November 22, 2018 November 22, 2018 10:00 PM PST 11:00 PM PST Mark your calendars  All GMAT Club Tests are free and open November 22nd to celebrate Thanksgiving Day! Access will be available from 0:01 AM to 11:59 PM, Pacific Time (USA) November 23, 2018 November 23, 2018 10:00 PM PST 11:00 PM PST Practice the one most important Quant section  Integer properties, and rapidly improve your skills.
Author 
Message 
TAGS:

Hide Tags

Manager
Joined: 20 Sep 2004
Posts: 62

A certain list consists of 3 different numbers. Does the med
[#permalink]
Show Tags
Updated on: 14 Nov 2013, 01:16
Question Stats:
57% (02:03) correct 43% (02:13) wrong based on 2028 sessions
HideShow timer Statistics
A certain list consists of 3 different numbers. Does the median of the 3 numbers equal the average (arithmetic mean) of the 3 numbers? (1) The range of the 3 numbers is equal to twice the difference between the greatest number and the median. (2) The sum of the 3 numbers is equal to 3 times one of the numbers.
Official Answer and Stats are available only to registered users. Register/ Login.
Originally posted by karovd on 30 Oct 2004, 10:45.
Last edited by Bunuel on 14 Nov 2013, 01:16, edited 1 time in total.
Renamed the topic, edited the question and added the OA.




Math Expert
Joined: 02 Sep 2009
Posts: 50712

Re: A certain list consists of 3 different numbers. Does the med
[#permalink]
Show Tags
30 Jul 2016, 06:23
HBSdetermined wrote: Bunuel plz help in the second statement how is that sufficient most of the explanations above are cryptic! A certain list consists of 3 different numbers. Does the median of the 3 numbers equal the average (arithmetic mean) of the 3 numbers?Say the three numbers are x, y, and x, where x < y < z. The median would be y and the average would be (x + y + z)/3. So, the question asks whether y = (x + y + z)/3, or whether 2y = x + z. (1) The range of the 3 numbers is equal to twice the difference between the greatest number and the median > the range is the difference between the largest and the smallest numbers of the set, so in our case z  x. We are given that z  x = 2(z  y) > 2y = x + z. Sufficient. (2) The sum of the 3 numbers is equal to 3 times one of the numbers > the sum cannot be 3 times smallest numbers or 3 times largest number, thus x + y + z = 3y > x + z = 2y. Sufficient. Answer: D. Hope it's clear.
_________________
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: 09 Jan 2013
Posts: 76
Concentration: Entrepreneurship, Sustainability
GMAT 1: 650 Q45 V34 GMAT 2: 740 Q51 V39
GPA: 3.76
WE: Other (Pharmaceuticals and Biotech)

A certain list consists of 3 different numbers. Does the med
[#permalink]
Show Tags
23 May 2015, 07:42
Question: Is median = mean? St1: tells us that the median is equidistant from the other two numbers on the number line. Thus, median = mean. Sufficient. Attachment:
Untitled.png [ 1.06 KiB  Viewed 28016 times ]
St2: sum of 3 no.s = 3* (one of the numbers) we know that sum of 3 no.s = 3* (mean) Thus, mean = one of the numbers. Now, as long as the 3 nos are distinct. the largest and smallest nos cannot be equal to mean. Thus, median = mean. Sufficient. Answer D. press kudos if the graphical representation helps you.




GMAT Club Legend
Joined: 15 Dec 2003
Posts: 4180

Got D here
1) ascertains that diff b/w largestmedian and smallestmedian number is same and answer would be yes
2) the only "one" number which would be equivalent to the sum of the other 3 would be the median. Hence, "yes", mean = median
_________________
Best Regards,
Paul



Current Student
Joined: 25 Sep 2012
Posts: 246
Location: India
Concentration: Strategy, Marketing
GMAT 1: 660 Q49 V31 GMAT 2: 680 Q48 V34

Paul wrote: Got D here 1) ascertains that diff b/w largestmedian and smallestmedian number is same and answer would be yes 2) the only "one" number which would be equivalent to the sum of the other 3 would be the median. Hence, "yes", mean = median Wow..I didn't understand anything while solving. Even after reading your explanation I can fully understand this. Can anyone shed some light If we take the no. as x,y,z 1. zx = 2(zy) zx = 2z 2y 2yx = z Couldn't conclude anything 2. x+y+z = 3(x or y or z) I was not sure what to do ahead. But still kind of realized that it could be y



Intern
Joined: 06 Dec 2013
Posts: 5

Re: A certain list consists of 3 different numbers. Does the med
[#permalink]
Show Tags
22 May 2014, 23:38
Hi b2bt! Here is my train of thoughts: Median equals average when you have evenly spaced set of numbers. (1) tells you that, so sufficient. (2) if a is a multiplier and n1, n2, n3 = 1, 2, 3 than numbers in your (evenly spaced?) set can be represented as following: a*n1, a*n2, a*n3. Let's find their sum. an1+an2+an3= a(n1+n2+n3)= a(n1+n1+1+n1+2)= a(3n1+3)= 3a(n1+1)= 3a*n2, so sufficient



Current Student
Joined: 25 Sep 2012
Posts: 246
Location: India
Concentration: Strategy, Marketing
GMAT 1: 660 Q49 V31 GMAT 2: 680 Q48 V34

Re: A certain list consists of 3 different numbers. Does the med
[#permalink]
Show Tags
22 May 2014, 23:48
bogdanbond wrote: Hi b2bt! Here is my train of thoughts: Median equals average when you have evenly spaced set of numbers. (1) tells you that, so sufficient. (2) if a is a multiplier and n1, n2, n3 = 1, 2, 3 than numbers in your (evenly spaced?) set can be represented as following: a*n1, a*n2, a*n3. Let's find their sum. an1+an2+an3= a(n1+n2+n3)= a(n1+n1+1+n1+2)= a(3n1+3)= 3a(n1+1)= 3a*n2, so sufficient It took me a while but I understood! Thanks! I think I lack conceptual clarity here..



Manager
Joined: 23 Nov 2014
Posts: 56
Location: India
GPA: 3.14
WE: Sales (Consumer Products)

Re: A certain list consists of 3 different numbers. Does the med
[#permalink]
Show Tags
18 May 2015, 14:15
Bunuel, Could you please help with interpreting statement #2? Thanks



eGMAT Representative
Joined: 04 Jan 2015
Posts: 2203

Re: A certain list consists of 3 different numbers. Does the med
[#permalink]
Show Tags
18 May 2015, 20:57
avgroh wrote: Bunuel, Could you please help with interpreting statement #2? Thanks Hi avgroh, Let's assume three numbers {a, b, c} arranged in ascending order. In this case b will be the median. StatementIIStII tells that the sum of these three number is equal to 3 times one of the numbers. Let's take all the possible cases: 1. a + b + c = 3a i.e. 2a = b + c. However we know that a > b and a > c, therefore 2a > b + c. Thus we can reject this case. 2. a + b + c = 3c i.e. 2c = a + b. However we know that c < a and c < b, therefore 2c < a + b. Thus we can reject this case too. 3. a + b + c = 3b i.e. 2b = a + c. We know that b < a but b > c, thus this is the only possible case. Solving this would give us b = (a + c)/2 i.e. b is the mean of a & c. Since the only other number in the set is b, we can say that b is the mean of the set {a, b, c}. As b is also the median of this set we can definitely say that mean of the set = median of the set. Hence stII is sufficient to answer the question. StatementIAlso adding the explanation for StI here: StI tells us that the range of 3 numbers is twice the difference between the greatest number and the median. For the set {a, b, c} arranged in ascending order, range would be the difference between the greatest and the smallest number i.e. stI tells us that a  c = 2(a b) i.e. b = (a + c)/2 which again tells us that b is the mean of the numbers a & c. Since the only other number in the set is b, we can say that b is the mean of the set {a, b, c}. As b is also the median of this set we can definitely say that mean of the set = median of the set. Hence stI is sufficient to answer the question. Hope this helps Regards Harsh
_________________
Register for free sessions Number Properties  Algebra Quant Workshop
Success Stories Guillermo's Success Story  Carrie's Success Story
Ace GMAT quant Articles and Question to reach Q51  Question of the week
Must Read Articles Number Properties – Even Odd  LCM GCD  Statistics1  Statistics2 Word Problems – Percentage 1  Percentage 2  Time and Work 1  Time and Work 2  Time, Speed and Distance 1  Time, Speed and Distance 2 Advanced Topics Permutation and Combination 1  Permutation and Combination 2  Permutation and Combination 3  Probability Geometry Triangles 1  Triangles 2  Triangles 3  Common Mistakes in Geometry Algebra Wavy line  Inequalities Practice Questions Number Properties 1  Number Properties 2  Algebra 1  Geometry  Prime Numbers  Absolute value equations  Sets
 '4 out of Top 5' Instructors on gmatclub  70 point improvement guarantee  www.egmat.com



Intern
Joined: 22 Aug 2014
Posts: 49
GPA: 3.6

Re: A certain list consists of 3 different numbers. Does the med
[#permalink]
Show Tags
29 Jul 2015, 06:20
I think the solution provided in the OG is messed up for this question. Bunuel can you please check and tell



Current Student
Joined: 09 Aug 2015
Posts: 85
GPA: 2.3

A certain list consists of 3 different numbers. Does the med
[#permalink]
Show Tags
11 Aug 2015, 18:56
Heres how to translate statement #2 in two steps:
The sum of the 3 numbers is equal to 3 times one of the numbers
=> The (sum of the 3 numbers) divided by 3 is equal to one of the numbers => The mean is equal to one of the numbers
=> Mean can only be equal to the median # in an oddly sized set, sufficient



Manager
Joined: 11 Sep 2013
Posts: 157
Concentration: Finance, Finance

A certain list consists of 3 different numbers. Does the med
[#permalink]
Show Tags
Updated on: 30 Dec 2017, 05:38
My approach for statement 2
Take any number as "one of the numbers"
Let 5 is that number. So the sum is 5*3 = 15. The sum of other two numbers is 155 = 10 So, we get the following combinations of two other different numbers (1,9),(2,8), (3,7), (4,6) In all the cases median and mean is 5. Sufficient
Another approach(Logical) for 2
We know that sum of 3 numbers = 3* Average (one of the numbers is THE AVERAGE)
Now, since all the numbers are different, 2 other numbers will be smallest and largest number. So, that one number is the Median Sufficient.
Originally posted by Raihanuddin on 01 Sep 2015, 10:36.
Last edited by Raihanuddin on 30 Dec 2017, 05:38, edited 1 time in total.



Math Revolution GMAT Instructor
Joined: 16 Aug 2015
Posts: 6531
GPA: 3.82

A certain list consists of 3 different numbers. Does the med
[#permalink]
Show Tags
05 Sep 2015, 22:05
Forget conventional ways of solving math questions. In DS, Variable approach is the easiest and quickest way to find the answer without actually solving the problem. Remember equal number of variables and equations ensures a solution. A certain list consists of 3 different numbers. Does the median of the 3 numbers equal the average (arithmetic mean) of the 3 numbers? (1) The range of the 3 numbers is equal to twice the difference between the greatest number and the median. (2) The sum of the 3 numbers is equal to 3 times one of the numbers. ==> according to variable approach method, we have 3 variables listed a<M<b. Transforming the original condition and the question we have M=(a+M+b)/3? and thus 3M=a+M+b. Since this is same as 2), 2) itself is sufficient. Transforming again gives us 2M=a+b, and since a=2Mb > range=ba=b(2Mb)=2b2M=2(bM) is the same as 1), this is also sufficient. Therefore the answer is D.
_________________
MathRevolution: Finish GMAT Quant Section with 10 minutes to spare The oneandonly World’s First Variable Approach for DS and IVY Approach for PS with ease, speed and accuracy. "Only $99 for 3 month Online Course" "Free Resources30 day online access & Diagnostic Test" "Unlimited Access to over 120 free video lessons  try it yourself"



Director
Joined: 10 Mar 2013
Posts: 512
Location: Germany
Concentration: Finance, Entrepreneurship
GPA: 3.88
WE: Information Technology (Consulting)

A certain list consists of 3 different numbers. Does the med
[#permalink]
Show Tags
23 Sep 2015, 13:20
Solved it by picking some numbers : Median = Average in 2 cases: 1. Evenly spaced set of numbers 2. All numbers are equal 1. let's say our numbers are: 4,8,12 124=2(128) Ok, if it's not evenly spaced then use this case 2,5,7 > 72=/2(75) Sufficient 2. This statement tells us directly that all the numbers are equal Sufficient (D) Here we can pick some varriables in ascending order to check my solution: x + y + z =3x,(y − x) + (z − x) = 0 > y=x, z=x > y=z=x we'll get the same solution for all 3 cases =3x, 3z or 3y
_________________
When you’re up, your friends know who you are. When you’re down, you know who your friends are.
Share some Kudos, if my posts help you. Thank you !
800Score ONLY QUANT CAT1 51, CAT2 50, CAT3 50 GMAT PREP 670 MGMAT CAT 630 KAPLAN CAT 660



Intern
Joined: 21 Apr 2015
Posts: 5

A certain list consists of 3 different numbers. Does the med
[#permalink]
Show Tags
12 Oct 2015, 08:47
EgmatQuantExpert wrote: avgroh wrote: Bunuel, Could you please help with interpreting statement #2? Thanks Hi avgroh, Let's assume three numbers {a, b, c} arranged in ascending descending order. In this case b will be the median. StatementIIStII tells that the sum of these three number is equal to 3 times one of the numbers. Let's take all the possible cases: 1. a + b + c = 3a i.e. 2a = b + c. However we know that a > b and a > c, therefore 2a > b + c. Thus we can reject this case. 2. a + b + c = 3c i.e. 2c = a + b. However we know that c < a and c < b, therefore 2c < a + b. Thus we can reject this case too. 3. a + b + c = 3b i.e. 2b = a + c. We know that b < a but b > c, thus this is the only possible case. Solving this would give us b = (a + c)/2 i.e. b is the mean of a & c. Since the only other number in the set is b, we can say that b is the mean of the set {a, b, c}. As b is also the median of this set we can definitely say that mean of the set = median of the set. Hence stII is sufficient to answer the question. StatementIAlso adding the explanation for StI here: StI tells us that the range of 3 numbers is twice the difference between the greatest number and the median. For the set {a, b, c} arranged in ascending descending order, range would be the difference between the greatest and the smallest number i.e. stI tells us that a  c = 2(a b) i.e. b = (a + c)/2 which again tells us that b is the mean of the numbers a & c. Since the only other number in the set is b, we can say that b is the mean of the set {a, b, c}. As b is also the median of this set we can definitely say that mean of the set = median of the set. Hence stI is sufficient to answer the question. Hope this helps Regards Harsh Hi Harsh, I believe in the above statements you mean three numbers {a, b, c} arranged in descending order? Looks like a typo.



Intern
Joined: 16 Jul 2015
Posts: 41
GMAT 1: 580 Q37 V33 GMAT 2: 580 Q39 V31 GMAT 3: 560 Q40 V28 GMAT 4: 580 Q37 V32 GMAT 5: 680 Q45 V37 GMAT 6: 690 Q47 V37

Re: A certain list consists of 3 different numbers. Does the med
[#permalink]
Show Tags
06 Apr 2016, 12:36
Bunuel,please explain this question.Not able to understand how statement 2 is sufficient



Current Student
Joined: 20 Oct 2014
Posts: 38

Re: A certain list consists of 3 different numbers. Does the med
[#permalink]
Show Tags
07 Apr 2016, 07:29
karovd wrote: A certain list consists of 3 different numbers. Does the median of the 3 numbers equal the average (arithmetic mean) of the 3 numbers?
(1) The range of the 3 numbers is equal to twice the difference between the greatest number and the median. (2) The sum of the 3 numbers is equal to 3 times one of the numbers. Let the 3 numbers be x,y and z(in ascending order). From statement 1, we have, zx = 2(zy) or ,



Current Student
Joined: 20 Oct 2014
Posts: 38

Re: A certain list consists of 3 different numbers. Does the med
[#permalink]
Show Tags
07 Apr 2016, 07:33
karovd wrote: A certain list consists of 3 different numbers. Does the median of the 3 numbers equal the average (arithmetic mean) of the 3 numbers?
(1) The range of the 3 numbers is equal to twice the difference between the greatest number and the median. (2) The sum of the 3 numbers is equal to 3 times one of the numbers. Let the 3 numbers be x,y and z(in ascending order). From statement 1, we have, zx = 2(zy) or ,zx = 2z  2y or, y = (zx)/2. Thus, y (the median) is also the average. Hence statement 1 is sufficient. For statement 2, think of the given info conceptually. The sum of the 3 numbers cannot be equal to 3 times the highest or the lowest number. Either the 3 numbers have to be equal or the only other possibility is that the sum of the 3 numbers is equal to 3 times the middle number. Therefore, option (D) is correct.



Manager
Joined: 04 Feb 2012
Posts: 163
Location: India
Concentration: General Management, Strategy
GPA: 3.96
WE: Research (Pharmaceuticals and Biotech)

Re: A certain list consists of 3 different numbers. Does the med
[#permalink]
Show Tags
30 Jul 2016, 05:11
Bunuel plz help in the second statement how is that sufficient most of the explanations above are cryptic!



Manager
Joined: 04 Feb 2012
Posts: 163
Location: India
Concentration: General Management, Strategy
GPA: 3.96
WE: Research (Pharmaceuticals and Biotech)

Re: A certain list consists of 3 different numbers. Does the med
[#permalink]
Show Tags
31 Jul 2016, 00:08
Bunuel wrote: HBSdetermined wrote: Bunuel plz help in the second statement how is that sufficient most of the explanations above are cryptic! A certain list consists of 3 different numbers. Does the median of the 3 numbers equal the average (arithmetic mean) of the 3 numbers?(2) The sum of the 3 numbers is equal to 3 times one of the numbers > the sum cannot be 3 times smallest numbers or 3 times largest number, thus x + y + z = 3y > x + z = 2y. Sufficient. Bunuel Thanks, more than getting it right I have always gained a new perspectives with most of your explanations!




Re: A certain list consists of 3 different numbers. Does the med &nbs
[#permalink]
31 Jul 2016, 00:08



Go to page
1 2
Next
[ 32 posts ]



