Last visit was: 18 Nov 2025, 19:04 It is currently 18 Nov 2025, 19:04
Home
GMAT
Messages
Tests
Schools
Events
Rewards
Chat
My Profile
Close
GMAT Club Daily Prep
Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track
Your Progress

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History
Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.
Go to My Error Log Learn more
Close
Request Expert Reply
Confirm Cancel
Back to Forum
Create Topic
   1   2 
805+ Level|   Assumption|            
User avatar
hadimadi
User avatar
Joined: 26 Oct 2021
Last visit: 03 Dec 2022
Posts: 114
Own Kudos:
31
Given Kudos: 94
Posts: 114
Kudos: 31
Blood banks will shortly start to screen all donors for NANB hepatitis 14 May 2022, 08:41
Kudos
Add Kudos
Bookmarks
Bookmark this Post
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?
User avatar
josephineestrela
User avatar
Joined: 20 Jan 2022
Last visit: 14 May 2022
Posts: 5
Location: Argentina
Posts: 5
Kudos: 0
Blood banks will shortly start to screen all donors for NANB hepatitis 14 May 2022, 11:33
Kudos
Add Kudos
Bookmarks
Bookmark this Post
What a really difficult question, I thought the answer was A, but it turned out to be wrong. So what is the correct answer in the end?
User avatar
AjiteshArun
User avatar
Major Poster
Joined: 15 Jul 2015
Last visit: 18 Nov 2025
Posts: 5,949
Own Kudos:
5,080
 [3]
Given Kudos: 732
Location: India
GMAT Focus 1: 715 Q83 V90 DI83
GMAT 1: 780 Q50 V51
GRE 1: Q170 V169
Expert
Expert reply
GMAT Focus 1: 715 Q83 V90 DI83
GMAT 1: 780 Q50 V51
GRE 1: Q170 V169
Posts: 5,949
Kudos: 5,080
 [3]
Blood banks will shortly start to screen all donors for NANB hepatitis 14 May 2022, 21:55
3
Kudos
Add Kudos
Bookmarks
Bookmark this Post
hadimadi
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?
Show more
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.
User avatar
KarishmaB
User avatar
Joined: 16 Oct 2010
Last visit: 18 Nov 2025
Posts: 16,265
Own Kudos:
76,982
 [3]
Given Kudos: 482
Location: Pune, India
Expert
Expert reply
Active GMAT Club Expert! Tag them with @ followed by their username for a faster response.
Posts: 16,265
Kudos: 76,982
 [3]
Blood banks will shortly start to screen all donors for NANB hepatitis 14 May 2022, 23:07
3
Kudos
Add Kudos
Bookmarks
Bookmark this Post
hadimadi
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?
Show more

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.
User avatar
hadimadi
User avatar
Joined: 26 Oct 2021
Last visit: 03 Dec 2022
Posts: 114
Own Kudos:
31
Given Kudos: 94
Posts: 114
Kudos: 31
Blood banks will shortly start to screen all donors for NANB hepatitis 15 May 2022, 04:54
Kudos
Add Kudos
Bookmarks
Bookmark this Post
AjiteshArun
hadimadi
AjiteshArun, KarishmaB

Hi AjiteshArun,

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?
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.
Show more

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 :D

Thanks for your tremendous help!!
User avatar
AjiteshArun
User avatar
Major Poster
Joined: 15 Jul 2015
Last visit: 18 Nov 2025
Posts: 5,949
Own Kudos:
5,080
 [2]
Given Kudos: 732
Location: India
GMAT Focus 1: 715 Q83 V90 DI83
GMAT 1: 780 Q50 V51
GRE 1: Q170 V169
Expert
Expert reply
GMAT Focus 1: 715 Q83 V90 DI83
GMAT 1: 780 Q50 V51
GRE 1: Q170 V169
Posts: 5,949
Kudos: 5,080
 [2]
Blood banks will shortly start to screen all donors for NANB hepatitis 15 May 2022, 17:00
2
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Hi hadimadi,

I'll try to address both your points.

hadimadi
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
Show more
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.

hadimadi
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'
Show more
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 \(\left ( 100-d \right )\)?
User avatar
hadimadi
User avatar
Joined: 26 Oct 2021
Last visit: 03 Dec 2022
Posts: 114
Own Kudos:
31
 [1]
Given Kudos: 94
Posts: 114
Kudos: 31
 [1]
Blood banks will shortly start to screen all donors for NANB hepatitis 16 May 2022, 06:11
1
Kudos
Add Kudos
Bookmarks
Bookmark this Post
AjiteshArun
Hi hadimadi,

I'll try to address both your points.

hadimadi
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
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.

hadimadi
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'
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 \(\left ( 100-d \right )\)?
Show more

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
User avatar
AjiteshArun
User avatar
Major Poster
Joined: 15 Jul 2015
Last visit: 18 Nov 2025
Posts: 5,949
Own Kudos:
5,080
 [1]
Given Kudos: 732
Location: India
GMAT Focus 1: 715 Q83 V90 DI83
GMAT 1: 780 Q50 V51
GRE 1: Q170 V169
Expert
Expert reply
GMAT Focus 1: 715 Q83 V90 DI83
GMAT 1: 780 Q50 V51
GRE 1: Q170 V169
Posts: 5,949
Kudos: 5,080
 [1]
Blood banks will shortly start to screen all donors for NANB hepatitis 16 May 2022, 19:07
1
Kudos
Add Kudos
Bookmarks
Bookmark this Post
hadimadi
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.
Show more
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.
User avatar
hadimadi
User avatar
Joined: 26 Oct 2021
Last visit: 03 Dec 2022
Posts: 114
Own Kudos:
31
 [1]
Given Kudos: 94
Posts: 114
Kudos: 31
 [1]
Blood banks will shortly start to screen all donors for NANB hepatitis 17 May 2022, 00:26
1
Kudos
Add Kudos
Bookmarks
Bookmark this Post
AjiteshArun
hadimadi
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.
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.
Show more

Hi AjiteshArun,

thanks for your help, you always put a lot of time and effort to explain things clearly and in detail, and I really appreciate it.
Your explanations made me understand CR questions in general much better.

Huge thanks for your help
User avatar
stackskillz
User avatar
Joined: 28 Feb 2022
Last visit: 11 Jul 2025
Posts: 62
Own Kudos:
13
Given Kudos: 165
Posts: 62
Kudos: 13
Blood banks will shortly start to screen all donors for NANB hepatitis 14 Apr 2024, 11:46
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Conc: Therefore, about 10 percent of actual donors will still supply NANB-contaminated blood.
Did 10% of actual donors not get filtered or still supply contaminated blood?

(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, it does support the conclusion that blood donors who don't get filtered out end up passing on the infection. Let's negate to check -"Most donors with hepatitis carry other infections that are reliably screened and routinely checked." If that's the case then, the number of donors supplying contaminated blood will be much less than 10%, i.e. ,weakens the conclusion on negation. Keep

(B) Donors carrying NANB hepatitis do not, in a large percentage of cases, develop the disease themselves at any point. Whether the donors develop the disease themselves or is transferred to them by someone, doesn't give us the indication on the % of actual donors with the infection not getting filtered out. Drop

(C) The estimate of the number of donors who would be disqualified by tests for NANB hepatitis is an underestimate. - Premises can't be challenged. Even if they can, this does undermine the conclusion, hence not a required assumption. Drop

(D) The incidence of NANB hepatitis is lower among the potential blood donors than it is in the population at large. The population at large could've 15%, 20% or even higher incidence of hepatitis, however, that doesn't help us solve for the % of infected patients not filtered out. Drop

(E) The donors who will still supply NANB-contaminated blood will donate blood at the average frequency for all donors. Frequency of supply doesn't matter. Conclusion is focused on the number of patients who don't get filtered out. Drop­
User avatar
VerbalBot
User avatar
Non-Human User
Joined: 01 Oct 2013
Last visit: 04 Jan 2021
Posts: 18,836
Own Kudos:
986
Posts: 18,836
Kudos: 986
Blood banks will shortly start to screen all donors for NANB hepatitis 23 Apr 2025, 09:56
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Hello from the GMAT Club VerbalBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
   1   2 
Moderators:
GMATNinja
GMAT Club Verbal Expert
7445 posts
GMATNinjaTwo
GMAT Club Verbal Expert
234 posts
miag
188 posts