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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
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A. 1/4
B. 4/15
C. 3/7
D. 4/9
E. 7/15
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Archit3110
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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
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
Bunuel
gmatophobia
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Bunuel
\(3x = 3y = z\)
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
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Power of Tiny Gains
1.01^(365) = 37.78
0.99^(365) = 0.03
Power of Tiny Gains
1.01^(365) = 37.78
0.99^(365) = 0.03
General Discussion
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Updated on: 16 Jul 2024, 04:35
Originally posted by YogeshBardia on 12 Aug 2023, 06:38.
Last edited by YogeshBardia on 16 Jul 2024, 04:35, edited 1 time in total.
Last edited by YogeshBardia on 16 Jul 2024, 04:35, edited 1 time in total.
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
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
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
=>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
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Bunuel
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(1/3) + y(1/2) + z(1/2)]/(x + y + z)
Since x = z/3 and y = z/3, we have:
[(z/3)(1/3) + (z/3)(1/2) + z(1/2)]/(z/3 + z/3 + z) =
(1/9 + 1/6 + 1/2)/(1/3 + 1/3 + 1) =
(14/18)/(5/3) = 7/15
Answer: E
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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
(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
Posts: 9
gmatophobia
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
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Posts: 3,174
coffeeplease123
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 = \(\frac{\text{Time the celebrity host narrates}}{\text{Total Duration}}\)
= \(\frac{\frac{7x}{3}}{5x}\)
= \(\frac{7x}{3*5x}\)
= \(\frac{7}{15}\)
Hope this clarifies !
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Power of Tiny Gains
1.01^(365) = 37.78
0.99^(365) = 0.03
Power of Tiny Gains
1.01^(365) = 37.78
0.99^(365) = 0.03
Bunuel
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
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