What is the value of z/x? (1) 2x – y + 3z = 5 (2) x + 2y – z = -10

Question

What is the value of  \frac{z}{x} ?

(1)  2x - y + 3z = 5

(2)  x + 2y - z = -10

yashikaaggarwal · Answer

To Find : the value of z/x ?

(1) 2x−y+3z=5
=> 3 variables and 1 equation, ( Not Sufficient )

(2) x+2y−z=−10
=> 3 variables and 1 equation, ( Not Sufficient )

Together 1 and 2 : 
(2x−y+3z=5)*2
x+2y−z=−10
=> 4x-2y+6z = 10
=> x+2y-z = -10
using elimination,
5x+5z = 0
x+z = 0
x = -z
so z/x = -1 ( sufficient)

answer is C

Russ19 · Answer

Hi

You have written :

(1) 2x−y+3z=5
=> 3 variables and 1 equation, ( Not Sufficient )

My question is, how is that insufficient? Do you mean if we have 3 variables in a single equation, it always gets insufficient?

Do you clarify and write here the concepts, please?

Chethan92 · Answer

Hi  sjuniv32 ,

Usually, the rule is that n variables require n equation in order to find the value of an individual variable.

say a+3 = 0. 1 equation, 1 variable. This is easy. a = -3

Next, consider, a-b+5 = 0. 1 equation and 2 variables. You cannot solve as a and b can take any values. However if the question had asked the value of a-b, we could easily say the value of a-b = -5.

In this question, we are asked to find the value of z/x. Hence 2 equations are sufficient.
If the question had asked to find the value of all the 3 variables, then we require 3 equations.
Try equating the value of x = -z. You'll get only one equation x-y = 5.
Hence, we cannot determine individual values with 2 equations.

Hope this helps.

yashikaaggarwal · Answer

Chethan92  have already briefed it precisely. I will suggest don't indulge in values much. See what the question is asking. Let's suppose question would have been what's the value of x+y+z = ? 
We already know, N variable needs n equations.
And we only have two. So you can directly chose option E. But since the two variables were not in addition or multiplication we had to solve equation to determine whether we can get the asked value or not.

Posted from my mobile device

Papist · Answer

In algebra, you need two equations to solve for two variables and three variables (although the latter depends on whether you can make a variable cancel out using substitution or elimination). However, you should not declare a statement sufficient or insufficient on that basis alone because it really depends on (1) what the question is asking and (2) what constraints are provided. For example, if a question asks you to determine the value of x-y and Statement 1 is 2x + 5y = 15, that would be insufficient because there are an infinite number of solutions. However, if the prompt states that x and y are positive integers, the only possible solution is x=5, y=1 and the statement becomes sufficient. Likewise, a statement could tell us the value of x-y without us having any idea what x and y are and it would be sufficient because we were asked to determine the value of x-y, not x or y individually.

The moral of the story is that understanding the rules of math is important, but understanding what the prompt is asking and telling you is more important.

What is the value of z/x? (1) 2x – y + 3z = 5 (2) x + 2y – z = -10

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