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This year, x people won an Olympic medal for water

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This year, x people won an Olympic medal for water

by AAPL » Thu Jan 10, 2019 4:41 am

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This year, x people won an Olympic medal for water competitions. One-third of the winners earned a medal for swimming and one-fourth of those who earned a medal for swimming also earned a medal for diving. How many people won an Olympic medal for water competitions but did not both receive a medal for swimming and a medal for diving?

A. 11x/12
B. 7x/12
C. 5x/12
D. 6x/7
E. x/7

OA A
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by fskilnik@GMATH » Thu Jan 10, 2019 9:23 am
AAPL wrote:Veritas Prep

This year, x people won an Olympic medal for water competitions. One-third of the winners earned a medal for swimming and one-fourth of those who earned a medal for swimming also earned a medal for diving. How many people won an Olympic medal for water competitions but did not both receive a medal for swimming and a medal for diving?

A. 11x/12
B. 7x/12
C. 5x/12
D. 6x/7
E. x/7
$$x\,\,\left( {{\rm{water}}} \right)\,\,\left\{ \matrix{
\,{x \over 3}\,\,\left( {{\rm{swim}}} \right)\,\,\, \to \,\,\,\left\{ \matrix{
\,{1 \over 4}\left( {{x \over 3}} \right)\,\,\left( {{\rm{swim}}\,\,{\rm{\& }}\,\,{\rm{dive}}} \right) \hfill \cr
\,{3 \over 4}\left( {{x \over 3}} \right)\,\,\left( {{\rm{swim}}\,\,{\rm{\& }}\,\,{\rm{not}}\,\,{\rm{dive}}} \right) \hfill \cr} \right. \hfill \cr
\,{{2x} \over 3}\,\,\left( {{\rm{not}}\,\,{\rm{swim}}} \right) \hfill \cr} \right.$$
$$? = \left( {{\rm{water}}} \right) - \left( {{\rm{swim}}\,\,{\rm{\& }}\,\,{\rm{dive}}} \right) = x - {1 \over 4}\left( {{x \over 3}} \right) = {{11} \over {12}}x$$

This solution follows the notations and rationale taught in the GMATH method.

Regards,
Fabio.
Fabio Skilnik :: GMATH method creator ( Math for the GMAT)
English-speakers :: https://www.gmath.net
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by GMATGuruNY » Thu Jan 10, 2019 9:53 am
AAPL wrote:Veritas Prep

This year, x people won an Olympic medal for water competitions. One-third of the winners earned a medal for swimming and one-fourth of those who earned a medal for swimming also earned a medal for diving. How many people won an Olympic medal for water competitions but did not both receive a medal for swimming and a medal for diving?

A. 11x/12
B. 7x/12
C. 5x/12
D. 6x/7
E. x/7
Let x = the product of the two denominators in the prompt = 3*4 = 12.
Since 1/3 won a medal for swimming, the number who won a medal for swimming = (1/3)(12) = 4.
Since 1/4 of the medal winners for swimming also won a medal for diving, the number who won both a medal for swimming and a medal for diving = (1/4)(4) = 1.

How many people won an Olympic medal for water competitions but did not both receive a medal for swimming and a medal for diving?
Since only 1 winner received both a medal for swimming and a medal for diving, the remaining 11 did not.
The correct answer must yield a value of 11 when x=12.
Only A works:
(11/12)x = (11/12)(12) = 11.

The correct answer is A.
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by [email protected] » Thu Jan 10, 2019 11:27 am
Hi All,

This question can be solved by TESTing VALUES (and taking a few notes).

We're told that X people won a medal for water competitions. Of those X people, 1/3 won a medal for swimming; of those who won a medal for SWIMMING, 1/4 also won a medal for diving.

The common denominator between 1/3 and 1/4 is 12, so let's TEST X = 12....

X = 12 medal winners

(1/3)(12) = 4 won a medal for swimming
(1/4)(4) = 1 of the swimming winners ALSO won a medal for diving

We're asked how many of the X people did NOT win a medal for BOTH swimming and diving.

Since there were 12 people, and only 1 won BOTH medals, the other 11 won JUST ONE medal - thus, the answer to the question is 11 (when X = 12). The answers are written in such a way that you don't have to do much math to find the correct answer.

Final Answer: A

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by Scott@TargetTestPrep » Mon Jan 21, 2019 5:41 pm
AAPL wrote:Veritas Prep

This year, x people won an Olympic medal for water competitions. One-third of the winners earned a medal for swimming and one-fourth of those who earned a medal for swimming also earned a medal for diving. How many people won an Olympic medal for water competitions but did not both receive a medal for swimming and a medal for diving?

A. 11x/12
B. 7x/12
C. 5x/12
D. 6x/7
E. x/7
We see that ⅓(¼x) = (1/12)x = x/12 people won a medal in both swimming and dividing.

Thus x - x/12 = 12x/12 - x/12 = 11x/12 people did not win a medal in both swimming and dividing.

Answer: A

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