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15 Sep 2019, 21:14
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D
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
55%
(hard)
Question Stats:
70% (02:17) correct
30%
(02:36)
wrong
based on 367
sessions
History
Date
Time
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Not Attempted Yet
Zen and Noah decided to read a novel. When Noah started reading the novel, Zen had finished 60 pages. After 30 minutes, Noah overtakes Zen and both continue to read at their own speeds. How many pages will Noah be ahead of Zen, 50 minutes after Noah and Zen reading the same page?
(A) 40
(B) 60
(C) 80
(D) 100
(E) 120
15 Sep 2019, 23:49
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let Zen reading speed be = x pages/min
Noah reading speed be = y pages/min
--initially, Zen had already read 60 pages when Noah started
after 30 min Noah overtakes Zen
--pages read by Zen in 30 min = 60+30x
--pages read by Noah in 30 min = 30y
60+30x = 30y
y-x = 2
pages read by Noah and Zen 50 minutes after Noah and Zen reading the same page
-Noah = 50y
-Zen = 50x
pages Noah will be ahead of Zen = 50(y-x) = 50*2 = 100
D is the correct answer
Noah reading speed be = y pages/min
--initially, Zen had already read 60 pages when Noah started
after 30 min Noah overtakes Zen
--pages read by Zen in 30 min = 60+30x
--pages read by Noah in 30 min = 30y
60+30x = 30y
y-x = 2
pages read by Noah and Zen 50 minutes after Noah and Zen reading the same page
-Noah = 50y
-Zen = 50x
pages Noah will be ahead of Zen = 50(y-x) = 50*2 = 100
D is the correct answer
15 Sep 2019, 21:43
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AFTER 30 MINUTES,
1) Zen finished reading another \(k\) pages. Zen's reading speed is \(k/30\) pages per minute.
2) Noah finished reading \((k+60)\) pages. Noah's reading speed is \((k+60)/30=k/30+2\) pages per minute.
AFTER 50 MINUTES,
1) Zen will read \(50*k/30 =5k/3\) pages.
2) Noah will read another \(50*(k/30+2)=5k/3+100\) pages.
Therefore, Noah will read \((5k/3+100)-(5k/3)=100\) more pages ahead of Zen.
Answer is (D)
1) Zen finished reading another \(k\) pages. Zen's reading speed is \(k/30\) pages per minute.
2) Noah finished reading \((k+60)\) pages. Noah's reading speed is \((k+60)/30=k/30+2\) pages per minute.
AFTER 50 MINUTES,
1) Zen will read \(50*k/30 =5k/3\) pages.
2) Noah will read another \(50*(k/30+2)=5k/3+100\) pages.
Therefore, Noah will read \((5k/3+100)-(5k/3)=100\) more pages ahead of Zen.
Answer is (D)
