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# At a college football game, 4/5 of the seats in the lower deck of the

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At a college football game, 4/5 of the seats in the lower deck of the  [#permalink]

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18 Jun 2017, 11:02
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35% (medium)

Question Stats:

81% (01:55) correct 19% (01:56) wrong based on 118 sessions

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At a college football game, 4/5 of the seats in the lower deck of the stadium were sold. If 1/4 of all the seating in the stadium is located in the lower deck, and if 2/3 of all the seats in the stadium were sold, what fraction of the unsold seats in the stadium were in the lower deck?

(A) 3/20
(B) 1/6
(C) 1/5
(D) 1/3
(E) 7/15

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At a college football game, 4/5 of the seats in the lower deck of the  [#permalink]

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18 Jun 2017, 11:11
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Bunuel wrote:
At a college football game, 4/5 of the seats in the lower deck of the stadium were sold. If 1/4 of all the seating in the stadium is located in the lower deck, and if 2/3 of all the seats in the stadium were sold, what fraction of the unsold seats in the stadium were in the lower deck?

(A) 3/20
(B) 1/6
(C) 1/5
(D) 1/3
(E) 7/15

Let total number of seats be = 120

1/4 of seating in stadium is located in the lower deck $$= \frac{1}{4} * 120 = 30$$

4/5 of the seats in the lower deck of stadium were sold $$= \frac{4}{5} * 30 = 24$$

Number of seats in the lower deck not sold $$= 30 - 24 = 6$$

2/3 of all the seats in the stadium were sold $$= \frac{2}{3} * 120 = 80$$

Number of seats in the stadium not sold $$= 120 - 80 = 40$$

Required fraction $$= \frac{6}{40} = \frac{3}{20}.$$ Answer (A)...
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Re: At a college football game, 4/5 of the seats in the lower deck of the  [#permalink]

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18 Jun 2017, 11:15
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let the total no. of seats be 60(lcm of 3,4 and 5 i.e denominator of all the fractions)
total no. of seats sold= 2/3 of 60=40
no of unsold seats=60-40=20
no.of seats in lower deck=1/4 of 60=15
seats sold in lower deck=4/5 of 15=12
unsold seats in lower deck=3
hence fraction of no of unsold seats in lower deck and total unsold seats =3/20
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Re: At a college football game, 4/5 of the seats in the lower deck of the  [#permalink]

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18 Jun 2017, 11:22
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I will take a dig at it.

4/5 seats in LD are sold. That implies 1/5 are not sold (1-4/5)

Now 1/4 of the total seats of the stadium comes from Lower deck.
Hence fraction of unsold seats coming from Lower deck is 1/4*1/5 = 1/20

we also know that a total of 1/3 seats are unsold. (2/3-1) *given in the question.

Therefore, the fraction of unsold seats coming from from Lower deck to total number of unsold seats is :
(1/20)/(1/3) i.e 3/20

For me answer is A. Waiting for the OA
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Re: At a college football game, 4/5 of the seats in the lower deck of the  [#permalink]

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18 Jun 2017, 11:24
Bunuel wrote:
At a college football game, 4/5 of the seats in the lower deck of the stadium were sold. If 1/4 of all the seating in the stadium is located in the lower deck, and if 2/3 of all the seats in the stadium were sold, what fraction of the unsold seats in the stadium were in the lower deck?

(A) 3/20
(B) 1/6
(C) 1/5
(D) 1/3
(E) 7/15

LCM ( 5 , 4 & 3 ) = 60

Lower Deck Seats is $$60*\frac{1}{4}$$ = $$15$$
Lower Deck Sold Seats is $$15*\frac{4}{5}$$ = $$12$$ , Unsold Lower Deck Sold Seats is $$3$$

Total Sold Seats is $$60*\frac{2}{3}$$ = $$40$$ , So Unsold Seats is $$20$$

Fraction of the unsold seats in the stadium were in the lower deck is $$\frac{3}{20}$$

Answer will definitely be (A) $$\frac{3}{20}$$
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Re: At a college football game, 4/5 of the seats in the lower deck of the  [#permalink]

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18 Jun 2017, 11:30
let total seats in the stadium be 60(LCM of 4,3,and 5). Now two-third of the total seats i.e. 40 are sold and hence total unsold seats are 20. Also one-fourth of the total no. of seats are in the lower deck, 15 seats, and 4/5 of the lower deck seats are sold and hence 1/5 seats at lower deck remain unsold, i.e. 3 seats. So fraction of unsold seats in the lower deck is 3/20 - -->> option A
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Re: At a college football game, 4/5 of the seats in the lower deck of the  [#permalink]

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19 Jun 2017, 08:11
We know that 1/4 seats are in the lower deck, and 2/3 of the total stadium seats are sold.
4/5 of the lower deck seats are sold, which means that (4/5)*(1/4) = 1/5 of the total seats are both sold and in the lower deck.
The number of decks in the lower deck that are unsold are 1/20 of the total seats ((1/4)-(1/5)).
Divide this by the total fraction of unsold tickets (1/3) gives 3/20.

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Re: At a college football game, 4/5 of the seats in the lower deck of the  [#permalink]

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22 Jun 2017, 07:16
LOWER DECK 4/5 SOLD ----> 1/5 UNSOLD
1/4(TOT) ---> LOWER DECK

SO... (1/5)(1/4)(TOT) ---> 1/20X UNSOLD IN THE LOWER DECK

2/3(TOT) SOLD ----> 1/3(TOT) UNSOLD

SO IN THE END i need LOWERDECK UNSOLD / TOT UNSOLD that is:

1/20(TOT) / 1/3(TOT) ---> 3/20
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Re: At a college football game, 4/5 of the seats in the lower deck of the  [#permalink]

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21 Aug 2018, 09:18
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