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If v is 1/2 of 3w, 2w is 1/3 of 4x, 3x is 1/4 of 5y, and 4y is 1/5of 6

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If v is 1/2 of 3w, 2w is 1/3 of 4x, 3x is 1/4 of 5y, and 4y is 1/5of 6  [#permalink]

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New post 14 Jan 2020, 05:11
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Re: If v is 1/2 of 3w, 2w is 1/3 of 4x, 3x is 1/4 of 5y, and 4y is 1/5of 6  [#permalink]

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New post 14 Jan 2020, 07:35
given
v=1/2 * 3w
2w=4x/3
3x=5y/4
4y=6z/5
find 5v=7z* U
find U
solve for each given relation we get
U = 5/56
IMO B


Bunuel wrote:
If \(v\) is \(\frac{1}{2}\) of \(3w\), \(2w\) is \(\frac{1}{3}\) of \(4x\), \(3x\) is \(\frac{1}{4}\) of \(5y\), and \(4y\) is \(\frac{1}{5}\) of \(6z\), then \(5v\) is what fraction of \(7z\) ?

A. 1/61

B. 5/56

C. 5/6

D. 1/6

E. 5/8


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Re: If v is 1/2 of 3w, 2w is 1/3 of 4x, 3x is 1/4 of 5y, and 4y is 1/5of 6  [#permalink]

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New post 14 Jan 2020, 10:14
\(\frac{v}{w}=\frac{3}{2}=\frac{15}{10}\)

\(\frac{w}{x}=\frac{2}{3}=\frac{10}{15}\)

\(\frac{x}{y}=\frac{5}{12}=\frac{15}{36}\)

\(\frac{y}{z}=\frac{3}{10}=\frac{36}{120}\)

\(\frac{v}{w} * \frac{w}{x} * \frac{x}{y} * \frac{y}{z}\) = \(\frac{15}{10} * \frac{10}{15} * \frac{15}{36} * \frac{36}{120 }\)

\(\frac{v}{z} = \frac{15}{120} = \frac{1}{8 }\)

\(\frac{5v}{7z}= \frac{5}{7} * \frac{v}{z}= \frac{5}{56}\)



Bunuel wrote:
If \(v\) is \(\frac{1}{2}\) of \(3w\), \(2w\) is \(\frac{1}{3}\) of \(4x\), \(3x\) is \(\frac{1}{4}\) of \(5y\), and \(4y\) is \(\frac{1}{5}\) of \(6z\), then \(5v\) is what fraction of \(7z\) ?

A. 1/61

B. 5/56

C. 5/6

D. 1/6

E. 5/8


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Re: If v is 1/2 of 3w, 2w is 1/3 of 4x, 3x is 1/4 of 5y, and 4y is 1/5of 6  [#permalink]

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New post 14 Jan 2020, 10:53
Bunuel wrote:
If \(v\) is \(\frac{1}{2}\) of \(3w\), \(2w\) is \(\frac{1}{3}\) of \(4x\), \(3x\) is \(\frac{1}{4}\) of \(5y\), and \(4y\) is \(\frac{1}{5}\) of \(6z\), then \(5v\) is what fraction of \(7z\) ?

A. 1/61

B. 5/56

C. 5/6

D. 1/6

E. 5/8


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v = 3w/2
2w = 4x/3
3x = 5y/4
4y = 6z/5
5v = k 7z
k = ?
5v = 15w/2 = 5x = 25y/12 = 25z/40 = 5z/8 = (5/56)7z

IMO B

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Re: If v is 1/2 of 3w, 2w is 1/3 of 4x, 3x is 1/4 of 5y, and 4y is 1/5of 6  [#permalink]

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New post 16 Jan 2020, 07:23
Bunuel wrote:
If \(v\) is \(\frac{1}{2}\) of \(3w\), \(2w\) is \(\frac{1}{3}\) of \(4x\), \(3x\) is \(\frac{1}{4}\) of \(5y\), and \(4y\) is \(\frac{1}{5}\) of \(6z\), then \(5v\) is what fraction of \(7z\) ?

A. 1/61

B. 5/56

C. 5/6

D. 1/6

E. 5/8


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The LCD of all the given fractions is 120, so a smart choice for z is 120; thus:

4y = 6 * z/5

4y = 6 * 120 / 5

y = 36

Then:

3x = 9 * 5

x = 15

Then:

2w = 5 * 4

w = 10

Then:

v = 3 * 5 = 15

Thus,

5v/7z = (5 * 15)/(7 * 120) = 15/(7 * 24) = 5/56

Answer: B

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Re: If v is 1/2 of 3w, 2w is 1/3 of 4x, 3x is 1/4 of 5y, and 4y is 1/5of 6   [#permalink] 16 Jan 2020, 07:23
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