GMAT Question of the Day - Daily to your Mailbox; hard ones only

It is currently 24 Aug 2019, 13:16

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

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

  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: 57279
A bicycle rider coasts down the hill, travelling 4ft in the first seco  [#permalink]

Show Tags

New post 30 Jul 2019, 23:16
00:00
A
B
C
D
E

Difficulty:

  45% (medium)

Question Stats:

62% (01:42) correct 38% (01:48) wrong based on 93 sessions

HideShow 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

_________________
Senior Manager
Senior Manager
User avatar
P
Joined: 16 Jan 2019
Posts: 426
Location: India
Concentration: General Management
WE: Sales (Other)
Re: A bicycle rider coasts down the hill, travelling 4ft in the first seco  [#permalink]

Show Tags

New post 30 Jul 2019, 23:31
1
1
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)
Intern
Intern
avatar
B
Joined: 24 Jul 2017
Posts: 2
GMAT 1: 460 Q43 V12
GMAT 2: 700 Q50 V34
A bicycle rider coasts down the hill, travelling 4ft in the first seco  [#permalink]

Show Tags

New post 30 Jul 2019, 23:39
1
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
VP
VP
User avatar
P
Joined: 03 Jun 2019
Posts: 1080
Location: India
A bicycle rider coasts down the hill, travelling 4ft in the first seco  [#permalink]

Show Tags

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
_________________
"Success is not final; failure is not fatal: It is the courage to continue that counts."

Please provide kudos if you like my post. Kudos encourage active discussions.

My GMAT Resources: -

Efficient Learning

Tele: +91-11-40396815
Mobile : +91-9910661622
E-mail : kinshook.chaturvedi@gmail.com
Intern
Intern
avatar
B
Joined: 13 Mar 2019
Posts: 27
CAT Tests
Re: A bicycle rider coasts down the hill, travelling 4ft in the first seco  [#permalink]

Show Tags

New post 08 Aug 2019, 20:44
1
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.
Manager
Manager
avatar
S
Joined: 09 Nov 2015
Posts: 109
Re: A bicycle rider coasts down the hill, travelling 4ft in the first seco  [#permalink]

Show Tags

New post 09 Aug 2019, 23:10
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!
Target Test Prep Representative
User avatar
D
Status: Founder & CEO
Affiliations: Target Test Prep
Joined: 14 Oct 2015
Posts: 7467
Location: United States (CA)
Re: A bicycle rider coasts down the hill, travelling 4ft in the first seco  [#permalink]

Show Tags

New post 12 Aug 2019, 19:30
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
_________________

Scott Woodbury-Stewart

Founder and CEO

Scott@TargetTestPrep.com
TTP - Target Test Prep Logo
122 Reviews

5-star rated online GMAT quant
self study course

See why Target Test Prep is the top rated GMAT quant course on GMAT Club. Read Our Reviews

If you find one of my posts helpful, please take a moment to click on the "Kudos" button.

GMAT Club Bot
Re: A bicycle rider coasts down the hill, travelling 4ft in the first seco   [#permalink] 12 Aug 2019, 19:30
Display posts from previous: Sort by

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

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





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