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This year, \(x\) people won an Olympic medal for water

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by BTGmoderatorLU » Sat Jun 29, 2019 6:13 am

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Source: 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. \(\frac{11x}{12}\)

B. \(\frac{7x}{12}\)

C. \(\frac{5x}{12}\)

D. \(\frac{6x}{7}\)

E. \(\frac{x}{7}\)

The OA is A
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Source: — Problem Solving |

by Scott@TargetTestPrep » Sat Jul 06, 2019 4:59 pm
BTGmoderatorLU wrote:Source: 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. \(\frac{11x}{12}\)

B. \(\frac{7x}{12}\)

C. \(\frac{5x}{12}\)

D. \(\frac{6x}{7}\)

E. \(\frac{x}{7}\)

The OA is A
We see that ⅓(¼x) = (1/12)x = x/12 people won a medal in both swimming and diving.

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

Answer: A

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