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Difficulty:
35%
(medium)
Question Stats:
73% (01:49) correct
27%
(02:00)
wrong
based on 5154
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History
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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?
A. 1.35%
B. 6.67%
C. 13.50%
D. 15.00%
E. 42.00%
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A. 1.35%
B. 6.67%
C. 13.50%
D. 15.00%
E. 42.00%
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Quote:
dyee630k
dyee630k - The key phrasing is not easy to translate.
If you had a Venn diagram, with a circle for A only, a circle for B only, and overlap of A and B, the question asks what percentage of circle "A only" the overlap "A and B" is.
Let's say 100 people, so
45 = A only
3 = A and B
"the percent of those with the type A antigen [45] . . . who also had the type B antigen? [3]" IS WHAT?
Or, "What percent of 45 is 3?"
Or, "3 is what percent of 45?"
The percentage is the variable: (\(\frac{x}{100}\))(45) = 3
\(\frac{x}{100}\) = \(\frac{3}{45}\)
45x = 300
x = 6.67
Hope it helps.
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carcass
Type A = 45
Type A and B = 3.
The percent of those with the type A antigen who also had the type B antigen \(= \frac{(Type \ A \ and \ B)}{(Type \ A)}*100 = \frac{3}{45}*100 = \frac{20}{3} \approx 6.67%\).
Answer: B.
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I couldn't solve it because I failed to grasp the question.
I just couldn't think of what on earth "the percent of those with the type A antigen who also had the type B antigen" means. Poor me!
If it read "what percent of those with the type A antigen is those with both type A and B antigen, it would have been a better prospect for me.
Maybe that's the GMAT's way.
I just couldn't think of what on earth "the percent of those with the type A antigen who also had the type B antigen" means. Poor me!
If it read "what percent of those with the type A antigen is those with both type A and B antigen, it would have been a better prospect for me.
Maybe that's the GMAT's way.
General Discussion
ScottTargetTestPrep
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carcass
We can let the total people = 100. Since 45 percent of them had the type A antigen, we know that 45 of the people had the type A antigen. We also know that 3 percent had both the A and B antigen in their blood. Thus, of the 45 people who had the type A antigen, 3 of them also had the type B antigen. Thus, the percentage is 3/45 x 100% = 6.67%.
Answer: B
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Why can't the trick .45 * .03 be used here?
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Bunuel
Bunuel, Why are we dividing 3 by 45 to find answer? Is the question not asking us to find 3% of 45% and then that represents how much of total as a percent?
Moreover, I am confused whether the question says 3% of 45% or 3% of total?
Do not mean to trouble you.
siddreal
Say there are 100 people.
45 out of 100 had the type A antigen;
3 out of 100 had both the type A antigen and the type B antigen.
The question asks: what percent of those who had the type A antigen (45) also had the type B antigen (3)? So, what percent of those who had the type A antigen (45) had both (3). Basically we should find what percent is 3 of 45: \(\frac{3}{45}*100\).
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ScottTargetTestPrep
Why it's over 45? Shouldn't it be over the total of 100?
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lakshya14
We are looking for "percent of A" who also had B, so we have 3/45 x 100.
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Type A antigen: 45%
Type A and B: 3%
Percent of those with the type A antigen who also had the type B antigen (Transforming into the equation)
=> Percent of (Type A) = also had the type B
=> Let it be x% of TYPE A who had both A and B.
=> \(\frac{x }{ 100}\) * 45 = 3
=> x = \(\frac{300}{45}\)
=> x = 6.67%
Answer B
Type A and B: 3%
Percent of those with the type A antigen who also had the type B antigen (Transforming into the equation)
=> Percent of (Type A) = also had the type B
=> Let it be x% of TYPE A who had both A and B.
=> \(\frac{x }{ 100}\) * 45 = 3
=> x = \(\frac{300}{45}\)
=> x = 6.67%
Answer B
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If anyone actually communicated this way in real life, they should be fired. This is the most poorly written question I have ever come across while studying for the GMAT - simply poor use of the English language. It's as if the writer said, "I'm tired of writing. I'm just going to create an equation, then word it in a manner that is convoluted and can be broadly interpreted, and let others justify how I communicated it."
Hi avigutman - Two followups when reviewing the question : Which is closest to the percent of those with the type A antigen who also had the type B antigen?
Isn't there a partition missing ?
If i want to ask about 3 % of A specifically -- looking at other official overlapping set problems here and here -- The verbiage with transposed data for 3 % of A specifically should be
There is a clear partition seperating the denominator (which comes first) + partition + numerator
Is "HAD" perhaps the partition ?
Isn't there a partition missing ?
If i want to ask about 3 % of A specifically -- looking at other official overlapping set problems here and here -- The verbiage with transposed data for 3 % of A specifically should be
Quote:
There is a clear partition seperating the denominator (which comes first) + partition + numerator
Is "HAD" perhaps the partition ?
Hi avigutman - q2
If "HAD" is perhaps the partition , that takes care of the denominator but the numerator still can have 2 interpretations intereprations
Why do you think interpretation # 2 is not an accurate way of thinking about the original sentence.
If "HAD" is perhaps the partition , that takes care of the denominator but the numerator still can have 2 interpretations intereprations
- [interpretation # 1] (A and B) / A
or
[interpretation # 2] (A or B) / A
Why do you think interpretation # 2 is not an accurate way of thinking about the original sentence.
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Expert reply
jabhatta2
Quote:
Every fraction or percent or rate or ratio has a top and a bottom (a numerator and a denominator).
I color coded the parts of the text in the hopes that this will remove all doubts.
I invite others to color code the parts of the text in ways that would lead to different meanings - I cannot think of any other way in which to color code them.
jabhatta2 interpretation # 2 is not accurate because of the word also in the original text. To your first question: the partition is who.
carcass
For people struggling with calculation, let me help you.
you do not need ot find the excat number to get the answer right.
here we go: rephrase the question (which for me is the hardest step of the question).
"3 is what percent of 45"
10% of 45 is 4.5; 5% of 45 is 2.25.
therefore, 3 is between 10% and 5% +> the only answer possible is 6.67%
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Bunuel
While I have understood how this question was solved, can I ask someone to confirm if this essentially means:
Only A = 42
A + B = 3
Total A = 45
Would this be the correct break-up of the data?
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aakritibirla11
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Yes, that's correct.
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Appreciate it. Thank you.
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It took some time to understand the last line of the question, but got the right answer in the end
3/45*100=6.67% ie. B
3/45*100=6.67% ie. B
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