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If w/(x + y) = 1, what is the value of (x + y)/y ?

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Bunuel
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If w/(x + y) = 1, what is the value of (x + y)/y ? [#permalink] New post   13 Aug 2018, 03:23
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If w/(x + y) = 1, what is the value of (x + y)/y ?


(1) x/y = 3/2

(2) y/w = 2/5
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D
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chetan2u
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Re: If w/(x + y) = 1, what is the value of (x + y)/y ? [#permalink] New post   13 Aug 2018, 03:35
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If w/(x + y) = 1, what is the value of (x + y)/y ?

\(\frac{x+y}{y}\)=\(1+\frac{x}{y}\)


(1) x/y = 3/2
So Ans 1+3/2=5/2
Suff

(2) y/w = 2/5
Now \(\frac{w}{x+y}\)=1 or \(\frac{x+y}{w}=1\)
x/w=1-2/5=3/5
So ratio of x:y:z=3:2:5 and thus x/y=3/2
Ans 1+3/2=5/2
Sufficient

D
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If w/(x + y) = 1, what is the value of (x + y)/y ? [#permalink] New post   13 Aug 2018, 07:16
Bunuel wrote:
If w/(x + y) = 1, what is the value of (x + y)/y ?


(1) x/y = 3/2

(2) y/w = 2/5


Given, w/(x + y) = 1
St1:- \(\frac{x}{y} = \frac{3}{2}\)
Or, \(\frac{x}{y}+1 = \frac{3}{2}+1\)
Or, \(\frac{x+y}{y} = \frac{5}{2}\)
Sufficient.

St2:- \(\frac{y}{w} = \frac{2}{5}\)
Or, \(w=\frac{5}{2}*y\)

Substituting 'w' in (1), we can express 'x' in terms of y, vice-versa.

Again, we can substitute the value of x or y in question stem and determine \(\frac{(x+y)}{y}\).

Sufficient.

Ans. (D)
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Re: If w/(x + y) = 1, what is the value of (x + y)/y ? [#permalink] New post   13 Aug 2018, 10:06
\(\frac{(x+y)}{y}\)= \(\frac{x}{y}\)+1............................(a)

(1) \(\frac{x}{y}\)=\(\frac{3}{2}\). Put this value in the above modified equation (a)

\(\frac{3}{2}\)+1= \(\frac{5}{2}\) [Suff]

\(\frac{w}{(x+y)}\)= 1...........................(b)

(2) \(\frac{y}{w}\)= \(\frac{2}{5}\) or 2w= 5y or w= \(\frac{5y}{2}\)

Put this value of w in the above equation (b)

\(\frac{5y}{2(x+y)}\)= 1 or \(\frac{2(x+y)}{5y}\)= 1 or \(\frac{(x+y)}{y}\)= \(\frac{5}{2}\) [Suff]

Answer: D.
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If w/(x + y) = 1, what is the value of (x + y)/y ? [#permalink] New post   26 Jul 2020, 14:33
Bunuel wrote:
If w/(x + y) = 1, what is the value of (x + y)/y ?


(1) x/y = 3/2

(2) y/w = 2/5


w/(x + y) = 1
(x + y)/y = ? <=> `x/y + 1 = ?

(1) x/y = 3/2. Clearly sufficient.

(2) y/w = 2/5.
We already know the fact that w/(x + y) = 1 <=> w = x + y --> y/(x + y) = 2/5 <=> (x + y)/y = 5/2. Sufficient.

Answer: (D)
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Re: If w/(x + y) = 1, what is the value of (x + y)/y ? [#permalink] New post   10 Jan 2022, 07:37
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Bunuel wrote:
If w/(x + y) = 1, what is the value of (x + y)/y ?

(1) x/y = 3/2

(2) y/w = 2/5

Given: w/(x + y) = 1

Target question: What is the value of (x + y)/y ?

Statement 1: x/y = 3/2
Useful (and often-tested) fraction property: (a+b)/c = a/c + b/c
The target question asks us to find the value of (x + y)/y.
When we apply the above property, we see that (x + y)/y = x/y + y/y = x/y + 1
So, if x/y = 3/2, then we can substitute to get: (x + y)/y = x/y + y/y = 3/2 + 1 = 5/2
Since we can answer the target question with certainty, statement 1 is SUFFICIENT

Statement 2: y/w = 2/5
Let's first take the given equation: w/(x + y) = 1
The fraction equals 1, we know that the numerator and denominator must be equal.
In other words: w = x + y
We can take the target question, What is the value of (x + y)/y ? and substitute to get the rephrased target question What is the value of w/y ?
Statement 2 tells us that y/w = 2/5.
Taking the reciprocal of both sides we get: w/y = 5/2
Since we can answer the rephrased target question with certainty, statement 2 is SUFFICIENT

Answer: D

Cheers,
Brent
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Re: If w/(x + y) = 1, what is the value of (x + y)/y ? [#permalink] New post   20 Feb 2023, 08:15
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