Find all School-related info fast with the new School-Specific MBA Forum

It is currently 23 Sep 2014, 11:02

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.

Events & Promotions

Events & Promotions in June
Open Detailed Calendar

Set A contains 50 different positive integers, the

  Question banks Downloads My Bookmarks Reviews Important topics  
Author Message
TAGS:
GMAT Instructor
avatar
Joined: 04 Jul 2006
Posts: 1270
Location: Madrid
Followers: 23

Kudos [?]: 126 [0], given: 0

Set A contains 50 different positive integers, the [#permalink] New post 12 Jul 2006, 15:31
00:00
A
B
C
D
E

Difficulty:

(N/A)

Question Stats:

0% (00:00) correct 0% (00:00) wrong based on 0 sessions
Set A contains 50 different positive integers, the arithmetic mean of which is 60. Are any less than 35?

(1) 10 of the digits are above 85.
(2) 8 of the digits are above 90.
Intern
Intern
User avatar
Joined: 11 Jul 2006
Posts: 38
Location: Boston
Followers: 0

Kudos [?]: 1 [0], given: 0

Re: DS: Any number less than 35? [#permalink] New post 12 Jul 2006, 16:13
Set A contains 50 different positive integers, the arithmetic mean of which is 60. Are any less than 35?

(1) 10 of the digits are above 85.
(2) 8 of the digits are above 90.


The problem statement indicates that the sum of the numbers is 50 * 60 = 300

Consider (1)
10 are above 85
the lowest that these could be is 86-95, and their sum is (86+95)/2 * 10 = 905.
The rest should make up 2095.
Consider the lowest combination of the rest 40 numbers >= 35, this is 35 – 74
Sum of these is (35+74)/2 * 40 = 2180, which is greater than the available limit.

So there should be numbers below 35 in the sequence.

So (1) alone is sufficient.


Consider (2)
Along the same line
Total of 8 above 90 = (91+98)/2 * 8 = 756
The rest should make up = 3000 – 756 = 2244
Lowest possible combination >= 35 is 35 – 76
Sum is (35+76)/2 * 42 = 2331, which is greater than 2244
So again there should be a no below 35

So (2) alone is sufficient,

SO FINALLY, (1) and (2) both alone are sufficient.

Hope this helps...and hopefully this is right.
Anand

kevincan wrote:
Set A contains 50 different positive integers, the arithmetic mean of which is 60. Are any less than 35?

(1) 10 of the digits are above 85.
(2) 8 of the digits are above 90.
GMAT Instructor
avatar
Joined: 04 Jul 2006
Posts: 1270
Location: Madrid
Followers: 23

Kudos [?]: 126 [0], given: 0

 [#permalink] New post 12 Jul 2006, 16:28
Nice work, but a bit too long! Can we find a way that involves crunching smaller numbers?
Manager
Manager
avatar
Joined: 04 Jul 2006
Posts: 57
Followers: 1

Kudos [?]: 1 [0], given: 0

 [#permalink] New post 12 Jul 2006, 16:39
Ass.: 50 different integers, no integer is less than 35 and their mean is 60. This set is unique. Its elements are 35, 36, 37, 38, ..57, 58, 59, 61, 62, 63, 83, 84, 85.

... see below

Hence, A and B are each alone sufficient.
=> D.

Last edited by game over on 12 Jul 2006, 18:48, edited 1 time in total.
Intern
Intern
User avatar
Joined: 11 Jul 2006
Posts: 38
Location: Boston
Followers: 0

Kudos [?]: 1 [0], given: 0

 [#permalink] New post 12 Jul 2006, 16:49
You made it look simple enough..but can u explain...how is that set unique?



game over wrote:
Ass.: 50 different integers, no integer is less than 35 and their mean is 60. This set is unique. Its elements are 35, 36, 37, 38, ..57, 58, 59, 61, 62, 63, 83, 84, 85.
Hence, A and B are each alone sufficient.
=> D.
Manager
Manager
avatar
Joined: 04 Jul 2006
Posts: 57
Followers: 1

Kudos [?]: 1 [0], given: 0

 [#permalink] New post 12 Jul 2006, 17:12
sorry, my argument wasn't complete.

[You had probably the following in mind:]

consider a new set, which is similar to the old set but has two different elements: one element >60 is replaced by 60. To get mean=60, we can always replace just one element >60 by a new element >85.
How many elements can we replace at most?
Consider: 85 => 60 (this means that 85 is replaced by 60). There are 25 "free points".
=> 84 => 86, 83=>87, 82=>88, 81=> 89, 80 => 90. At most, we can have 5 elements > 85.

Therefore: If we have more than 5 elements >85 (>90), there must be an element <35.
GMAT Instructor
avatar
Joined: 04 Jul 2006
Posts: 1270
Location: Madrid
Followers: 23

Kudos [?]: 126 [0], given: 0

 [#permalink] New post 13 Jul 2006, 00:24
game over wrote:
sorry, my argument wasn't complete.

[You had probably the following in mind:]

consider a new set, which is similar to the old set but has two different elements: one element >60 is replaced by 60. To get mean=60, we can always replace just one element >60 by a new element >85.
How many elements can we replace at most?
Consider: 85 => 60 (this means that 85 is replaced by 60). There are 25 "free points".
=> 84 => 86, 83=>87, 82=>88, 81=> 89, 80 => 90. At most, we can have 4 elements > 85.

Therefore: If we have more than 4 elements >85 (>90), there must be an element <35.


A trivial correction makes yours a very elegant OE!
Intern
Intern
User avatar
Joined: 11 Jul 2006
Posts: 38
Location: Boston
Followers: 0

Kudos [?]: 1 [0], given: 0

 [#permalink] New post 13 Jul 2006, 07:01
makes sense....thanks for the explaination.

kevincan wrote:
game over wrote:
sorry, my argument wasn't complete.

[You had probably the following in mind:]

consider a new set, which is similar to the old set but has two different elements: one element >60 is replaced by 60. To get mean=60, we can always replace just one element >60 by a new element >85.
How many elements can we replace at most?
Consider: 85 => 60 (this means that 85 is replaced by 60). There are 25 "free points".
=> 84 => 86, 83=>87, 82=>88, 81=> 89, 80 => 90. At most, we can have 4 elements > 85.

Therefore: If we have more than 4 elements >85 (>90), there must be an element <35.


A trivial correction makes yours a very elegant OE!
  [#permalink] 13 Jul 2006, 07:01
    Similar topics Author Replies Last post
Similar
Topics:
2 Set A contains three different positive odd integers and two oss198 3 03 Aug 2014, 11:05
1 Experts publish their posts in the topic S is a set containing 8 different positive odd numbers danzig 2 25 Oct 2012, 13:40
Set A contains 50 different integers, the arithmetic mean of kevincan 9 27 Sep 2006, 02:29
Set A contains 50 different positive integers, the kevincan 2 17 Sep 2006, 08:56
Set D contains 88 different positive integers. Is the median kevincan 1 09 Jul 2006, 01:58
Display posts from previous: Sort by

Set A contains 50 different positive integers, the

  Question banks Downloads My Bookmarks Reviews Important topics  


GMAT Club MBA Forum Home| About| Privacy Policy| Terms and Conditions| GMAT Club Rules| Contact| Sitemap

Powered by phpBB © phpBB Group and phpBB SEO

Kindly note that the GMAT® test is a registered trademark of the Graduate Management Admission Council®, and this site has neither been reviewed nor endorsed by GMAC®.