GMAT Question of the Day: Daily via email | Daily via Instagram New to GMAT Club? Watch this Video

It is currently 24 Jan 2020, 12:50

Close

GMAT 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

we will pick new questions that match your level based on your Timer History

Track
Your Progress

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History

Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.

Close

Request Expert Reply

Confirm Cancel

Aliens who live 1,000,000 miles from Earth decide to come to our plane

  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics  
Author Message
TAGS:

Hide Tags

Find Similar Topics 
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 60647
Aliens who live 1,000,000 miles from Earth decide to come to our plane  [#permalink]

Show Tags

New post 02 Dec 2019, 00:16
00:00
A
B
C
D
E

Difficulty:

  85% (hard)

Question Stats:

53% (03:21) correct 47% (03:41) wrong based on 49 sessions

HideShow timer Statistics

Competition Mode Question



Aliens who live 1,000,000 miles from Earth decide to come to our planet for a visit. They program their space shuttle to travel 100,000 miles per hour for the first 500,000 miles, 200,000 miles per hour for the next 250,000 miles, 400,000 miles for the next 125,000 miles and so on, doubling the speed every time half of the remaining distance is covered. If this pattern is maintained until the aliens reach earth, what will their average speed for the trip be in miles per hour?

A. 120,000
B. 125,000
C. 135,000
D. 150,000
E. 162,000

Are You Up For the Challenge: 700 Level Questions

_________________
Most Helpful Community Reply
Senior Manager
Senior Manager
avatar
P
Joined: 25 Jul 2018
Posts: 482
Re: Aliens who live 1,000,000 miles from Earth decide to come to our plane  [#permalink]

Show Tags

New post 02 Dec 2019, 18:51
2
3
\(Speed(ave.)= (D_1+D_2+...D_n)/(T_1+T_2+...+T_n)\)

\(D_1=500000 ml\)
\(Speed_1=100000 mph\)
--> \(Time_1= \frac{500000}{100000}=5 h\)

\(D_2=250000\) ml
\(Speed_2=200000\) mph
--> \(Time_2=\frac{5}{4}\)

\(D_3=125000\) ml
\(Speed_3= 400000\) mph
--> \(Time_3= \frac{5}{16}\)

As you see the Distance and Time, they are creating the Infinite terms of Geometric Progressions series (\(S_∞=\frac{b}{(1-q)}\) )
--> b is the first term, q is the common ratio (\(\frac{b_n}{b_{n-1}}\))

Distance:

b= 500000
\(q = \frac{b_2}{b_1}= \frac{250000}{500000}= \frac{1}{2}\)
--> \(S_∞= \frac{500000}{(1-1/2)}= 1000000\)

Time:

b=5
\(q= \frac{b_2}{b_1}= \frac{1.25}{5}= \frac{1}{4} \)
--> \(S_∞= \frac{5}{(1-1/4)}= \frac{20}{3}\)

\(Speed(ave.)= \frac{Distance}{Time}= \frac{1000000}{(20/3)}= 150000\)

The answer is D
General Discussion
VP
VP
avatar
P
Joined: 24 Nov 2016
Posts: 1110
Location: United States
CAT Tests
Re: Aliens who live 1,000,000 miles from Earth decide to come to our plane  [#permalink]

Show Tags

New post 02 Dec 2019, 05:51
1
1
Quote:
Aliens who live 1,000,000 miles from Earth decide to come to our planet for a visit. They program their space shuttle to travel 100,000 miles per hour for the first 500,000 miles, 200,000 miles per hour for the next 250,000 miles, 400,000 miles for the next 125,000 miles and so on, doubling the speed every time half of the remaining distance is covered. If this pattern is maintained until the aliens reach earth, what will their average speed for the trip be in miles per hour?

A. 120,000
B. 125,000
C. 135,000
D. 150,000
E. 162,000


rate*time=distance
d1=500…r1=100…t1=500/100=5
d2=250…r2=200…t2=250/200=5/4
d3=125…r3=400…t3=125/400=25/80=5/16
d4=75…r4=800…t4=75/800=15/160=3/32
d5 to dn = 5%d… r5 to rn > 1600… t5 to tn < 50/1600 = 5/160 = 1/32

t=5+5/4+5/16+3/32+1/32=5+5/4+14/32 < 6.25 + 0.5 ~ 6.666
d=1000

rate=distance/time=1000/6.666=~150mph

Ans (D)
Director
Director
avatar
V
Joined: 30 Sep 2017
Posts: 590
GMAT 1: 720 Q49 V40
GPA: 3.8
Premium Member Reviews Badge
Re: Aliens who live 1,000,000 miles from Earth decide to come to our plane  [#permalink]

Show Tags

New post 02 Dec 2019, 09:08
2
Timing for each distance:
D1=500,000 miles, v1= 100mph and t1=D1/v1= 5 hours
D2=250,000 miles, v2= 200mph and t2=D2/v2= 1.25 hours
D3=125,000 miles, v3= 400mph and t3=D3/v3= 0.3125 hours, et cetera.

D (Total Distance) = 1,000,000 miles.
T (Total Time) = 5 + 1.25 + 0.3125 +... = 5/(1-0.25) = 20/3 hours.
Thus, v (average speed) = D / T = 150,000 mph

Final answer is (D)
Director
Director
avatar
P
Joined: 18 May 2019
Posts: 661
GMAT ToolKit User Premium Member CAT Tests
Re: Aliens who live 1,000,000 miles from Earth decide to come to our plane  [#permalink]

Show Tags

New post 02 Dec 2019, 20:12
1
Average Speed = Distance / Time
we need to determine the total distance.
Time to reach earth = 500,000/100,000 + 250,000/200,000 + 125,000/400,000 + 62,500/800,000 + 31,250/1,600,000 +...
=5 + 5/4 + 5/16 + 5/64 + ...
=5(1+1/4+1/16+1/64+...)
So we can look at this as an infinite geometric series.
common ratio = 1/4
so S=S1/(1-r) = 5/(1-1/4) = 5/(3/4) = 20/3
Hence Time taken = 20/3

Average Speed = 1,000,000/(20/3)= 3*50,000 = 150,000mph

The answer is option D.
Senior Manager
Senior Manager
avatar
P
Joined: 01 Mar 2019
Posts: 404
Location: India
Concentration: Strategy, Social Entrepreneurship
Schools: Ross '22, ISB '20, NUS '20
GPA: 4
Reviews Badge
Re: Aliens who live 1,000,000 miles from Earth decide to come to our plane  [#permalink]

Show Tags

New post 02 Dec 2019, 21:27
1
let d=1,000,000 miles, s=100,000 miles per hour
average speed= total distance/total time
= d/(d/2s)+(d/8s)+......= d/[d/s(1/2+1/8+1/32........)]
here denominator is a infinite GP series...whose sum = a/1-r
= (1/2)/(1-1/4) = 2/3
average speed= 3s/2=150,000 miles per hour

OA:D
SVP
SVP
User avatar
D
Joined: 03 Jun 2019
Posts: 1942
Location: India
GMAT 1: 690 Q50 V34
Premium Member Reviews Badge CAT Tests
Re: Aliens who live 1,000,000 miles from Earth decide to come to our plane  [#permalink]

Show Tags

New post 03 Dec 2019, 09:03
Given:
1. Aliens who live 1,000,000 miles from Earth decide to come to our planet for a visit. They program their space shuttle to travel 100,000 miles per hour for the first 500,000 miles, 200,000 miles per hour for the next 250,000 miles, 400,000 miles for the next 125,000 miles and so on, doubling the speed every time half of the remaining distance is covered.

Asked: If this pattern is maintained until the aliens reach earth, what will their average speed for the trip be in miles per hour?

Total distance travelled = 1,000,000 miles

Total time taken = 5 + 5/4 + 5/4^2 + .... = 5/(1-1/4) = 5*4/3 = 20/3 hrs

Average speed = 1000,000 miles / (20/3) hrs = 3000,000/20 = 150,000 miles/hrs

IMO D
GMAT Club Bot
Re: Aliens who live 1,000,000 miles from Earth decide to come to our plane   [#permalink] 03 Dec 2019, 09:03
Display posts from previous: Sort by

Aliens who live 1,000,000 miles from Earth decide to come to our plane

  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics  





cron

Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne