Percent problem........OG2018

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Mo2men: Legendary Member; Posts: 712; Joined: Fri Sep 25, 2015 4:39 amFollowed by: 5 members; Thanked: 14 times

by Mo2men » Thu Jul 27, 2017 2:02 pm

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%

OA: B

I do not understand how the percent equation should be established? Is it percent of A & B relative to A or relative to the people surveyed?

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Source: Beat The GMAT — Problem Solving | Thu Jul 27, 2017 2:02 pm

GMATGuruNY: GMAT Instructor; Posts: 15539; Joined: Tue May 25, 2010 12:04 pmFollowed by: 1906 members; Location: New York, NY; Thanked: 13060 times; GMAT Score:790

by GMATGuruNY » Thu Jul 27, 2017 2:22 pm

Mo2men wrote: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%

Let the total number of people = 100.
Total with both A and B = 3% of 100 = 3.
Total with A = 45% of 100 = 45.
Implication:
Of the 45 people with A, 3 had both A and B.
Thus:
Of the people with A, the percentage who also had B = (total with both)/(total with A) * 100 = (3/45) * 100 = (1/15)(100) = (1/3)(20) = 6.67.

The correct answer is B.

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by [email protected] » Fri Jul 28, 2017 11:03 am

Hi Mo2men,

This prompt is essentially a scaled-down Overlapping Sets question without all of the typical steps. We have a total (100%), a Group A (those with Type A Blood = 45%) and a Both 'group' (those with Both Type A and Type B = 3%). Rather than plug those values into the Overlapping Sets Formula or Tic-Tac-Toe/Matrix grid, we simply have to consider the ratio of those with Both to those with Type A:

3%/45% = 1/15 = 6 2/3%

Final Answer: B

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Matt@VeritasPrep: GMAT Instructor; Posts: 2630; Joined: Wed Sep 12, 2012 3:32 pmFollowed by: 119 members; Location: East Bay all the way; Thanked: 625 times; GMAT Score:780

by Matt@VeritasPrep » Sun Aug 06, 2017 11:25 pm

We know (A and B) is a subset of A, and we want a ratio, so we can say

(A and B) / A = our ratio

3 / 45 = our ratio

1/15 = our ratio

From here, we want 1/15 = x/100. Multiplying both sides by 100 gives us x = 100/15 = 20/3 = 6 + (2/3) â‰ˆ 6.67%

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Jeff@TargetTestPrep: GMAT Instructor; Posts: 1462; Joined: Thu Apr 09, 2015 9:34 amFollowed by: 22 members; Location: New York, NY; Thanked: 39 times

by Jeff@TargetTestPrep » Wed Aug 09, 2017 12:40 pm

Mo2men wrote: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%

OA: B

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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