Buttercup3 wrote:

At a dinner party, 40% of the guests wore both jackets and ties. If 50% of the guests who wore jackets did not wear ties, what percent of the guests wore jackets?

A. 20%

B. 40%

C. 60%

D. 70%

E. 80%

Assign a number for total guestsLet there be 20 people at this dinner party.

40%, or

8 people,

wore BOTH jacket and tie

50%

of the guests who wore jackets did not wear ties

Put those two statements together. The logic is binary:

A person wore a jacket WITH a tie or

A person wore a jacket WITHOUT a tie

40% of ALL the partygoers wore a jacket WITH a tie.

That number = 8

If 50% wore a jacket WITHOUT a tie, then

the 8 who wore a jacket WITH a tie

were

the other 50% of all jacket-wearers.

8 = 50% of all jacket-wearers

8 = \(\frac{1}{2}\) of all jacket-wearers

16 = the number of all jacket-wearers16 people wore jackets (8 with and 8 without a tie)

What percent of the guests

wore jackets?

Total jacket wearers: 16

Total guests: 20

\((\frac{16}{20} * 100) = (.80 * 100)\) = 80 %

Answer E

PercentsAlternatively, 40% of ALL guests wore a jacket WITH a tie,

whereas

50% of ALL WHO WORE JACKETS

wore a jacket WITHOUT a tie

The 40% category (jacket-wearers WITH ties)

constitutes the other 50% of all jacket-wearers

40% of ALL guests wore jackets WITH ties and

40% of ALL guests wore jackets WITHOUT ties

(40% + 40%) = 80% of all guests wore jackets

Answer E

_________________

The only thing more dangerous than ignorance is arrogance.

-- Albert Einstein