vinegar and water

[leonswati]

A certain 4-liter solution of vinegar and water consists of x liters of vinegar and y liters of water. How many liters of vinegar does the solution contain?

(1) x/4 = 3/8
(2) y/4 = 5/8

the answer is D, but can anyone plz help me solve it using equations ....... a complete answer... thank you...

[kanwar86]

A certain 4-liter solution of vinegar and water consists of x liters of vinegar and y liters of water. How many liters of vinegar does the solution contain?

(1) x/4 = 3/8
(2) y/4 = 5/8

the answer is D, but can anyone plz help me solve it using equations ....... a complete answer... thank you...

Approach - 1) From (1), x xan be found.
2) From (2), y can be found, which when subtracted from total volume of solution gives the value of x.

[shankar.ashwin]

Given x + y = 4

1) gives you x -> 3/2 (sufficient)

2) gives you y -> 5/2 (and) x = 4 - 5/2 = 3/2 (sufficient)

[neelgandham]

The question can be rephrased to,

If x+y =4, then x = ?

(1) x/4 = 3/8

We get the value of x by simplifying. Hence, sufficient

(2) y/4 = 5/8

y = A fraction and x+y =4 ; x = 4- A fraction. Hence, sufficient

Option D

[Stuart@KaplanGMAT]

A certain 4-liter solution of vinegar and water consists of x liters of vinegar and y liters of water. How many liters of vinegar does the solution contain?

(1) x/4 = 3/8
(2) y/4 = 5/8

the answer is D, but can anyone plz help me solve it using equations ....... a complete answer... thank you...

Hi!

This question is a great illustration of the most powerful rule to remember for data sufficiency: number of equations vs number of unknowns.

Here's the "official" wording of the rule:

To solve a system with n variables, one requires n distinct, linear, equations.

Put more simply, if you have the same number of linear equations as you have variables, you can answer any question about the system.

Applying the rule to your question:

Q: gives you 1 equation with 2 variables. We're missing 1 more equation.

(1) gives us another linear equation, no new variables: sufficient.

(2) gives us another linear equation, no new variables: sufficient.

Choose (D)!