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Zen and Noah decided to read a novel. When Noah started reading the no

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Zen and Noah decided to read a novel. When Noah started reading the no  [#permalink]

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New post 15 Sep 2019, 21:14
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A
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D
E

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  65% (hard)

Question Stats:

59% (02:32) correct 41% (02:07) wrong based on 46 sessions

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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

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Re: Zen and Noah decided to read a novel. When Noah started reading the no  [#permalink]

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New post 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)
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Re: Zen and Noah decided to read a novel. When Noah started reading the no  [#permalink]

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New post 15 Sep 2019, 22:22
1
Let the number of pages read by Noah in 30 minutes be x. This implies Zen would have read x-60 pages in 30 minutes.
Now since we are talking about how many more pages Noah would have read ahead of zen, then we can look at it as though they are starting at the 30th minute mark when they are on the same page.
So in 50 minutes, Zen would have read 50(x-60)/30 = (5x/3 - 100) pages.
While Noah would have read 50x/30 = 5x/3 pages.

Hence Noah would have read 5x/3 -(5x/3-100) pages more than Zen, which is equal to 100 pages.

The answer is therefore D imo.

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Re: Zen and Noah decided to read a novel. When Noah started reading the no  [#permalink]

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New post 15 Sep 2019, 23:49
1
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
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Re: Zen and Noah decided to read a novel. When Noah started reading the no  [#permalink]

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New post 16 Sep 2019, 00:03
1
D.

Since the difference in speed is 60pages/30mins-> 2page/mins

One they reach at same page, in 50 mins, Noah will be ahead by 50*(2page/min)= 100 pages

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Re: Zen and Noah decided to read a novel. When Noah started reading the no  [#permalink]

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New post 16 Sep 2019, 02:55
60+30X=30Y
2+X=Y
That is Noah reads 2 pages more than Zen per minute.
After 50 minutes; 50Y=50(X+2)=50X+100.
Option D

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Re: Zen and Noah decided to read a novel. When Noah started reading the no  [#permalink]

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New post 16 Sep 2019, 05:44
Quote:
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


pages after 30 mins = 60 + rate of zen • 30 mins
pages after 30 mins = rate of noah • 30 mins
pages after 30 mins: 60+30z=30n…n-z=2
pages 50 mins after they are reading the same page: (n-z) • 50 mins = (2)•50 = 100 pages

Answer (D)
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Re: Zen and Noah decided to read a novel. When Noah started reading the no  [#permalink]

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New post 17 Sep 2019, 01:41
in 30 mins Noah has read x pages and zen ; x+60
rate of Noah ; x/30 and zen ; x+60/30 ; x/30+2
so in 50 mins
5x/3 = 5x/3+100
100 pages
IMO D

Bunuel wrote:

Competition Mode Question



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
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Re: Zen and Noah decided to read a novel. When Noah started reading the no  [#permalink]

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New post 20 Sep 2019, 17:35
In 30 MINUTES,
NOAH reads 60 pages EXTRA.
IN 1 MINUTE,
NOAH reads 2 pages EXTRA.
IN 50 MINUTES,
NOAH reads 100 pages EXTRA.

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Re: Zen and Noah decided to read a novel. When Noah started reading the no   [#permalink] 20 Sep 2019, 17:35
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