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C
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Difficulty:
35%
(medium)
Question Stats:
81% (02:11) correct
19%
(03:02)
wrong
based on 21
sessions
History
Date
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At the Cesarene Film Festival, three films—a drama, a comedy and a documentary—are shown. The drama is 75 percent longer than each of the other two films. A spectator watches all three films, with two breaks of 20 minutes each between the screenings.
If the spectator’s total viewing time, including the breaks, is 400 minutes, how many minutes does the documentary last ?
A. 84
B. 90
C. 96
D. 120
E. 160
If the spectator’s total viewing time, including the breaks, is 400 minutes, how many minutes does the documentary last ?
A. 84
B. 90
C. 96
D. 120
E. 160
10 Mar 2026, 00:50
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kevincan
Drama is (3/4) longer than each of the other two films.
Drama = 1+ (3/4) * comedy or documentary
Drama = (7/4) comedy or documentary
Drama : comedy : documentary = 7x : 4x : 4x = 15x
We have two breaks of 20 mins = 2*20 = 40 mins.
Total screening time = 15x + 40 = 400 minutes.
15x = 360 minutes.
x = 24 minutes.
Lowest time = 4x = 4*24 = 96 minutes.
Option C
10 Mar 2026, 02:00
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Nice linear equation problem. The key concept being tested is translating "X percent/fraction longer" correctly — a very common source of errors in Problem Solving.
Step 1 — Translate "3/4 longer" into math.
"The drama is 3/4 longer than each of the other two films" means:
Drama = shorter film + (3/4) × shorter film = (1 + 3/4) × shorter film = (7/4) × shorter film
This is NOT the same as drama = (3/4) × shorter film. "3/4 longer" means you ADD 3/4 of the base, giving a multiplier of 7/4.
Step 2 — Set up variables.
Let the comedy = documentary = x minutes (the two shorter films have the same length).
Drama = (7/4)x minutes.
Step 3 — Account for all time.
Total time = drama + comedy + documentary + 2 breaks
400 = (7/4)x + x + x + 2(20)
400 = (7/4)x + 2x + 40
360 = (7/4)x + 2x
360 = (7/4)x + (8/4)x
360 = (15/4)x
x = 360 × (4/15) = 96 minutes
Step 4 — Answer the question asked.
The documentary = x = 96 minutes.
Answer: C (96 minutes)
Common trap: Many students read "3/4 longer" and compute drama = (3/4)x instead of (7/4)x. If you make this mistake, you get (3/4)x + x + x + 40 = 400, which gives x = 128 — not one of the answer choices, which should signal an error in your setup.
A second trap: the question asks for the documentary specifically, but since comedy = documentary = x, this doesn't change the final answer here. Still, always re-read what is being asked before writing down your answer.
Takeaway: Whenever you see "A is [fraction] longer than B," always write A = (1 + fraction) × B, never A = fraction × B.
Step 1 — Translate "3/4 longer" into math.
"The drama is 3/4 longer than each of the other two films" means:
Drama = shorter film + (3/4) × shorter film = (1 + 3/4) × shorter film = (7/4) × shorter film
This is NOT the same as drama = (3/4) × shorter film. "3/4 longer" means you ADD 3/4 of the base, giving a multiplier of 7/4.
Step 2 — Set up variables.
Let the comedy = documentary = x minutes (the two shorter films have the same length).
Drama = (7/4)x minutes.
Step 3 — Account for all time.
Total time = drama + comedy + documentary + 2 breaks
400 = (7/4)x + x + x + 2(20)
400 = (7/4)x + 2x + 40
360 = (7/4)x + 2x
360 = (7/4)x + (8/4)x
360 = (15/4)x
x = 360 × (4/15) = 96 minutes
Step 4 — Answer the question asked.
The documentary = x = 96 minutes.
Answer: C (96 minutes)
Common trap: Many students read "3/4 longer" and compute drama = (3/4)x instead of (7/4)x. If you make this mistake, you get (3/4)x + x + x + 40 = 400, which gives x = 128 — not one of the answer choices, which should signal an error in your setup.
A second trap: the question asks for the documentary specifically, but since comedy = documentary = x, this doesn't change the final answer here. Still, always re-read what is being asked before writing down your answer.
Takeaway: Whenever you see "A is [fraction] longer than B," always write A = (1 + fraction) × B, never A = fraction × B.
