or how small) can d be and how large (or how small) must F be so that \frac{2}{3}H is close to 10% of \left ( 100-d \right ) ?

hadimadi · Answer

Hi  AjiteshArun ,

we have:

(1)  (1/3)H+F<=5 and H,F, and (1/3)H needs to be a positive integer, and F>=0 
 (2)  (2/3)H/100-((1/3)H-F)=0.1

From (1) -> (H,F)=(3,4), (6,3), (9,2), (12,1), (15,0)
Using this finding for (2): Only (15,0) is valid to yield about 10%.

Now plugging in the numbers, we get that (15,0) is the only solution which yields our result.

However, this is NOT the point I made in my previous comment. What I said is:

The assumption that there are no false positives in  necessary  for the argument, but not the only necessary argument for the statement to hold true.This, however, doesn't mean that the author in his statement made this assumption. He could mistakenly NOT make it. It is nowhere mentioned that he assumed that there are 0 false positives (however, it is necessary).

Now, the other necessary argument is (A). I initially didn't get that (A) is necessary (my first post in this thread), but I laid out in my previous comment that I made a mistake and it indeed is necessary, even if we use false positives.

Please correct me if I am wrong here.

Thanks

AjiteshArun · Answer

My apologies. I focused on addressing the two specific points you raised (the yellow and red portions). I should have addressed your entire post.

That said, it's good to see that you're comfortable with A now. Every question we learn from is a little win that helps us get closer to our target score.

Blood banks will shortly start to screen all donors for NANB hepatitis

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Blood banks will shortly start to screen all donors for NANB hepatitis

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