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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, 02:25
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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, 02:37
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, 05:27
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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Originally posted by DavidTutorexamPAL on 25 Oct 2018, 04:52.
Last edited by DavidTutorexamPAL on 26 Oct 2018, 05:27, edited 2 times in total.
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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, 05:30
_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).
_________________

Originally posted by DavidTutorexamPAL on 25 Oct 2018, 04:54.
Last edited by DavidTutorexamPAL on 26 Oct 2018, 05:30, edited 1 time in total.
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If the average (arithmetic mean) of seven unequal numbers is 20, what  [#permalink]

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25 Oct 2018, 05:03
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, 05:32
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

@shashank_shekhar I made mistake and corrected my above post, please view
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Originally posted by DavidTutorexamPAL on 25 Oct 2018, 05:12.
Last edited by DavidTutorexamPAL on 26 Oct 2018, 05:32, edited 1 time in total.
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Posts: 3230
Re: If the average (arithmetic mean) of seven unequal numbers is 20, what  [#permalink]

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25 Oct 2018, 06:30

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.

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

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25 Oct 2018, 06:37
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)
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If the average (arithmetic mean) of seven unequal numbers is 20, what  [#permalink]

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25 Oct 2018, 08:14
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.
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Re: If the average (arithmetic mean) of seven unequal numbers is 20, what  [#permalink]

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25 Oct 2018, 09:29
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.

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

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26 Oct 2018, 01:28
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.

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

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26 Oct 2018, 01:58
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.
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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, 05:35
_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.
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Originally posted by DavidTutorexamPAL on 26 Oct 2018, 05:14.
Last edited by DavidTutorexamPAL on 26 Oct 2018, 05:35, edited 1 time in total.
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Re: If the average (arithmetic mean) of seven unequal numbers is 20, what  [#permalink]

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26 Oct 2018, 05:23
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   [#permalink] 26 Oct 2018, 05:23
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