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

It is currently 26 Jul 2014, 03:16

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.

Events & Promotions

Events & Promotions in June
Open Detailed Calendar

If the average of four distinct positive integers is 60

  Question banks Downloads My Bookmarks Reviews Important topics  
Author Message
TAGS:
Moderator
Moderator
User avatar
Joined: 10 May 2010
Posts: 812
Followers: 21

Kudos [?]: 305 [0], given: 190

GMAT ToolKit User GMAT Tests User Premium Member
If the average of four distinct positive integers is 60 [#permalink] New post 08 Sep 2012, 09:32
2
This post was
BOOKMARKED
00:00
A
B
C
D
E

Difficulty:

  5% (low)

Question Stats:

24% (01:56) correct 76% (01:11) wrong based on 59 sessions
If the average of four distinct positive integers is 60, how many integers of these four are less than 50?

(1) The sum of two largest integers is 190.

(2) The median of the four integers is 50.

CORRECT QUESTION WITH A SOLUTION: m8-q28-138554.html#p1120013
[Reveal] Spoiler: OA

_________________

The question is not can you rise up to iconic! The real question is will you ?


Last edited by walker on 16 Jul 2013, 19:18, edited 3 times in total.
Renamed the topic and edited the question.
Kaplan Promo CodeKnewton GMAT Discount CodesManhattan GMAT Discount Codes
Moderator
Moderator
User avatar
Joined: 10 May 2010
Posts: 812
Followers: 21

Kudos [?]: 305 [0], given: 190

GMAT ToolKit User GMAT Tests User Premium Member
Re: M8 - Q28 [#permalink] New post 08 Sep 2012, 09:35
From Statement 1: a + b + c + d = 240
c + d = 190
a+ b = 50

We can have a situation where c < 50 say c = 40 and d = 150.

Here the no of integers less than 50 = 3.

Or we can have c > 50 c = 90

Here the no of integers less than 50 = 2.

Not Sufficient

IMO the answer should be B
_________________

The question is not can you rise up to iconic! The real question is will you ?


Last edited by AbhiJ on 08 Sep 2012, 22:09, edited 1 time in total.
Intern
Intern
avatar
Joined: 30 Dec 2010
Posts: 10
Followers: 0

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

Re: M8 - Q28 [#permalink] New post 08 Sep 2012, 09:54
If the average of four distinct positive integers is 60, how many integers of these four are less than 50?

(1) The sum of two largest integers is 190.

(2) The median of the four integers is 50.

The answer should be C.
Explanation:
From the main statement, it is given that a+b+c+d = 240, now if you look at the statement (1) , it says that c+d = 190 ( assuming that c and d are two largest integers out of 4 positive integers. which also means that a+b = 240-190 = 50
from statment (2), it says that median of the four integers is 50. which means that (b+c)/2 = 50 ( assuming that a<b<c<d or assume that b and c are the middle two integers. so, it means b+c = 100
Now if you combine both statements, you will find that a+b = 50 and b+c = 100 now, if a+b = 50 so the largest value of b = 49 and if so then then c > 50 because b+c = 100. and d of course would be greater than 50 from the statement c+d = 190.
So, we can deduce that both statements together are sufficient to answer ( ans : c & d) this question. So, the answer will be C.
Senior Manager
Senior Manager
User avatar
Joined: 11 May 2011
Posts: 379
Location: US
Followers: 2

Kudos [?]: 60 [0], given: 46

Re: M8 - Q28 [#permalink] New post 08 Sep 2012, 10:54
My answer is C as well.
_________________

-----------------------------------------------------------------------------------------
What you do TODAY is important because you're exchanging a day of your life for it!
-----------------------------------------------------------------------------------------

Manager
Manager
avatar
Joined: 02 Jun 2011
Posts: 114
Followers: 0

Kudos [?]: 21 [0], given: 5

Re: M8 - Q28 [#permalink] New post 08 Sep 2012, 20:39
AbhiJ wrote:
If the average of four distinct positive integers is 60, how many integers of these four are less than 50?

(1) The sum of two largest integers is 190. Means that two of the numbers are greator than 60. avg be 95. so we need to have two nos. whose avg should be 25. so rest two no. should always be less than 50. therefore it give answer to above question.
(2) The median of the four integers is 50.
Median is 50 means middle two no. avg is 50. so one of them should be greator than 50 other less than 50. so from rest two no. one no. should be less than 50 and other more than 50. therefore this also gives the answer.

For me 'D' is the right choice.
Manager
Manager
avatar
Joined: 25 Jun 2012
Posts: 115
Location: United States
GMAT 1: 700 Q47 V40
GMAT 2: 740 Q48 V44
GPA: 3.48
Followers: 2

Kudos [?]: 17 [0], given: 18

Re: M8 - Q28 [#permalink] New post 08 Sep 2012, 23:03
AbhiJ wrote:
From Statement 1: a + b + c + d = 240
c + d = 190
a+ b = 50

We can have a situation where c < 50 say c = 40 and d = 150.

Here the no of integers less than 50 = 3.

Or we can have c > 50 c = 90

Here the no of integers less than 50 = 2.

Not Sufficient

IMO the answer should be B


I got the same thing
Expert Post
Math Expert
User avatar
Joined: 02 Sep 2009
Posts: 18741
Followers: 3250

Kudos [?]: 22434 [0], given: 2619

Re: M8 - Q28 [#permalink] New post 09 Sep 2012, 02:42
Expert's post
AbhiJ wrote:
If the average of four distinct positive integers is 60, how many integers of these four are less than 50?

(1) The sum of two largest integers is 190.

(2) The median of the four integers is 50.


THIS IS THE OLD VERSION OF THE QUESTION. REVISED VERSION OF THE QUESTION IS BELOW:

If the average of four distinct positive integers is 60, how many integers of these four are less than 50?

It's almost always better to express the average in terms of the sum: the average of four distinct positive integers is 60, means that the sum of four distinct positive> integers is 4*60=240.

Say four integers are a, b, c and d so that 0<a<b<c<d. So, we have that a+b+c+d=240.

(1) The median of the three largest integers is 51 and the sum of two largest integers is 190. The mdian of \{b,c,d\} is 51 means that c=51. Now, if b=50, then only a, will be less than 50, but if b<50, then both a and b, will be less than 50. But we are also given that c+d=190. Substitute this value in the above equation: a+b+190=240, which boils down to a+b=50. Now, since given that all integers are positive then both a and b must be less than 50. Sufficient.

(2) The median of the four integers is 50. The median of a set with even number of terms is the average of two middle terms, so median=\frac{b+c}{2}=50. Since given that b<c then b<50<c, so both a and b are less than 50. Sufficient.

Answer: D.
_________________

NEW TO MATH FORUM? PLEASE READ THIS: ALL YOU NEED FOR QUANT!!!

PLEASE READ AND FOLLOW: 11 Rules for Posting!!!

RESOURCES: [GMAT MATH BOOK]; 1. Triangles; 2. Polygons; 3. Coordinate Geometry; 4. Factorials; 5. Circles; 6. Number Theory; 7. Remainders; 8. Overlapping Sets; 9. PDF of Math Book; 10. Remainders; 11. GMAT Prep Software Analysis NEW!!!; 12. SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) NEW!!!; 12. Tricky questions from previous years. NEW!!!;

COLLECTION OF QUESTIONS:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS ; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


What are GMAT Club Tests?
25 extra-hard Quant Tests

Get the best GMAT Prep Resources with GMAT Club Premium Membership

Manager
Manager
User avatar
Joined: 27 Feb 2007
Posts: 68
Followers: 1

Kudos [?]: 4 [0], given: 1

Re: If the average of four distinct positive integers is 60 [#permalink] New post 09 Sep 2012, 10:23
Hi Bunuel,

Isn’t the first data in Statement (1) of the problem (median 51) redundant? Because, even if we just know that the sum of the two largest integers is 190, we can answer the question – that there are 2 integers less than 50.

Regards
rakesh.id
Manager
Manager
avatar
Joined: 25 Jun 2012
Posts: 115
Location: United States
GMAT 1: 700 Q47 V40
GMAT 2: 740 Q48 V44
GPA: 3.48
Followers: 2

Kudos [?]: 17 [0], given: 18

Re: M8 - Q28 [#permalink] New post 09 Sep 2012, 13:12
Bunuel wrote:
AbhiJ wrote:
If the average of four distinct positive integers is 60, how many integers of these four are less than 50?

(1) The sum of two largest integers is 190.

(2) The median of the four integers is 50.


THIS IS THE OLD VERSION OF THE QUESTION. REVISED VERSION OF THE QUESTION IS BELOW:

If the average of four distinct positive integers is 60, how many integers of these four are less than 50?

It's almost always better to express the average in terms of the sum: the average of four distinct positive integers is 60, means that the sum of four distinct positive> integers is 4*60=240.

Say four integers are a, b, c and d so that 0<a<b<c<d. So, we have that a+b+c+d=240.

(1) The median of the three largest integers is 51 and the sum of two largest integers is 190. The mdian of \{b,c,d\} is 51 means that c=51. Now, if b=50, then only a, will be less than 50, but if b<50, then both a and b, will be less than 50. But we are also given that c+d=190. Substitute this value in the above equation: a+b+190=240, which boils down to a+b=50. Now, since given that all integers are positive then both a and b must be less than 50. Sufficient.

(2) The median of the four integers is 50. The median of a set with even number of terms is the average of two middle terms, so median=\frac{b+c}{2}=50. Since given that b<c then b<50<c, so both a and b are less than 50. Sufficient.

Answer: D.


Thanks Bunuel. That makes a lot more sense
Director
Director
User avatar
Joined: 22 Mar 2011
Posts: 613
WE: Science (Education)
Followers: 65

Kudos [?]: 475 [0], given: 43

GMAT Tests User
Re: M8 - Q28 [#permalink] New post 09 Sep 2012, 14:13
Bunuel wrote:
AbhiJ wrote:
If the average of four distinct positive integers is 60, how many integers of these four are less than 50?

(1) The sum of two largest integers is 190.

(2) The median of the four integers is 50.


THIS IS THE OLD VERSION OF THE QUESTION. REVISED VERSION OF THE QUESTION IS BELOW:

If the average of four distinct positive integers is 60, how many integers of these four are less than 50?

It's almost always better to express the average in terms of the sum: the average of four distinct positive integers is 60, means that the sum of four distinct positive> integers is 4*60=240.

Say four integers are a, b, c and d so that 0<a<b<c<d. So, we have that a+b+c+d=240.

(1) The median of the three largest integers is 51 and the sum of two largest integers is 190. The mdian of \{b,c,d\} is 51 means that c=51. Now, if b=50, then only a, will be less than 50, but if b<50, then both a and b, will be less than 50. But we are also given that c+d=190. Substitute this value in the above equation: a+b+190=240, which boils down to a+b=50. Now, since given that all integers are positive then both a and b must be less than 50. Sufficient.

(2) The median of the four integers is 50. The median of a set with even number of terms is the average of two middle terms, so median=\frac{b+c}{2}=50. Since given that b<c then b<50<c, so both a and b are less than 50. Sufficient.

Answer: D.


(1) The median of the three largest integers is 51 - where did this come from? I don't see it in the question...
_________________

PhD in Applied Mathematics
Love GMAT Quant questions and running.

Expert Post
Veritas Prep GMAT Instructor
User avatar
Joined: 16 Oct 2010
Posts: 4579
Location: Pune, India
Followers: 1031

Kudos [?]: 4492 [0], given: 162

Re: If the average of four distinct positive integers is 60 [#permalink] New post 09 Sep 2012, 21:24
Expert's post
I think there are two versions of this question:

Version 1:

If the average of four distinct positive integers is 60, how many integers of these four are less than 50?

(1) The sum of two largest integers is 190.

(2) The median of the four integers is 50.

Here the answer is (B)

Here statement 1 is not sufficient. Let me show by taking 2 cases:
Case 1: Numbers are 24, 26, 30, 160
Case 2: Numbers are 20, 30, 90, 100
Number of numbers which are less than 50 are different in these two cases. So statement 1 alone is not sufficient.

Version 2:
If the average of four distinct positive integers is 60, how many integers of these four are less than 50?

(1) The median of the three largest integers is 51 and the sum of two largest integers is 190.

(2) The median of the four integers is 50.

Answer (D)
Here statement 1 is sufficient too. Since median of the three largest integers is 51, the middle of the three largest integers must be 51.
So the numbers are <51, <51, 51, >51
Since the sum of the two largest numbers is 190, the largest number must be 190 - 51 = 139 i.e. 79 more than the average of 60. Since 51 is 9 less than 60, we need to balance out another 70 in the two smallest numbers to get an average of 60. The numbers must be all distinct. Can one of the two smallest numbers be equal to 50? No! If it is equal to 50, it will balance out 10 of the 70 and we will need to balance out 60 from the smallest number. That will make the smallest number = 0 but all numbers must be positive. So, the two smallest numbers must be less than 50.

(The concept of mean I am using here is very simple and intuitive. I have explained it in detail here: http://www.veritasprep.com/blog/2012/04 ... etic-mean/)
_________________

Karishma
Veritas Prep | GMAT Instructor
My Blog

Save $100 on Veritas Prep GMAT Courses And Admissions Consulting
Enroll now. Pay later. Take advantage of Veritas Prep's flexible payment plan options.

Veritas Prep Reviews

Re: If the average of four distinct positive integers is 60   [#permalink] 09 Sep 2012, 21:24
    Similar topics Author Replies Last post
Similar
Topics:
1 Experts publish their posts in the topic The average (arithmetic mean) of the four distinct positive jlgdr 2 01 Feb 2014, 14:19
Experts publish their posts in the topic If the average of four distinct positive integers is 60, how xyztroy 3 02 Jan 2010, 08:13
2 Experts publish their posts in the topic If the average of four distinct positive integers is 60, how Jivana 9 04 Sep 2009, 17:50
The average of four distinct positive integers is 60. How bigfernhead 3 29 Nov 2008, 14:36
Average of 4 distinct positive integers is 60. How many of jamesrwrightiii 5 05 Sep 2007, 16:04
Display posts from previous: Sort by

If the average of four distinct positive integers is 60

  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®.