NEW HERE? LEARN MORE
closeclose
Last visit was: 26 Apr 2024, 12:00 It is currently 26 Apr 2024, 12:00
Decision Tracker
My Rewards
New posts
New comers' posts

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.
Go to My Error Log Learn more
Close
Request Expert Reply
Confirm Cancel

A bicycle rider coasts down the hill, travelling 4ft in the first seco

SORT BY:
Date
Kudos
Tags:
Find Similar Topics 
Show Tags
Hide Tags
User avatar
L
Bunuel
Math Expert
Joined: 02 Sep 2009
Posts: 92948
Own Kudos [?]: 619222 [6]
Given Kudos: 81609
Send PM
CAT Tests Forum Quiz Mode
A bicycle rider coasts down the hill, travelling 4ft in the first seco [#permalink] New post   30 Jul 2019, 23:16
6
Bookmarks
Expert Reply
00:00
A
B
C
D
E

Difficulty:

55% (hard)

Question Stats:

65% (01:57) correct 35% (01:45) wrong based on 198 sessions
Hide Show timer Statistics
A bicycle rider coasts down the hill, travelling 4ft in the first second. In each succeeding second, he travels 5ft farther than in the preceeding second. If the rider reaches the bottom of the hill in 11 seconds, find the total distance travelled.

A. 54
B. 304
C. 309
D. 314
E. 319
ShowHide Answer
Official Answer
E
avatar
B
Skate
Intern
Intern
Joined: 24 Jul 2017
Posts: 2
Own Kudos [?]: 1 [1]
Given Kudos: 7
GMAT 1: 460 Q43 V12
GMAT 2: 700 Q50 V34
Send PM
A bicycle rider coasts down the hill, travelling 4ft in the first seco [#permalink] New post   30 Jul 2019, 23:39
1
Kudos
Distance traveled at 11th sec = Distance traveled at 1st sec + (11-1) * 5 = 54
Sum = 11/2 * (1st + 11th) = 11/2 * (4+54) = 319
Answer: E
avatar
B
sarphant
Intern
Intern
Joined: 13 Mar 2019
Posts: 22
Own Kudos [?]: 8 [1]
Given Kudos: 33
Send PM
Re: A bicycle rider coasts down the hill, travelling 4ft in the first seco [#permalink] New post   08 Aug 2019, 20:44
1
Kudos
Check the pattern -
!st sec - 4ft.
2nd - 4+5
3rd - 4+2*5
....
11th - 4+10.5

So Total = 44+(1+2+3+4.....10)*5 = 319.
User avatar
G
effatara
Manager
Manager
Joined: 09 Nov 2015
Posts: 202
Own Kudos [?]: 320 [1]
Given Kudos: 96
Send PM
Re: A bicycle rider coasts down the hill, travelling 4ft in the first seco [#permalink] New post   09 Aug 2019, 23:10
1
Kudos
I guess we could shave off a few seconds by eliminating the step of calculating the distance traveled in the 11th second and directly applying the formula for 'Sum of an Arithmetic Series':
Sn=(n/2){2a+(n-1)d} where 'n' is the number of terms, 'a' is the 1st term and 'd' is the Common Difference (difference between one term and the next).
Total distance traveled = (11/2){2*4+(11-1)*5} = 319 ANS: E

Any time saving, however small, helps!
User avatar
L
firas92
Current Student
Joined: 16 Jan 2019
Posts: 631
Own Kudos [?]: 1444 [4]
Given Kudos: 144
Location: India
Concentration: General Management
Schools: Tepper '23 (M$) Foster '23 (D)
GMAT 1: 740 Q50 V40
WE:Sales (Other)
Send PM
Reviews Badge
Re: A bicycle rider coasts down the hill, travelling 4ft in the first seco [#permalink] New post   30 Jul 2019, 23:31
3
Bookmarks
We have an arithmetic sequence with first term \(a_1=4\) and common difference \(d=5\)

The 11th term \(a_{11}=a_1+(11-1)*d = 4+50=54\)

Sum of terms \(= \frac{n}{2}(a_1+a_{11}) = \frac{11}{2}(4+54) = 319\)

Answer is (E)
User avatar
L
Kinshook
GMAT Club Legend
GMAT Club Legend
Joined: 03 Jun 2019
Posts: 5344
Own Kudos [?]: 3967 [0]
Given Kudos: 160
Location: India
Schools: HBS '22 CBS '22 Wharton '22
GMAT 1: 690 Q50 V34
WE:Engineering (Transportation)
Send PM
Reviews Badge
A bicycle rider coasts down the hill, travelling 4ft in the first seco [#permalink] New post   31 Jul 2019, 00:43
Bunuel wrote:
A bicycle rider coasts down the hill, travelling 4ft in the first second. In each succeeding second, he travels 5ft farther than in the preceeding second. If the rider reaches the bottom of the hill in 11 seconds, find the total distance travelled.

A. 54
B. 304
C. 309
D. 314
E. 319



Given: A bicycle rider coasts down the hill, travelling 4ft in the first second. In each succeeding second, he travels 5ft farther than in the preceeding second. The rider reaches the bottom of the hill in 11 seconds.

Asked: Find the total distance travelled.

The distance travelled in first second = 4 m = 5-1 ft
The distance travelled in second second = 4 + 5 ft = 5*2 -1 ft = 9ft
In general
The distance travelled in nth second = 5n -1 ft
Total distance travelle in n seconds = 5n(n+1)/2 - n ft
Sum of 11 terms of the sequence = 5*11*12/2 - 11 = 30*11 -11 = 29*11 = 319 ft
Total distance travelled.= 319 ft


IMO E
User avatar
L
ScottTargetTestPrep
Target Test Prep Representative
Joined: 14 Oct 2015
Status:Founder & CEO
Affiliations: Target Test Prep
Posts: 18767
Own Kudos [?]: 22062 [0]
Given Kudos: 283
Location: United States (CA)
Send PM
Re: A bicycle rider coasts down the hill, travelling 4ft in the first seco [#permalink] New post   12 Aug 2019, 19:30
Expert Reply
Bunuel wrote:
A bicycle rider coasts down the hill, travelling 4ft in the first second. In each succeeding second, he travels 5ft farther than in the preceeding second. If the rider reaches the bottom of the hill in 11 seconds, find the total distance travelled.

A. 54
B. 304
C. 309
D. 314
E. 319


We can use the formula sum = avg x quantity

avg = (4 + 4 + 5 x 10)/2 = 58/2 = 29

Thus, the distance traveled was 29 x 11 = 319 ft.

Answer: E
User avatar
bumpbot
Non-Human User
Joined: 09 Sep 2013
Posts: 32688
Own Kudos [?]: 822 [0]
Given Kudos: 0
Send PM
Re: A bicycle rider coasts down the hill, travelling 4ft in the first seco [#permalink] New post   18 Mar 2024, 12:13
Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
GMAT Club Bot
gmatclubot
Re: A bicycle rider coasts down the hill, travelling 4ft in the first seco [#permalink]
18 Mar 2024, 12:13
Moderators:
Bunuel
Math Expert
92948 posts
yashikaaggarwal
Senior Moderator - Masters Forum
3137 posts

Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne
Main navigation
GMAT Resources
Partners
MBA Resources
www.gmac.com|www.mba.com | | GMAT Club Rules | Terms and Conditions