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# The average of six number is 30.

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The average of six number is 30. [#permalink]  15 Dec 2011, 07:55
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Difficulty:

55% (medium)

Question Stats:

18% (01:59) correct 82% (01:09) wrong based on 74 sessions
The average of six numbers is 30. If the average of first four is 25 and that of last three is 35, the fourth number is?

a) 25 b) 30 c) 35 d) 40

[Reveal] Spoiler: OA
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Re: The average of six number is 30. [#permalink]  15 Dec 2011, 08:12
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newmoon wrote:
The average of six numbers is 30. If the average of first four is 25 and that of last three is 35, the fourth number is?

a) 25 b) 30 c) 35 d) 40

My answer is A. Here is the explanation -
The average of first four is 25 => total = 25*4 = 100
The average of last three is 35 => total = 35*3 = 105
The average of six is 30 => total = 30*6 = 180

So we can form an equation - assuming fourth number = x
100+105-x = 180
Hence x = 25.

Cheers!
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Re: The average of six number is 30. [#permalink]  15 Dec 2011, 08:20
Thanks Capricorn369. I get A too. The answer provided may be is wrong. Lets see what other people come up with.
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Re: The average of six number is 30. [#permalink]  15 Dec 2011, 08:22
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Expert's post
Hi @newmoon,

What's the source of this question? I first noticed that, unlike a typical GMAT question, this question only has 4 answer choices. Also, the question does not specify the order of the numbers, so finding the fourth number could be ambiguous. Lastly, I get an answer different than the OA.

If we assume the 4th number is the one that exists in both sets, then we could solve the question as follows
1. The first four numbers have an average of 25, therefore their sum must be 100 (because 100/4 = 25)
2. The last three numbers have an average of 35, therefore their sum must be 105
3. All six numbers have an average of 30, therefore their sum must be 180

Let's call our six numbers: A, B, C, D, E, F, G
A + B + C + D = 100
D + E + F = 105
A + B + C + D + E + F = 180

using substitution we get:
100 + 105 - D = 180 (we have to subtract D because it was in both sets)
205 - D = 180
D = 25
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Re: The average of six number is 30. [#permalink]  15 Dec 2011, 09:00
I've just re-read the question and it is true, answer is not 35, as I thought, I'm ediding to avoid confussion. Regards!!

Last edited by cuet16 on 15 Dec 2011, 14:11, edited 1 time in total.
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Re: The average of six number is 30. [#permalink]  15 Dec 2011, 09:13
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Lets say numbers are n1, n2, n3, n4, n5, n6

Average of six numbers is 30. n1+n2+n3+n4+n5+n6 = 30*6 = 180
Average of first four is 25. n1+n2+n3+n4 = 25*4 = 100

From the above two statements, n5+n6 = 80

Average of last three is 35. n4+n5+n6 = 35*3 = 105

So n4 = 105 - 80 =25
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Re: The average of six number is 30. [#permalink]  15 Dec 2011, 10:18
6 numbers = a,b,c,d,e,f,

(a+b+c+d+e+f/6)=30

a+b+c+d+e+f=180

(a+b+c+d)/4=25

So,
(a+b+c+d)=100

(d+e+f)/3=35

So, d+e+f=105

so the fourth number(d) is :{[(a+b+c+d)+(d+e+f)]-(a+b+c+d+e+f)} = d = (100+105)-180
i.e 25

The answer given as 35 is def wrong.Change it to A (25)
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Re: The average of six number is 30.   [#permalink] 15 Dec 2011, 10:18
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# The average of six number is 30.

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