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# In a certain performance of a 3-act play, the first act was 18 minutes

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Intern
Joined: 03 Dec 2010
Posts: 30
In a certain performance of a 3-act play, the first act was 18 minutes  [#permalink]

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06 Apr 2011, 11:22
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Difficulty:

25% (medium)

Question Stats:

82% (01:59) correct 18% (01:13) wrong based on 62 sessions

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In a certain performance of a 3-act play, the first act was 18 minutes shorter than the third act and half as long as the second act. If the average (arithmetic mean) length of the 3 acts was 46 minutes, how many minutes long was the third act?

(A) 30
(B) 39
(C) 46
(D) 48
(E) 66
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Posts: 1463
Re: In a certain performance of a 3-act play, the first act was 18 minutes  [#permalink]

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06 Apr 2011, 11:35
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Acer86 wrote:
18. In a certain performance of a 3-act play, the first act was 18 minutes shorter than the third act and half as long as the second act. If the average (arithmetic mean) length of the 3 acts was 46 minutes, how many minutes long was the third act?
(A) 30
(B) 39
(C) 46
(D) 48
(E) 66

Hey guys, the answer i am getting is 66...but the original answer is something else..can someone explain how.

Thanks!

Let the 3rd act be "x" minutes long.

the first act was 18 minutes shorter than the third act:
1st act = x-18

the first act was half as long as the second act
1st act = 1/2(Second act)
Second act = 2*(1st act)= 2(x-18)= 2x-36

average (arithmetic mean) length of the 3 acts was 46 minutes

$$\frac{(x-18)+(2x-36)+x}{3}=46$$

$$4x-54=46*3=138$$

$$4x=138+54=192$$

$$x=\frac{192}{4}=48 min$$

Ans: "D"
Intern
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Posts: 30
Re: In a certain performance of a 3-act play, the first act was 18 minutes  [#permalink]

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06 Apr 2011, 11:39
thanks...i was taking second act to be 0.5x instead of 2x-36
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Joined: 01 Feb 2011
Posts: 490
Re: In a certain performance of a 3-act play, the first act was 18 minutes  [#permalink]

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06 Apr 2011, 17:57
first = third - 18
first = third/2

(first+second+third)/3 = 46 => third = 48

Manager
Joined: 17 Jan 2011
Posts: 200
Re: In a certain performance of a 3-act play, the first act was 18 minutes  [#permalink]

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06 Apr 2011, 18:45
Alternately, for average of numbers, idea is to balance all numbers to get the average value i.e.
Like fluke's post, lets assume the numbers to be
Ist - x-18
2nd - 2(x-18)
3rd - x
If x is 46, i.e. 3rd number is 46
1st should be 28 (now since 1st is short of average by 16, 2nd number should be 16 more than 46 i.e 62)
2nd is twice that of 1st number so it is 2 x 28 i.e. 56 which is 6 short of average. If this difference can be equally distributed across all number i.e. 2 to each, that would correct our assumption for the value of x
Or, the assumed value of x was slightly smaller than what it should be, so we can pick up the next higher value in the answer choices.
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Re: In a certain performance of a 3-act play, the first act was 18 minutes  [#permalink]

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06 Apr 2011, 18:53
A1 + A2 + A3 = 3 * 46 = 138

=> A1 + A1 + 18 + 2A1 = 138

=> 4A1 = 120

=> A1 = 30

So A1 = 48

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Re: In a certain performance of a 3-act play, the first act was 18 minutes  [#permalink]

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28 Sep 2015, 22:39
1
HI All,

This question can also be solved by TESTing THE ANSWERS.

We're told that the average length of 3 acts is 46 minutes, so the total length of time is 3(46) = 138 minutes. We're given two facts about how the lengths of the two acts:

1) The first act is 18 minutes shorter than the third act.
2) The first act is half the length of the second act.

We're asked for the length of the third act.

Since the first act is significantly shorter than the other two acts, it's likely that both the second and third acts are LONGER than the average...

Let's TEST Answer D: 48 minutes.

IF....
The third act is 48 minutes, then...
The first act is 48 - 18 = 30 minutes, and...
The second act is 2(30) = 60 minutes
The total is 48+30+60 = 138 minutes, which is an exact MATCH for what we were told. Thus, this MUST be the answer.

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Re: In a certain performance of a 3-act play, the first act was 18 minutes   [#permalink] 28 Sep 2015, 22:39