Author 
Message 
TAGS:

Hide Tags

Math Expert
Joined: 02 Sep 2009
Posts: 49300

The average (arithmetic mean) of 10 distinct odd integers in a set is
[#permalink]
Show Tags
13 Jul 2017, 23:54
Question Stats:
40% (01:42) correct 60% (01:36) wrong based on 145 sessions
HideShow timer Statistics



Director
Joined: 18 Aug 2016
Posts: 629
Concentration: Strategy, Technology
GMAT 1: 630 Q47 V29 GMAT 2: 740 Q51 V38

Re: The average (arithmetic mean) of 10 distinct odd integers in a set is
[#permalink]
Show Tags
14 Jul 2017, 01:58
Bunuel wrote: The average (arithmetic mean) of 10 distinct odd integers in a set is 55. What is the median of these 10 integers?
(1) The largest integer is 65. (2) The smallest integer is 41. The total sum of 10 distinct odd integers is 550 (1) the largest integer is 65...not sufficient ( Longer WayMaking Sets is to write 55 ten times and then play with numbers) 65,63,61,59,57,55,51,49,47,43 Mean is 55 and Median is 56 65,63,61,59,57,53,51,49,47,45 Mean is 55 and Median is 55 (2) the smallest integer is 41.....not sufficient 41,43,45,47,53,57,63,65,67,69 Mean is 55 and Median is 55 41,43,45,47,55,57,61,65,67,69 Mean is 55 and Median is 56 ON combining 41,45,51,53,55,57,59,61,63,65 Mean is 55 and Median is 56 41,47,49,53,55,57,59,61,63,65 Mean is 55 and Median is 56 Hence C
_________________
We must try to achieve the best within us
Thanks Luckisnoexcuse



Senior Manager
Joined: 06 Jul 2016
Posts: 399
Location: Singapore
Concentration: Strategy, Finance

Re: The average (arithmetic mean) of 10 distinct odd integers in a set is
[#permalink]
Show Tags
14 Jul 2017, 07:48
Bunuel wrote: The average (arithmetic mean) of 10 distinct odd integers in a set is 55. What is the median of these 10 integers?
(1) The largest integer is 65. (2) The smallest integer is 41. 1) Largest Int = 65 Insufficient. Multiple values possible. 2) Smallest int = 41 Insufficient. Multiple values possible. 1+2) 41 < 8 odd integers < 65 mean = 55 The mean is closer to 65, and we've lost leverage in terms of going below 41, or above 65 => the only place where I can switch numbers around is near 41. So the median remains the same at 56. Below are the cases. Case 1  41,45,51,53,55,57,59,61,63,65 Case 2  41,47,49,53,55,57,59,61,63,65 Sufficient. Answer is C IMO. My questionI took around 3.05 minutes to solve this, and I feel it's way too long. Is there a shorter way to do this question? Is there something I missed i.e. a shortcut?
_________________
Put in the work, and that dream score is yours!



Director
Joined: 21 Mar 2016
Posts: 531

Re: The average (arithmetic mean) of 10 distinct odd integers in a set is
[#permalink]
Show Tags
14 Jul 2017, 11:25
akshayk wrote: Bunuel wrote: The average (arithmetic mean) of 10 distinct odd integers in a set is 55. What is the median of these 10 integers?
(1) The largest integer is 65. (2) The smallest integer is 41. 1) Largest Int = 65 Insufficient. Multiple values possible. 2) Smallest int = 41 Insufficient. Multiple values possible. 1+2) 41 < 8 odd integers < 65 mean = 55 The mean is closer to 65, and we've lost leverage in terms of going below 41, or above 65 => the only place where I can switch numbers around is near 41. S o the median remains the same at 56.Below are the cases. Case 1  41,45,51,53,55,57,59,61,63,65 Case 2  41,47,49,53,55,57,59,61,63,65 Sufficient. Answer is C IMO. My questionI took around 3.05 minutes to solve this, and I feel it's way too long. Is there a shorter way to do this question? Is there something I missed i.e. a shortcut? akshayk how do u say that mean remains at 56,,on what basis???



Senior Manager
Joined: 06 Jul 2016
Posts: 399
Location: Singapore
Concentration: Strategy, Finance

Re: The average (arithmetic mean) of 10 distinct odd integers in a set is
[#permalink]
Show Tags
14 Jul 2017, 11:47
mohshu wrote: akshayk wrote: Bunuel wrote: The average (arithmetic mean) of 10 distinct odd integers in a set is 55. What is the median of these 10 integers?
(1) The largest integer is 65. (2) The smallest integer is 41. 1) Largest Int = 65 Insufficient. Multiple values possible. 2) Smallest int = 41 Insufficient. Multiple values possible. 1+2) 41 < 8 odd integers < 65 mean = 55 The mean is closer to 65, and we've lost leverage in terms of going below 41, or above 65 => the only place where I can switch numbers around is near 41. S o the median remains the same at 56.Below are the cases. Case 1  41,45,51,53,55,57,59,61,63,65 Case 2  41,47,49,53,55,57,59,61,63,65 Sufficient. Answer is C IMO. My questionI took around 3.05 minutes to solve this, and I feel it's way too long. Is there a shorter way to do this question? Is there something I missed i.e. a shortcut? akshayk how do u say that mean remains at 56,,on what basis??? Case 1  41,45,51,53 ,55,57,59,61,63,65 Case 2  41,47,49,53, 55,57,59,61,63,65 The middle 2 numbers in both cases are 55 and 57 (55 + 57)/2 = 112/2 = 56 So the median is 56. I couldn't come up with another possibility after combining the 2 statements.
_________________
Put in the work, and that dream score is yours!



Manager
Joined: 09 Oct 2015
Posts: 221

Re: The average (arithmetic mean) of 10 distinct odd integers in a set is
[#permalink]
Show Tags
10 Aug 2017, 03:01
Bunuel can you please help us in solving this in a systematic approach



Manager
Joined: 07 Jan 2015
Posts: 67
Location: United States
GPA: 3.4
WE: Engineering (Manufacturing)

Re: The average (arithmetic mean) of 10 distinct odd integers in a set is
[#permalink]
Show Tags
10 Aug 2017, 03:09
I really hope there is a fast way as compared to the case method that seems a longer method



Current Student
Joined: 22 Sep 2016
Posts: 186
Location: India
GPA: 4

Re: The average (arithmetic mean) of 10 distinct odd integers in a set is
[#permalink]
Show Tags
18 Aug 2017, 21:42
Bunuel wrote: The average (arithmetic mean) of 10 distinct odd integers in a set is 55. What is the median of these 10 integers?
(1) The largest integer is 65. (2) The smallest integer is 41. Hey Bunuel , I took the long road and evaluated the values. Is there an algebraic approach/ a more logical approach to this? It took me 4 minutes to do this! :(
_________________
Desperately need 'KUDOS' !!



Intern
Joined: 02 Jul 2017
Posts: 11

Re: The average (arithmetic mean) of 10 distinct odd integers in a set is
[#permalink]
Show Tags
18 Aug 2017, 22:16
Sum = AVG*number of terms (n) Sum of the sequence =10(first term +last term)/2 using the first term/ last term we can find the median using arithmetic progression Sent from my XT1706 using GMAT Club Forum mobile app



Intern
Joined: 02 Jul 2017
Posts: 11

Re: The average (arithmetic mean) of 10 distinct odd integers in a set is
[#permalink]
Show Tags
18 Aug 2017, 22:20
Bunuel wrote: The average (arithmetic mean) of 10 distinct odd integers in a set is 55. What is the median of these 10 integers?
(1) The largest integer is 65. (2) The smallest integer is 41. Is this data sufficiency question Sent from my XT1706 using GMAT Club Forum mobile app



Math Expert
Joined: 02 Sep 2009
Posts: 49300

Re: The average (arithmetic mean) of 10 distinct odd integers in a set is
[#permalink]
Show Tags
19 Aug 2017, 03:17
Jagdishvenkat wrote: Bunuel wrote: The average (arithmetic mean) of 10 distinct odd integers in a set is 55. What is the median of these 10 integers?
(1) The largest integer is 65. (2) The smallest integer is 41. Is this data sufficiency question Sent from my XT1706 using GMAT Club Forum mobile appYes, this is a data sufficiency question. Options for DS questions are always the same. The data sufficiency problem consists of a question and two statements, labeled (1) and (2), in which certain data are given. You have to decide whether the data given in the statements are sufficient for answering the question. Using the data given in the statements, plus your knowledge of mathematics and everyday facts (such as the number of days in July or the meaning of the word counterclockwise), you must indicate whether— A. Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient to answer the question asked. B. Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient to answer the question asked. C. BOTH statements (1) and (2) TOGETHER are sufficient to answer the question asked, but NEITHER statement ALONE is sufficient to answer the question asked. D. EACH statement ALONE is sufficient to answer the question asked. E. Statements (1) and (2) TOGETHER are NOT sufficient to answer the question asked, and additional data specific to the problem are needed. I suggest you to go through the following posts: ALL YOU NEED FOR QUANT. Ultimate GMAT Quantitative MegathreadHope this helps.
_________________
New to the Math Forum? Please read this: Ultimate GMAT Quantitative Megathread  All You Need for Quant  PLEASE READ AND FOLLOW: 12 Rules for Posting!!! Resources: GMAT Math Book  Triangles  Polygons  Coordinate Geometry  Factorials  Circles  Number Theory  Remainders; 8. Overlapping Sets  PDF of Math Book; 10. Remainders  GMAT Prep Software Analysis  SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS)  Tricky questions from previous years.
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? Extrahard Quant Tests with Brilliant Analytics



Manager
Joined: 10 Sep 2015
Posts: 66
Location: India
Concentration: Finance, Human Resources
GPA: 4

Re: The average (arithmetic mean) of 10 distinct odd integers in a set is
[#permalink]
Show Tags
07 Sep 2017, 01:55
Is there any shorter way to do it instead of writing all the possible numbers.



Manager
Joined: 14 Jun 2016
Posts: 66
Location: India
WE: Engineering (Manufacturing)

Re: The average (arithmetic mean) of 10 distinct odd integers in a set is
[#permalink]
Show Tags
09 Nov 2017, 09:17
asthagupta wrote: Is there any shorter way to do it instead of writing all the possible numbers. Hi Bunuel, Can u please post the shortcut solution...thanks
_________________
If you appreciate my post then please click +1Kudos




Re: The average (arithmetic mean) of 10 distinct odd integers in a set is &nbs
[#permalink]
09 Nov 2017, 09:17






