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# If the average (arithmetic mean) of seven unequal numbers is 20, what

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If the average (arithmetic mean) of seven unequal numbers is 20, what  [#permalink]

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25 Oct 2018, 01:25
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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.

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If the average (arithmetic mean) of seven unequal numbers is 20, what  [#permalink]

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25 Oct 2018, 01:37
1
(seven nos)/7 =20
=>total sum = 140

let x be median,
1) 1/6 (140-x) = 120
=> 140= 7x
=> x= 20 -> median

2) 140-x=120
=>x=20 -> median

EACH statement ALONE is sufficient
hence (D)
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If the average (arithmetic mean) of seven unequal numbers is 20, what  [#permalink]

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Updated on: 26 Oct 2018, 04:27
1
1
1) From the data, we can create an equation with one variable (median*6=(140-median)/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!
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The best DEAL of the year has finally arrived! Save up to $320 on your GMAT course. Expires on Nov 24th. Originally posted by DavidTutorexamPAL on 25 Oct 2018, 03:52. Last edited by DavidTutorexamPAL on 26 Oct 2018, 04:27, edited 2 times in total. examPAL Representative Joined: 07 Dec 2017 Posts: 806 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 (140-x) = 120 => 140= 7x => x= 20 -> median 2) 140-x=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 (140-x) = 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). _________________ The best DEAL of the year has finally arrived! Save up to$320 on your GMAT course.

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Originally posted by DavidTutorexamPAL on 25 Oct 2018, 03:54.
Last edited by DavidTutorexamPAL on 26 Oct 2018, 04:30, edited 1 time in total.
Intern
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If the average (arithmetic mean) of seven unequal numbers is 20, what  [#permalink]

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25 Oct 2018, 04:03
DavidTutorexamPAL wrote:
_shashank_shekhar_ wrote:
(seven nos)/7 =20
=>total sum = 140

let x be median,
1) 1/6 (140-x) = 120
=> 140= 7x
=> x= 20 -> median

2) 140-x=120
=>x=20 -> median

EACH statement ALONE is sufficient
hence (D)

1) is insufficient. The mistake is here:

_shashank_shekhar_ wrote:
1/6 (140-x) = 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
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If the average (arithmetic mean) of seven unequal numbers is 20, what  [#permalink]

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Updated on: 26 Oct 2018, 04:32
1
_shashank_shekhar_ wrote:
DavidTutorexamPAL wrote:
_shashank_shekhar_ wrote:
(seven nos)/7 =20
=>total sum = 140

let x be median,
1) 1/6 (140-x) = 120
=> 140= 7x
=> x= 20 -> median

2) 140-x=120
=>x=20 -> median

EACH statement ALONE is sufficient
hence (D)

1) is insufficient. The mistake is here:

_shashank_shekhar_ wrote:
1/6 (140-x) = 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

_________________

The best DEAL of the year has finally arrived! Save up to $320 on your GMAT course. Expires on Nov 24th. Originally posted by DavidTutorexamPAL on 25 Oct 2018, 04:12. Last edited by DavidTutorexamPAL on 26 Oct 2018, 04:32, edited 1 time in total. e-GMAT Representative Joined: 04 Jan 2015 Posts: 2203 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 | Statistics-1 | Statistics-2 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.e-gmat.com Intern Joined: 04 Sep 2018 Posts: 4 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: 10 If the average (arithmetic mean) of seven unequal numbers is 20, what [#permalink] ### Show Tags 25 Oct 2018, 07:14 1 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: 134 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 341 times ] Sent from my Lenovo K33a42 using GMAT Club Forum mobile app _________________ IMPOSSIBLE IS JUST AN OPINION Intern Joined: 17 Apr 2018 Posts: 22 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 1 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 $$\frac{(sum-M)}{6}=M$$ , 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: D DavidTutorexamPAL 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 E-gmat 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. Bunuel EgmatQuantExpert DavidTutorexamPAL 1) 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: 806 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. Bunuel EgmatQuantExpert DavidTutorexamPAL 1) 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. _________________ The best DEAL of the year has finally arrived! Save up to$320 on your GMAT course.

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Originally posted by DavidTutorexamPAL on 26 Oct 2018, 04:14.
Last edited by DavidTutorexamPAL on 26 Oct 2018, 04:35, edited 1 time in total.
examPAL Representative
Joined: 07 Dec 2017
Posts: 806
Re: If the average (arithmetic mean) of seven unequal numbers is 20, what  [#permalink]

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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 $$\frac{(sum-M)}{6}=M$$ , 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.

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