GRE Prep Club Daily Prep
Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.
Customized
for You
Track
Your Progress
Practice
Pays
Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.
GRE Prep Club Team Member
Joined: 20 Feb 2017
Posts: 2506
Given Kudos: 1053
GPA: 3.39
A certain airline's fleet consisted of 60 type A planes at the beginni
[#permalink]
10 Apr 2022, 04:13
10 Apr 2022, 04:13
1
Expert Reply
3
Bookmarks
00:00
Question Stats:
62% (02:33) correct
37% (02:23) wrong based on 16 sessions
Hide Show timer Statistics
A certain airline's fleet consisted of 60 type A planes at the beginning of 1980. At the end of each year, starting with 1980, the airline retired 3 of the TYPE A planes and acquired 4 new type B plans. How many years did it take before the number of type A planes left in the airline's fleet was less than 50 percent of the fleet?
A. 6
B. 7
C. 8
D. 9
E. 10
A. 6
B. 7
C. 8
D. 9
E. 10
Re: A certain airline's fleet consisted of 60 type A planes at the beginni
[#permalink]
10 Apr 2022, 19:38
10 Apr 2022, 19:38
1
Quote:
A certain airline's fleet consisted of 60 type A planes at the beginning of 1980. At the end of each year, starting with 1980, the airline retired 3 of the TYPE A planes and acquired 4 new type B plans. How many years did it take before the number of type A planes left in the airline's fleet was less than 50 percent of the fleet?
For Type A:
at the end of the 1st year, number of planes are 60
at the end of the 2nd year, number of planes are 60 - 3
at the end of the 3rd year, number of planes are 60 - 3(2)
at the end of the nth year, number of planes are 60 - 3(n-1)
For Type B:
at the end of the 1st year, number of planes are 4
at the end of the 2nd year, number of planes are 4*2
at the end of the 3rd year, number of planes are 4*3
at the end of the nth year, number of planes are 4*n
Total planes at the end of the nth year = 60 - 3(n-1) + 4*n
As per the condition:
60 - 3(n-1) < 1/2 [60 - 3(n-1) + 4*n]
Solving the inequality
n > 8.5
Hence, n = 9
IMO D
Re: A certain airline's fleet consisted of 60 type A planes at the beginni
[#permalink]
02 May 2022, 00:26
02 May 2022, 00:26
kapil1 wrote:
Quote:
A certain airline's fleet consisted of 60 type A planes at the beginning of 1980. At the end of each year, starting with 1980, the airline retired 3 of the TYPE A planes and acquired 4 new type B plans. How many years did it take before the number of type A planes left in the airline's fleet was less than 50 percent of the fleet?
For Type A:
at the end of the 1st year, number of planes are 60
at the end of the 2nd year, number of planes are 60 - 3
at the end of the 3rd year, number of planes are 60 - 3(2)
at the end of the nth year, number of planes are 60 - 3(n-1)
For Type B:
at the end of the 1st year, number of planes are 4
at the end of the 2nd year, number of planes are 4*2
at the end of the 3rd year, number of planes are 4*3
at the end of the nth year, number of planes are 4*n
Total planes at the end of the nth year = 60 - 3(n-1) + 4*n
As per the condition:
60 - 3(n-1) < 1/2 [60 - 3(n-1) + 4*n]
Solving the inequality
n > 8.5
Hence, n = 9
IMO D
Could you please elaborate on solving the inequality?
