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

It is currently 16 Sep 2019, 09:29

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

Let a1, a2, ... , a52 be positive integers such that a1 < a2 < ...

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

Hide Tags

Find Similar Topics 
Intern
Intern
User avatar
B
Joined: 03 Jul 2019
Posts: 33
Location: India
Concentration: Leadership, Marketing
GPA: 3
WE: Sales (Venture Capital)
Let a1, a2, ... , a52 be positive integers such that a1 < a2 < ...  [#permalink]

Show Tags

New post 23 Aug 2019, 10:45
2
00:00
A
B
C
D
E

Difficulty:

  65% (hard)

Question Stats:

27% (02:27) correct 73% (03:16) wrong based on 11 sessions

HideShow timer Statistics

Let a1, a2, ... , a52 be positive integers such that a1 < a2 < ... < a52. Suppose, their arithmetic mean is one less than the arithmetic mean of a2, a3, ..., a52. If a52 = 100, then the largest possible value of a1 is

A. 48
B. 20
C. 45
D. 23
E. 43
Director
Director
avatar
D
Joined: 19 Oct 2018
Posts: 852
Location: India
Premium Member CAT Tests
Let a1, a2, ... , a52 be positive integers such that a1 < a2 < ...  [#permalink]

Show Tags

New post 23 Aug 2019, 15:29
1
1
\(\frac{a_1+a_2+ ... + a_{52}}{52} = \frac{a_2+a_3 ... a_{51}+ a_{52}}{51} - 1\)

\(a_1+51*52= a_2+a_3 ... a_{51}+ a_{52}\)

We want maximize \(a_1\), hence we have to maximize the sum of \(a_2\), \(a_3\), ..., \(a_{52}\).

Also, we know that \(a_1\) < \(a_2\) < ... < \(a_{52}\), and \(a_2\), ... , \(a_{52}\) are positive integers. Hence we can assign the consecutive integers from \(a_2\) to \(a_{52}\).

\(51a_1+51*52= 50+51+.....+99+100\)

\(51a_1+51*52= \frac{51}{2}*(50+100)\)

\(51a_1=51*75-51*52\)

\(51a_1=51(75-52)\)

\(a_1=23\)




AbdulMalikVT wrote:
Let a1, a2, ... , a52 be positive integers such that a1 < a2 < ... < a52. Suppose, their arithmetic mean is one less than the arithmetic mean of a2, a3, ..., a52. If a52 = 100, then the largest possible value of a1 is

A. 48
B. 20
C. 45
D. 23
E. 43
VP
VP
User avatar
P
Joined: 03 Jun 2019
Posts: 1496
Location: India
Premium Member Reviews Badge CAT Tests
Let a1, a2, ... , a52 be positive integers such that a1 < a2 < ...  [#permalink]

Show Tags

New post 23 Aug 2019, 23:10
1
AbdulMalikVT wrote:
Let a1, a2, ... , a52 be positive integers such that a1 < a2 < ... < a52. Suppose, their arithmetic mean is one less than the arithmetic mean of a2, a3, ..., a52. If a52 = 100, then the largest possible value of a1 is

A. 48
B. 20
C. 45
D. 23
E. 43


Given:
1. Let a1, a2, ... , a52 be positive integers such that a1 < a2 < ... < a52.
2. Suppose, their arithmetic mean is one less than the arithmetic mean of a2, a3, ..., a52.
3. a52 = 100

Asked: The largest possible value of a1 is

\(\frac{a1+a2+.... + a52}{52} = \frac{a2 + a3 + .... + a52}{51} -1\)
a52 = 100
\(\frac{a1}{52} + \frac{a2 + a3 + .... + 100}{52} = \frac{a2 + a3 + .... + 100}{51} -1\)
\(\frac{a1}{52} = (a2 + a3 + .... + 100) (\frac{1}{51} - \frac{1}{52}) -1\)
\(a1 = \frac{a2+a3+...+100}{51} - 52\)
For largest possible value of a1
a2=a3-1
a3=a4-1

a51=a52-1=99

{a52,a51,.... a2} = {100,99, ... 50}

Largest possible value of a1 = \(\frac{51}{2}\frac{(100+50)}{51} -52 = \frac{51*75}{51} - 52 = 23\)

IMO D
_________________
"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
All you need to know about GMAT quant

Tele: +91-11-40396815
Mobile : +91-9910661622
E-mail : kinshook.chaturvedi@gmail.com
GMAT Club Bot
Let a1, a2, ... , a52 be positive integers such that a1 < a2 < ...   [#permalink] 23 Aug 2019, 23:10
Display posts from previous: Sort by

Let a1, a2, ... , a52 be positive integers such that a1 < a2 < ...

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





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