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# If the average arithmetic mean of the five numbers x, 7, 2,

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Intern
Joined: 11 Feb 2019
Posts: 11
Re: If the average arithmetic mean of the five numbers x, 7, 2,  [#permalink]

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28 Mar 2019, 08:04
Does this question even need any of the answer choices?

As in, this question can be answered without using either of the two options.

Is there any other question type where value of x needs to be calculated in series where the answer choices really are needed?

Bunuel wrote:
vitamingmat wrote:
satishreddy wrote:
if the average arithmetic mean of the five numbers X, 7,2,16.11 is equal to the median of five numbers, what is the value of X

1) 7<X<11
2) X is the median of five numbers

first statement is definitely sufficient, but in the second statement, if X is the median, it can take three numbers, 10. 9, 8, so ...how is it sufficient, i might be missing some basic point here,,,,so need help,,,,as the second statement is also sufficient for this problem

I am not convinced with the above answers...

from 1 ) 7 < X< 11 === > X is like 7.1, or 7.2 or 7.5 or 8,8.1 or 9 0r 9.5 ...

there are so many possibilites so i can not take only 8,9,10 as X

so i can not decide from 1

from 2) X is the median of five numbers then === > X, 7,2,16,11 ....

==> how can i arrange if i dont know the value of X in either descending or ascending..

so from the both also it wont be possible to get the ans i believe...
So ans E ...

Do let me know if i am wrong....

There is one more thing we know from the stem: "the average arithmetic mean of the five numbers x, 7, 2, 16, 11 is equal to the median of five numbers" --> $$\frac{x+2+7+11+16}{5}=median$$. As there are odd number of terms then the median is the middle term when arranged in ascending (or descending) order but we don't know which one (median could be x, 7 or 11).

(1) 7 < x < 11 --> when ordered we'll get 2, 7, x, 11, 16 --> $$\frac{x+2+7+11+16}{5}=median=x$$ --> $$\frac{x+36}{5}=x$$ --> $$x=9$$. Sufficient.

(2) x is the median of five numbers --> the same info as above: $$\frac{x+2+7+11+16}{5}=median=x$$ --> $$\frac{x+36}{5}=x$$ --> $$x=9$$. Sufficient.

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Re: If the average arithmetic mean of the five numbers x, 7, 2,  [#permalink]

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28 Mar 2019, 08:27
prekshita wrote:
Does this question even need any of the answer choices?

As in, this question can be answered without using either of the two options.

Is there any other question type where value of x needs to be calculated in series where the answer choices really are needed?

It is not possible. Without the statements, you CANNOT get a single solution. X can be anything! Statements are given either to find a solution or to prove something asked in the question.

P.S: By taking your statement into consideration, why would the test takers give such a question where the statements are useless?
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Concentration: Technology, Real Estate
Re: If the average arithmetic mean of the five numbers x, 7, 2,  [#permalink]

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28 Mar 2019, 08:39
same equation will be formed in both cases hence option d
Re: If the average arithmetic mean of the five numbers x, 7, 2,   [#permalink] 28 Mar 2019, 08:39

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