January 19, 2019 January 19, 2019 07:00 AM PST 09:00 AM PST Aiming to score 760+? Attend this FREE session to learn how to Define your GMAT Strategy, Create your Study Plan and Master the Core Skills to excel on the GMAT. January 20, 2019 January 20, 2019 07:00 AM PST 07:00 AM PST Get personalized insights on how to achieve your Target Quant Score.
Author 
Message 
TAGS:

Hide Tags

Math Expert
Joined: 02 Sep 2009
Posts: 52279

If the average (arithmetic mean) of seven unequal numbers is 20, what
[#permalink]
Show Tags
25 Oct 2018, 01:25
Question Stats:
61% (01:27) correct 39% (01:02) wrong based on 57 sessions
HideShow timer Statistics



Intern
Joined: 05 Jan 2017
Posts: 40

If the average (arithmetic mean) of seven unequal numbers is 20, what
[#permalink]
Show Tags
25 Oct 2018, 01:37
(seven nos)/7 =20 =>total sum = 140 let x be median, 1) 1/6 (140x) = 120 => 140= 7x => x= 20 > median 2) 140x=120 =>x=20 > median EACH statement ALONE is sufficient hence (D)
_________________
 Kudos if my post helps!



examPAL Representative
Joined: 07 Dec 2017
Posts: 868

If the average (arithmetic mean) of seven unequal numbers is 20, what
[#permalink]
Show Tags
Updated on: 26 Oct 2018, 04:27
1) From the data, we can create an equation with one variable (median*6=(140median)/6): one equation, one variable  definitely solvable! this works for both the set 17,18,19,20,21,22,23 (median 20, average 20, 20*6=120) and for the set 13,18,19,21,22,23,24 (median 21, average 20, 21*6=146). Insufficient! 2) This means that the sum of the other 6 numbers is 20 (120/6=20), and we already know the overall average is 20, meaning the median must be 20 as well (same average+same average=same average). Sufficient! Answer D!
_________________
Sign up for 7day free trial



examPAL Representative
Joined: 07 Dec 2017
Posts: 868

If the average (arithmetic mean) of seven unequal numbers is 20, what
[#permalink]
Show Tags
Updated on: 26 Oct 2018, 04:30
_shashank_shekhar_ wrote: (seven nos)/7 =20 =>total sum = 140
let x be median, 1) 1/6 (140x) = 120 => 140= 7x => x= 20 > median
2) 140x=120 =>x=20 > median
EACH statement ALONE is sufficient hence (D) 1) is sufficient, but the solution is still not entirely accurate. The mistake is here: _shashank_shekhar_ wrote: 1/6 (140x) = 120 Nothing tells us that the right side of the equation has to equal 120! It could equal less (if the median is more than 20) or more (if the median is less than 20).
_________________
Sign up for 7day free trial



Intern
Joined: 05 Jan 2017
Posts: 40

If the average (arithmetic mean) of seven unequal numbers is 20, what
[#permalink]
Show Tags
25 Oct 2018, 04:03
DavidTutorexamPAL wrote: _shashank_shekhar_ wrote: (seven nos)/7 =20 =>total sum = 140
let x be median, 1) 1/6 (140x) = 120 => 140= 7x => x= 20 > median
2) 140x=120 =>x=20 > median
EACH statement ALONE is sufficient hence (D) 1) is insufficient. The mistake is here: _shashank_shekhar_ wrote: 1/6 (140x) = 120 Nothing tells us that the right side of the equation has to equal 120! It could equal less (if the median is more than 20) or more (if the median is less than 20). See my answer above for an example. Thanks for the clarification DavidTutorexamPAL . Seems like I made mistake in hurry
_________________
 Kudos if my post helps!



examPAL Representative
Joined: 07 Dec 2017
Posts: 868

If the average (arithmetic mean) of seven unequal numbers is 20, what
[#permalink]
Show Tags
Updated on: 26 Oct 2018, 04:32
_shashank_shekhar_ wrote: DavidTutorexamPAL wrote: _shashank_shekhar_ wrote: (seven nos)/7 =20 =>total sum = 140
let x be median, 1) 1/6 (140x) = 120 => 140= 7x => x= 20 > median
2) 140x=120 =>x=20 > median
EACH statement ALONE is sufficient hence (D) 1) is insufficient. The mistake is here: _shashank_shekhar_ wrote: 1/6 (140x) = 120 Nothing tells us that the right side of the equation has to equal 120! It could equal less (if the median is more than 20) or more (if the median is less than 20). See my answer above for an example. Thanks for the clarification DavidTutorexamPAL . Seems like I made mistake in hurry @shashank_shekhar I made mistake and corrected my above post, please view
_________________
Sign up for 7day free trial



eGMAT Representative
Joined: 04 Jan 2015
Posts: 2455

Re: If the average (arithmetic mean) of seven unequal numbers is 20, what
[#permalink]
Show Tags
25 Oct 2018, 05:30
Solution Given:• The average of 7 unequal numbers = 20 To find:• The median of these numbers Approach and Working: • Sum of the seven numbers = 20 * 7 = 140 Analysing Statement 1• Given, median = \(\frac{1}{6}\) * (sum of the seven numbers – median)
o Implies, \(median * (1 + \frac{1}{6}) = \frac{1}{6} * 140\) • Thus, median = \(\frac{140}{7} = 20\) Therefore, Statement 1 alone is sufficient to answer this question. Analysing Statement 2• Sum of the seven numbers – median = 120
o Implies, median = 140 120 =20 Therefore, Statement 2 is alone sufficient to answer this question. Hence, the correct answer is Option D. Answer: D
_________________
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  Remainders1  Remainders2 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: 04 Sep 2018
Posts: 9

Re: If the average (arithmetic mean) of seven unequal numbers is 20, what
[#permalink]
Show Tags
25 Oct 2018, 05:37
Bunuel wrote: If the average (arithmetic mean) of seven unequal numbers is 20, what is the median of these numbers?
(1) The median of the seven numbers is equal to 1/6 of the sum of the six numbers other than the median. (2) The sum of the six numbers other than the median is equal to 120. This is my first post so I do not know if I am doing it in the right way: But I also would say that the answer is (D) (1) => let m be the median then m = (140  m)/6  Hence m=20, (sufficient) (2) => let m be the median then 7x20 = 140 => 140  120 = 20 => m = 20 (sufficient)



Intern
Joined: 25 Jul 2018
Posts: 11

If the average (arithmetic mean) of seven unequal numbers is 20, what
[#permalink]
Show Tags
25 Oct 2018, 07:14
Prompt: 7 numbers avg.=20
S1: M=1/6*(sum of 7 numbers  median number) sum of 7 numbers from prompt: 7*20=140 ; M=1/6*140  1/6*M 7/6M=140/6 > 7M=140 ; M=20 . sufficient
S2: sum of 6 other than median = 120 ; sum of all 7 = 140 > difference must be median= 20 . sufficient
Since both statements yield the same result i guess D is the answer.
A general question: if both of our solutions yield the same results, it this a indicator that D must be right? Pls tell me if my reasoning is wrong.



Manager
Joined: 15 Feb 2017
Posts: 244

Re: If the average (arithmetic mean) of seven unequal numbers is 20, what
[#permalink]
Show Tags
25 Oct 2018, 08:29
Bunuel wrote: If the average (arithmetic mean) of seven unequal numbers is 20, what is the median of these numbers?
(1) The median of the seven numbers is equal to 1/6 of the sum of the six numbers other than the median. (2) The sum of the six numbers other than the median is equal to 120. Attachment:
IMG_20181025_215503.jpg [ 27.11 KiB  Viewed 429 times ]
Sent from my Lenovo K33a42 using GMAT Club Forum mobile app
_________________
IMPOSSIBLE IS JUST AN OPINION



Intern
Joined: 17 Apr 2018
Posts: 21
Location: Italy
Concentration: General Management, Entrepreneurship
GPA: 3.75

If the average (arithmetic mean) of seven unequal numbers is 20, what
[#permalink]
Show Tags
26 Oct 2018, 00:28
Bunuel wrote: If the average (arithmetic mean) of seven unequal numbers is 20, what is the median of these numbers?
(1) The median of the seven numbers is equal to 1/6 of the sum of the six numbers other than the median. (2) The sum of the six numbers other than the median is equal to 120. Time needed: 1min 43s Datas:From the question stem, we know: a) The sum of all the numbers(20*7=140) Process of elimination:1)We know that \(\frac{(sumM)}{6}=M\) , where M=median. Having a single variable equation, we can find M. Sufficient. Eliminate C and E. 2)Using (a), we can compute the median M. Sufficient. Eliminate A and B. Correct answer: DDavidTutorexamPAL Sir, are you sure your solution above is correct? Because: 1)21*6= 126 2) We are asked for the specific set with the characteristics given in statement 1. Thus, I think we can compute the expression I and Egmat came up with. Of course, this is not to attack you in any way, but if you were to agree with me, could you change your solution, please? I think it could mislead some distracted users
_________________
Give kudos if you found this post helpful :D
My GMAT history: 1st GMATPrep: 620 (Q46, V29) 2nd GMATPrep: 700(Q46, V40) 3rd GMATPrep: 720(Q49, V38)



Intern
Joined: 05 Jan 2017
Posts: 40

Re: If the average (arithmetic mean) of seven unequal numbers is 20, what
[#permalink]
Show Tags
26 Oct 2018, 00:58
Hi Experts, I am bit confused here. Can someone please explain the below mentioned statement. BunuelEgmatQuantExpert DavidTutorexamPAL1) this works for both the set 17,18,19,20,21,22,23 (median 20, average 20, 20*6=120) and for the set 13,18,19,21,22,23,24 (median 21, average 20, 21*6=146). Thanks.
_________________
 Kudos if my post helps!



examPAL Representative
Joined: 07 Dec 2017
Posts: 868

If the average (arithmetic mean) of seven unequal numbers is 20, what
[#permalink]
Show Tags
Updated on: 26 Oct 2018, 04:35
_shashank_shekhar_ wrote: Hi Experts, I am bit confused here. Can someone please explain the below mentioned statement. BunuelEgmatQuantExpert DavidTutorexamPAL1) this works for both the set 17,18,19,20,21,22,23 (median 20, average 20, 20*6=120) and for the set 13,18,19,21,22,23,24 (median 21, average 20, 21*6=146). Thanks. The above example was erroneous  my mistake, corrected it.
_________________
Sign up for 7day free trial



examPAL Representative
Joined: 07 Dec 2017
Posts: 868

Re: If the average (arithmetic mean) of seven unequal numbers is 20, what
[#permalink]
Show Tags
26 Oct 2018, 04:23
Italiandrummer97 wrote: Bunuel wrote: If the average (arithmetic mean) of seven unequal numbers is 20, what is the median of these numbers?
(1) The median of the seven numbers is equal to 1/6 of the sum of the six numbers other than the median. (2) The sum of the six numbers other than the median is equal to 120. Time needed: 1min 43s Datas:From the question stem, we know: a) The sum of all the numbers(20*7=140) Process of elimination:1)We know that \(\frac{(sumM)}{6}=M\) , where M=median. Having a single variable equation, we can find M. Sufficient. Eliminate C and E. 2)Using (a), we can compute the median M. Sufficient. Eliminate A and B. Correct answer: DDavidTutorexamPAL Sir, are you sure your solution above is correct? Because: 1)21*6= 126 2) We are asked for the specific set with the characteristics given in statement 1. Thus, I think we can compute the expression I and Egmat came up with. Of course, this is not to attack you in any way, but if you were to agree with me, could you change your solution, please? I think it could mislead some distracted users You are correct my friend! Thank you for the correction. I have changed my answer accordingly.
_________________
Sign up for 7day free trial




Re: If the average (arithmetic mean) of seven unequal numbers is 20, what &nbs
[#permalink]
26 Oct 2018, 04:23






