In a certain medical survey, 45 percent of the people surveyed had the

Question

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%

A. 1.35%

B. 6.67%

C. 13.50%

D. 15.00%

E. 42.00%

generis · Accepted Answer

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 . . . who also had the type B antigen? " 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.

Bunuel · Answer

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.

Tracy95 · Answer

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.

ScottTargetTestPrep · Answer

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

dyee630k · Answer

Why can't the trick .45 * .03 be used here?

targetbusiness · Answer

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.

Bunuel · Answer

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 .

lakshya14 · Answer

Why it's over 45? Shouldn't it be over the total of 100?

ScottTargetTestPrep · Answer

We are looking for "percent of A" who also had B, so we have 3/45 x 100.

MathRevolution · Answer

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

monwei82 · Answer

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."

jabhatta2 · Answer

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 ?

jabhatta2 · Answer

Hi  avigutman  - q2

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.

avigutman · Answer

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 .

Thib33600 · Answer

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%

aakritibirla11 · Answer

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?

Posted from my mobile device

Bunuel · Answer

_________________
Yes, that's correct.

aakritibirla11 · Answer

Appreciate it. Thank you.

Posted from my mobile device

lavanya.18 · Answer

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

In a certain medical survey, 45 percent of the people surveyed had the

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In a certain medical survey, 45 percent of the people surveyed had the

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