Data Sufficiency

BTGmoderatorDC wrote: ↑

Wed Jan 05, 2022 7:17 pm

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


(1) x/y = 3/2

(2) y/w = 2/5



OA D

Source: Magoosh

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