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

Question

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

Show Answer

Official Answer

D

(A) 30
(B) 39
(C) 46
(D) 48
(E) 66

fluke · Answer

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"

Acer86 · Answer

thanks...i was taking second act to be 0.5x instead of 2x-36

Spidy001 · Answer

first = third - 18
first = third/2

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

Answer D.

ravsg · Answer

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.

subhashghosh · Answer

A1 + A2 + A3 = 3 * 46 = 138

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

=> 4A1 = 120

=> A1 = 30

So A1 = 48

Answer - D

EMPOWERgmatRichC · Answer

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.

Final Answer:  D

GMAT assassins aren't born, they're made,
Rich

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

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

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