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

 It is currently 25 May 2020, 06:56 ### 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

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

Author Message
TAGS:

### Hide Tags

Math Expert V
Joined: 02 Sep 2009
Posts: 64101
Aliens who live 1,000,000 miles from Earth decide to come to our plane  [#permalink]

### Show Tags 00:00

Difficulty:   85% (hard)

Question Stats: 54% (03:22) correct 46% (03:35) wrong based on 57 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

_________________
Director  D
Joined: 25 Jul 2018
Posts: 712
Re: Aliens who live 1,000,000 miles from Earth decide to come to our plane  [#permalink]

### Show Tags

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

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

##### General Discussion
SVP  D
Joined: 24 Nov 2016
Posts: 1549
Location: United States
Re: Aliens who live 1,000,000 miles from Earth decide to come to our plane  [#permalink]

### Show Tags

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  V
Joined: 30 Sep 2017
Posts: 910
GMAT 1: 720 Q49 V40 GPA: 3.8
Re: Aliens who live 1,000,000 miles from Earth decide to come to our plane  [#permalink]

### Show Tags

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

CR Forum Moderator D
Joined: 18 May 2019
Posts: 811
Re: Aliens who live 1,000,000 miles from Earth decide to come to our plane  [#permalink]

### Show Tags

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

Director  P
Joined: 01 Mar 2019
Posts: 528
Location: India
Concentration: Strategy, Social Entrepreneurship
GMAT 1: 580 Q48 V21
GPA: 4
Re: Aliens who live 1,000,000 miles from Earth decide to come to our plane  [#permalink]

### Show Tags

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
CEO  V
Joined: 03 Jun 2019
Posts: 2889
Location: India
GMAT 1: 690 Q50 V34 WE: Engineering (Transportation)
Re: Aliens who live 1,000,000 miles from Earth decide to come to our plane  [#permalink]

### Show Tags

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
_________________
Kinshook Chaturvedi
Email: kinshook.chaturvedi@gmail.com Re: Aliens who live 1,000,000 miles from Earth decide to come to our plane   [#permalink] 03 Dec 2019, 08:03

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