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• ### $450 Tuition Credit & Official CAT Packs FREE November 15, 2018 November 15, 2018 10:00 PM MST 11:00 PM MST EMPOWERgmat is giving away the complete Official GMAT Exam Pack collection worth$100 with the 3 Month Pack ($299) # What is the average (arithmetic mean) of x1,x2,x3,x4,x5,x6 ?  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics Author Message TAGS: ### Hide Tags Retired Moderator Joined: 29 Apr 2015 Posts: 846 Location: Switzerland Concentration: Economics, Finance Schools: LBS MIF '19 WE: Asset Management (Investment Banking) What is the average (arithmetic mean) of x1,x2,x3,x4,x5,x6 ? [#permalink] ### Show Tags Updated on: 18 May 2015, 08:01 00:00 Difficulty: 25% (medium) Question Stats: 77% (01:31) correct 23% (01:28) wrong based on 109 sessions ### HideShow timer Statistics What is the average (arithmetic mean) of $$x_1$$, $$x_2$$, $$x_3$$, $$x_4$$, $$x_5$$, $$x_6$$ ? (1) The average of $$x_1$$, $$x_2$$, $$x_3$$, $$x_4$$ is 28. (2) The average of $$x_4$$, $$x_5$$, $$x_6$$ is 21. _________________ Saving was yesterday, heat up the gmatclub.forum's sentiment by spending KUDOS! PS Please send me PM if I do not respond to your question within 24 hours. Originally posted by reto on 17 May 2015, 09:10. Last edited by reto on 18 May 2015, 08:01, edited 2 times in total. EMPOWERgmat Instructor Status: GMAT Assassin/Co-Founder Affiliations: EMPOWERgmat Joined: 19 Dec 2014 Posts: 12852 Location: United States (CA) GMAT 1: 800 Q51 V49 GRE 1: Q170 V170 Re: What is the average (arithmetic mean) of x1,x2,x3,x4,x5,x6 ? [#permalink] ### Show Tags 17 May 2015, 11:26 Hi reto, The formatting of this question is unclear. Is the question referring to 6 different variables (using subscript) or is it referring to 1 variable with 6 different exponents? GMAT assassins aren't born, they're made, Rich _________________ 760+: Learn What GMAT Assassins Do to Score at the Highest Levels Contact Rich at: Rich.C@empowergmat.com # Rich Cohen Co-Founder & GMAT Assassin Special Offer: Save$75 + GMAT Club Tests Free
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Re: What is the average (arithmetic mean) of x1,x2,x3,x4,x5,x6 ?  [#permalink]

### Show Tags

17 May 2015, 19:57
1
reto wrote:
What is the average (arithmetic mean) of x1,x2,x3,x4,x5,x6 ?

(1) The average of x1,x2,x3,x4 is 28.
(2) The average of x4,x5,x6 is 21.

Given 6 Numbers : $$x_1,x_2,x_3,x_4,x_5,x_6$$ , what is average of these 6 numbers ?

(1) The average of $$x_1,x_2,x_3,x_4$$ is 28.
no info about $$x_5,x_6$$ . NS
(2) The average of $$x_4,x_5,x_6$$ is 21.
no info about $$x_1,x_2,x_3$$ . NS

Together :
Brute force approach(we know that $$x_4$$ is not known so answer is E but lets see why still insufficient)
$$x_1+x_2+x_3+x_4 = 28*4=112$$
and
$$x_4+x_5+x_6=21*3=63$$

So, $$x_1+x_2+x_3+x_4 +x_5 +x_6 = 175-x_4$$
Average= $$\frac{x_1+x_2+x_3+x_4 +x_5 +x_6}{6} = \frac{175-x_4}{6}$$
we do not know $$x_4$$ (it can be 0, or any other value) so the answer is E .
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Re: What is the average (arithmetic mean) of x1,x2,x3,x4,x5,x6 ?  [#permalink]

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21 Dec 2016, 15:55
Here is my solution to this one =>

To get the mean => We need the sum=> x1+x2+...x6

Statement 1=>
We have x1+x2+x3+x4
But er don't know the values of x5 and x6.
Hence insufficient

Statement 2=>
x4+x5+x6
Again insufficient for similar reasons

Combing the two statements =>

x1+x2+x3+x4 = 112
x4+x5+x6
No clue of x4
Hence insufficient

Hence E

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Re: What is the average (arithmetic mean) of x1,x2,x3,x4,x5,x6 ?  [#permalink]

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17 Dec 2017, 12:35
If I think of St 1) x1 ...x4 = 28*4 = 112

St 2) x4+x5..x6 = 21*3 = 63

If i combine and subtract one total from other - the difference (49) is x 4 (which is the overlap)

So we get: x1 + x2 + x3 + 49 + x5 + x6 -->now 112 - 49 = x1 + x2 + x3 and 63 -49 = x5 + x6

Thus we can divide the totals by 6.

Would like to know why E is the answer, and what is wrong with my logic
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Re: What is the average (arithmetic mean) of x1,x2,x3,x4,x5,x6 ?  [#permalink]

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17 Dec 2017, 20:56
If I think of St 1) x1 ...x4 = 28*4 = 112

St 2) x4+x5..x6 = 21*3 = 63

If i combine and subtract one total from other - the difference (49) is x 4 (which is the overlap)

So we get: x1 + x2 + x3 + 49 + x5 + x6 -->now 112 - 49 = x1 + x2 + x3 and 63 -49 = x5 + x6

Thus we can divide the totals by 6.

Would like to know why E is the answer, and what is wrong with my logic

Hi

So your first equation is: x1+x2+x3+x4 = 112
and your second equn is: x4+x5+x6 = 63

If you add the above two equations, you will get: x1+x2+x3+x4+x5+x6+x4 = 175 Or Total Sum+x4 = 175. Since we dont know x4, we cant find the total sum

Or instead of adding if we subtract the above two equations, x1+x2+x3-x5-x6 = 49. How does it give us the total sum? or how does it give us the value of x4? It doesnt. It only tells us that x4 will be subtracted and thus eliminated, and we are left with x1+x2+x3-x5-x6.. this doesnt help us to get the required sum at all.
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Re: What is the average (arithmetic mean) of x1,x2,x3,x4,x5,x6 ?  [#permalink]

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28 May 2018, 22:46
amanvermagmat wrote:
If I think of St 1) x1 ...x4 = 28*4 = 112

St 2) x4+x5..x6 = 21*3 = 63

If i combine and subtract one total from other - the difference (49) is x 4 (which is the overlap)

So we get: x1 + x2 + x3 + 49 + x5 + x6 -->now 112 - 49 = x1 + x2 + x3 and 63 -49 = x5 + x6

Thus we can divide the totals by 6.

Would like to know why E is the answer, and what is wrong with my logic

Hi

So your first equation is: x1+x2+x3+x4 = 112
and your second equn is: x4+x5+x6 = 63

If you add the above two equations, you will get: x1+x2+x3+x4+x5+x6+x4 = 175 Or Total Sum+x4 = 175. Since we dont know x4, we cant find the total sum

Or instead of adding if we subtract the above two equations, x1+x2+x3-x5-x6 = 49. How does it give us the total sum? or how does it give us the value of x4? It doesnt. It only tells us that x4 will be subtracted and thus eliminated, and we are left with x1+x2+x3-x5-x6.. this doesnt help us to get the required sum at all.

If we use both (i) and (ii), assuming x1 to x4, each the value is 28, so x4 = 28. If we know x4, then we can find x5 + x6 which is 35. Wouldnt this give us the total x1,x2,x3,x4,x5,x6 ?
Re: What is the average (arithmetic mean) of x1,x2,x3,x4,x5,x6 ? &nbs [#permalink] 28 May 2018, 22:46
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