GMAT 141

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ironsheep

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This question is from "GMAT Official Guide 2019 Quantitative Review". The question reads "In a certain medical survey, 45 percent of the people surveyed had the type A antigen in their blood and 3 percent had both the Type A antigen and the type B antigen. Which of the following is closest to the percent of those with the type A antigen who also had the type B antigen?" the answer is 6.67%

For me, I say it is 1.35% or it could be 3%. If you do 45 percent (.45) times 3 percent(.03) and that gets you .0135 or 1.35 percent. Or if you look at it this way, if there are 100 people in the survey, 45 have A and 3 people have A and B. If I had to choose between the two, I would go with 1.35%(maybe the book is wrong)

Is it okay if I post one question a day on this website? What are the rules?
 
suppose there are \(\displaystyle N\) people in the survey.

\(\displaystyle \text{$0.45 N$ have the A antigen. $0.03N$ have the A and B antigens.}\)

\(\displaystyle \text{The percent of those with the A antigen that also have the B antigen is $p = \dfrac{0.03N}{0.45N} = \dfrac{0.03}{0.45} = 0.6\bar{6} \approx 6.67\%$}\)
 
Also, why is the three on top of the 45? Also, is it okay for me to post one question a day on this forum??
 
Last edited:
I'm not in a position to say how often you can post.

In general how do you compute what percentage say x is of y?

You divide x by y and multiply by 100. Right? To find out what percent say 3 is of 15

you find (3/15)*100% = 20%

In this problem they want to know what percent of people with antigen A also have antigen B

As above this is (#with antigen A and B)/(# with antigen A) * 100% and we plug the appropriate numbers in.
 
ironsheep said:
Also, is it okay for me to post one question a day on this forum??
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There is no strict limit on how often you can post. As long as you show effort as you did in this thread, and post just one question per thread (a question may contain multiple parts), you'll be fine. :)
 
ironsheep said:
This question is from "GMAT Official Guide 2019 Quantitative Review". The question reads "In a certain medical survey, 45 percent of the people surveyed had the type A antigen in their blood and 3 percent had both the Type A antigen and the type B antigen. Which of the following is closest to the percent of those with the type A antigen who also had the type B antigen?" the answer is 6.67%

For me, I say it is 1.35% or it could be 3%. If you do 45 percent (.45) times 3 percent(.03) and that gets you .0135 or 1.35 percent. Or if you look at it this way, if there are 100 people in the survey, 45 have A and 3 people have A and B. If I had to choose between the two, I would go with 1.35%(maybe the book is wrong)
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What you did first (1.35%) would be appropriate if it said that 3% of those with type A also had type B. It doesn't say that, though I can see why you might briefly take it that way. (If they had intended that, they would not have said "had both the Type A and the Type B".)

Your second interpretation (apparently taking the two numbers as mutually exclusive) would be appropriate if it said that 45% had only the type A. Again, I can see why you might take it that way, based on everyday imprecise usage of words. In math, you have to read things literally, and be aware that we would say "only" if we meant it! Generally statements in math are inclusive ("had type A, and possibly others").

The correct interpretation is that, out of 100 people, 3 of the 45 with type A also have type B, and "3 of 45" translates to 3/45 = 0.06666... = 6.666...% .
 
Romsek's edited post said:
\(\displaystyle \dfrac{0.03}{0.45} = 0.6\bar{6} \approx 6.67\) %
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.

Alert to lookagain said:
Your post in the thread GMAT 141 was deleted. Reason: Thanks for noting a typo. It's been fixed.
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No, there was not "a" typo. There were two errors, so it was not finished being fixed after I posted.
A moderator didn't edit that decimal as I had had it. That is why I made this follow-up post.

This, or the equivalent to this, is the correction:


\(\displaystyle \dfrac{0.03}{0.45} = 0.0 6\bar{6} \approx 6.67\) %




Note: \(\displaystyle \ \ \ 0.6\bar{6} \ = \ 2/3, \ \ not \ \ 3/45 \ = \ 1/15 \).
 
lookagain said:
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No, there was not "a" typo. There were two errors, so it was not finished being fixed after I posted.
A moderator didn't edit that decimal as I had had it. That is why I made this follow-up post.

This, or the equivalent to this, is the correction:


\(\displaystyle \dfrac{0.03}{0.45} = 0.0 6\bar{6} \approx 6.67\) %




Note: \(\displaystyle \ \ \ 0.6\bar{6} \ = \ 2/3, \ \ not \ \ 3/45 \ = \ 1/15 \).
Click to expand...

You are correct. My abject apologies. Will ritual disembowelment be suitable?
 
Dr.Peterson said:
What you did first (1.35%) would be appropriate if it said that 3% of those with type A also had type B. It doesn't say that, though I can see why you might briefly take it that way. (If they had intended that, they would not have said "had both the Type A and the Type B".)

Your second interpretation (apparently taking the two numbers as mutually exclusive) would be appropriate if it said that 45% had only the type A. Again, I can see why you might take it that way, based on everyday imprecise usage of words. In math, you have to read things literally, and be aware that we would say "only" if we meant it! Generally statements in math are inclusive ("had type A, and possibly others").

The correct interpretation is that, out of 100 people, 3 of the 45 with type A also have type B, and "3 of 45" translates to 3/45 = 0.06666... = 6.666...% .
Click to expand...


I still feel confused by the wording of this problem. To me, it would seem that 52 percent has only type B, 3% of those surveyed has B and A, while 45% has only A. 52+3+48 equals 100%. Today is a different day, but now when I read it, it seems that they are Mutually exclusive, but yesterday I was thinking 3% of the 45%.


Not only that, but solving this problem is even more weird because you do (3/45) equals (x/100) and you cross multiply and then you end up with x equaling 6.666 or 6.67%, but this is strange. This implies that 45 is the 100 percent and you are trying to find 3% of 45. 45 is a percent of some unknown number not given. 45 is not a number.
 
In part, you just have to learn how to read technical writing, which does take some exposure. This could have been written better, but to me, with experience, it is reasonably clear that the 45% is not "only type A", but includes the 3%.

I don't see that it says anything at all about how many have type B; where do you get your 52%? (Are you assuming that everyone has at least one? Never assume anything you aren't told!)

Yes, it is asking for "the percent of those with the type A antigen", so the 45% with type A are the "whole" and the 3% with both are the "part".

If you don't like thinking of a percent of a percent, just think of a case with 100 people in all, of whom 45 have type A and 3 have both.
 
Dr.Peterson said:
In part, you just have to learn how to read technical writing, which does take some exposure. This could have been written better, but to me, with experience, it is reasonably clear that the 45% is not "only type A", but includes the 3%.

I don't see that it says anything at all about how many have type B; where do you get your 52%? (Are you assuming that everyone has at least one? Never assume anything you aren't told!)

Yes, it is asking for "the percent of those with the type A antigen", so the 45% with type A are the "whole" and the 3% with both are the "part".

If you don't like thinking of a percent of a percent, just think of a case with 100 people in all, of whom 45 have type A and 3 have both.
Click to expand...


If I do that, "If you don't like thinking of a percent of a percent, just think of a case with 100 people in all, of whom 45 have type A and 3 have both" then that means that it is mutually exclusive and the answer is 3 percent.
 
ironsheep said:
If I do that, "If you don't like thinking of a percent of a percent, just think of a case with 100 people in all, of whom 45 have type A and 3 have both" then that means that it is mutually exclusive and the answer is 3 percent.
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Why does that imply mutually exclusive? Doesn't "have both" mean they are included among the 45 who have type A??

And why would the answer be 3% then? If they had said, "45 percent of the people surveyed had ONLY the type A antigen in their blood and 3 percent had both the Type A antigen and the type B antigen", as I think you are taking it, then 48% would have type A, and 3/48 = 6.25% of those with type A would also have type B.

The important interpretation issue here is that you must learn to read literally. If it says someone has type A, it means only that, and not that they don't also have type B. We get used to everyday language in which, if someone had both, you would say so; that sort of inference is not valid in careful technical writing.
 
Dr.Peterson said:
Why does that imply mutually exclusive? Doesn't "have both" mean they are included among the 45 who have type A??

And why would the answer be 3% then? If they had said, "45 percent of the people surveyed had ONLY the type A antigen in their blood and 3 percent had both the Type A antigen and the type B antigen", as I think you are taking it, then 48% would have type A, and 3/48 = 6.25% of those with type A would also have type B.

The important interpretation issue here is that you must learn to read literally. If it says someone has type A, it means only that, and not that they don't also have type B. We get used to everyday language in which, if someone had both, you would say so; that sort of inference is not valid in careful technical writing.
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Other than doing a lot of GMAT problems, is there any other way to learn how to read literally. Any books you can recommend?
 
I still don't understand how to read this problem though--- can someone translate it and each part? So a survey was done and 45 percent of people surveyed has A in their blood. In that survey also, 3 percent had A and B, which percent of people in the survey has A and B. Why is 3% on top of the 45% in dividing??
 
I figured it out and it is from looking at, "Which of the following is closest to the percent of those with the type A antigen who also had the type B antigen?" (Don't look at the first half of the word problem). This little sentence that changes it all says that 45% of people have A in their blood, but of those same people(45%), 3 percent have A and B. This is why I did .03 times .45 yesterday. What would 3% of 45% be?? .03/.45 equals (x/100). Cross mulitply and you get 6.67%. 3% is 6.67% of 45%
 
This is a VERY badly worded problem. The information given about the percentage with both A and B does not specify whether it is 3% of those surveyed or 3% of those with A. The question as well does not specify what is the base against which the percentage is to be calculated. A percentage is always a percentage of some base, and, to avoid ambiguity, that base should be specified.

Once we are given the answer deemed correct, we can work backwards to what was intended, namely that those with type A and B are 3% of those surveyed and that the question aims at eliciting those with A and B as a percentage of those with A. But the suffering student does not enjoy our advantage of being able to interpret the ambiguous language in light of the answer deemed correct.
 
ironsheep said:
I figured it out and it is from looking at, "Which of the following is closest to the percent of those with the type A antigen who also had the type B antigen?" (Don't look at the first half of the word problem). This little sentence that changes it all says that 45% of people have A in their blood, but of those same people(45%), 3 percent have A and B. This is why I did .03 times .45 yesterday. What would 3% of 45% be?? .03/.45 equals (x/100). Cross mulitply and you get 6.67%. 3% is 6.67% of 45%
Click to expand...
I see your problem there. "3% of 45%" would be the multiplication you did; what you mean is "What percent of 45 is 3?" It's true that the numbers being percentages makes it easy to think wrongly; wording your own question ambiguously makes things worse.

As for the wording overall, I've said that it "could have been written better", but the reality is that you find a lot of less-than-clearly-written material in the real world, and with experience, you can get used to seeing the more subtle hints to the intended meaning. This is not a good one to be learning from, but it is something you'll have to be able to handle eventually. Whether it belongs on a test is another question. (Maybe they do better on the actual test, and want to get you thinking in your review.)

How to learn this? I doubt that any books focus on it at all; this is one of those things that authors don't even realize is a problem, because they have long ago mastered the language of their field. But thinking about wording (as we've been doing here) is a good habit to get into on your own.
 
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