A promotional video that lasts w minutes has 3 segments which last x

Question

﻿A promotional video that lasts w minutes has 3 segments which last x, y, and z minutes, respectively. A celebrity host narrates 1/3 of the first segment, 1/2 of the second segment, and 1/2 of the third segment. If 3x = 3y = z, what fraction of the w-minute video does the celebrity host narrate?

A. 1/4

B. 4/15

C. 3/7

D. 4/9

E. 7/15

Archit3110 · Accepted Answer

we can use smart numbers and solve
given that 3x = 3y = z and
1st segment is 1/3
2nd & 3rd segment are 1/2
let x=y=6 and z=18

so celebrity has narrated ; 2+3+9 ; 14 mins
and total x+y+z=30 mins
so fraction is 14/30 ; 7/15
option E

gmatophobia · Answer

3x = 3y = z

We can infer that the value of x and y is the same.

Time the celebrity host narrates =  \frac{x }{ 3} + \frac{y }{ 2} + \frac{z }{ 2}

=  \frac{x }{ 3} + \frac{x }{ 2} + \frac{3x }{ 2}  =  \frac{7x}{3}

Total Duration =  x + x + 3x = 5x

Required Ratio = \frac{7x}{3 * 5x}  =  \frac{7}{15}

Option E

YogeshBardia · Answer

Total length of the video = W minutes and it has 3 segments x,y and z

Hence W=x+y+z and we know that 3x=3y=z which can be written as x=y= \frac{z}{3}

Therefore W= x+x+3x

W=5x

Now time narrated by the celebrity is  \frac{x}{3} ,  \frac{y}{2} , \frac{z}{2} 
which will be
Total time taken by the celebrity =  \frac{x}{3} +  \frac{y}{2} + \frac{z}{2}

By putting in the values from x=y= \frac{z}{3}

we get total time narrated by celebrity =  \frac{x}{3} +  \frac{x}{2} + \frac{3x}{2} 
=  \frac{7x}{3}

Hence fraction of time will be =  \frac{time taken by celebrity}{ Total Time} 
=  \frac{7x}{3/5x} 
=  \frac{7}{15}

Option E

Paras96 · Answer

﻿A promotional video that lasts w minutes has 3 segments which last x, y, and z minutes, respectively. A celebrity host narrates 1/3 of the first segment, 1/2 of the second segment, and 1/2 of the third segment. If 3x = 3y = z, what fraction of the w-minute video does the celebrity host narrate?

=>w=x+y+z
=>w=z/3+z/3+z
=>w=5z/3

Total narration
=x/3 + y/2 + z/2
=z/9+z/6+z/2
=(2z+3z+9z)/18
=14z/18
=7z/9

fraction of the w-minute video the celebrity host narrates,
=(7z/9)/(5z/3)
=7/15

Hence E

JeffTargetTestPrep · Answer

The fraction of the whole video narrated by the celebrity can be expressed as a weighted average of the narrated fractions of the components:

/(x + y + z)

Since x = z/3 and y = z/3, we have:

/(z/3 + z/3 + z) =

(1/9 + 1/6 + 1/2)/(1/3 + 1/3 + 1) =

(14/18)/(5/3) = 7/15

Answer: E

liviofrol · Answer

ratios approach in 4 steps:
 (1)  3x=3y=z means that x:y:z = 1:1:3 and w = 5 ratio units.

we can expand the ratio by 6 because we are working with denominators of 2 and 3.
 (2)  x:y:z = 6:6:18 and w = 30 ratio units

(3)  it is given that the celebrity host narrates x/3 + y/2 + z/2 using the ratios above  (2)  that is equal to 2 + 3 + 9 = 14 ratio units.

(4)  what fraction of the total is that?
 14/30 reduce to 7/15

Answer E

coffeeplease123 · Answer

Why did you put 5x (total duration) in the denominator when calculating the required ratio? I got stuck at this point, because I think we should multiply 7x/3 by 5x, not to divide by 5x. Can someone please help me to understand why?

gmatophobia · Answer

Total Duration (w) = x + y + z

From the equation 3x = 3y = z, we can infer that

3x = 3y ⇒  x = y

3x = z

We can re-write the equation in terms of x

Total Duration = x + y + z

w = x + x + 3x = 5x

Question: "  what fraction of the w-minute video does the celebrity host narrate  "

Required Ratio =  \frac{	ext{Time the celebrity host narrates}}{	ext{Total Duration}}

=  \frac{\frac{7x}{3}}{5x}

=  \frac{7x}{3*5x}

=  \frac{7}{15}

Hope this clarifies !

KarishmaB · Answer

3x = 3y = z = k

x = k/3
y = k/3
z = k

Hence ratios of the time of the three segments is 1 : 1 : 3. So first and second segments are 1/5th of the video each and third segment is 3/5th of the video.

The host narrates  (\frac{1}{3})(\frac{1}{5}) + (\frac{1}{2})(\frac{1}{5}) + (\frac{1}{2})(\frac{3}{5}) = \frac{7}{15}

Note that this calculation is not required. He hosts 1/2 of two segments and 1/3 of a small one. So he hosts a little less than 1/2 of the entire show. Since denominator will be 30 or a factor of that, we know that answer must be 7/15

Answer (E)

Ratios discussed here:  https://youtu.be/5ODENGG5dvc

bumpbot · Answer

Automated notice from GMAT Club BumpBot:

A member just gave Kudos to this thread, showing it’s still useful. I’ve bumped it to the top so more people can benefit. Feel free to add your own questions or solutions.

This post was generated automatically.

A promotional video that lasts w minutes has 3 segments which last x

Prep Toolkit

Top 5 GMAT Debrief Videos

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards

GMAT Problem Solving (PS) Questions

A promotional video that lasts w minutes has 3 segments which last x

Prep Toolkit

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards