For the system of equations given, what is the value of z?

Question

x-4=z
y-x=8
8-z=t

(1) x = 7
(2) t = 5

Practice Questions 
Question: 36
Page: 278
Difficulty: 550

Bunuel · Answer

SOLUTION

x-4=z
y-x=8
8-z=t

For the system of equations given, what is the value of z?

(1) x = 7. Substitute the value of x in the first equation to find z. Sufficient.
(2) t = 5. Substitute the value of t in the third equation to find z. Sufficient.

Answer: D.

SOURH7WK · Answer

St 1: Sufficient: x=7, substituting in Eq 1, we will get value of Z, 7-4=z=3, 
ST 2. Sufficient: t=5, substituting in Eq 3, We will get value of Z, 8-Z=5, Z= 3.

Hence Answer D.

aeglorre · Answer

I didnt even solve for z, all I used was the fact that "ONE unknown and TWO knowns means you can solve for the unknown".

Hence, we are given x in s(1) and that is sufficent just by looking at the top equation. Then we are given t in s(2) which is enough for the third equation.

The reason this method is superior to any other is that you quickly can move on to the next quant problem on the test, I solved this q in 35 seconds using this method.

If there are any holes in this approach, please speak up and correct me.

gmatscore800 · Answer

Basic rule for solving linear equation

NO of Unknown === no of equation 
In this question :
NO of Unknown==4
no of equation ==3

both the statements are reducing 1 unknown making the equation solvable

hence D

JeffTargetTestPrep · Answer

We are given 3 equations:

1) x – 4 = z

2) y – x = 8

3) 8 – z = t

We need to determine the value of z.

Statement One Alone:

x = 7

We see that we can substitute 7 for x in the first equation and then determine the value of z.

x – 4 = z

7 – 4 = z

3 = z

Statement one alone is sufficient to answer the question. We can eliminate answer choices B, C, and E.

Statement Two Alone:

t = 5

We see that we can substitute 5 for t in equation 3 and then determine the value of z.

8 – z = t

8 – z = 5

3 = z

Statement two alone is sufficient to answer the question.

The answer is D.

BrentGMATPrepNow · Answer

Target question :    What is the value of z?

Statement 1 : x = 7   
Scanning the three given equations, we see that equation i is all we need to determine the value of z 
i) x - 4 = z
Replace x with 7 to get: 7 - 4 = z
So,  z = 3 
Since we can answer the  target question  with certainty, statement 1 is SUFFICIENT

Statement 2 : t = 5  
Scanning the three given equations, we see that equation iii is all we need to determine the value of z 
iii) 8 - z = t
Replace t with 5 to get: 8 - z = 5
So,  z = 3 
Since we can answer the  target question  with certainty, statement 2 is SUFFICIENT

Answer: D

Cheers,
Brent

shahidomer77 · Answer

With first option first equation is enough to get z
With second option third equation is enough to get z

Kudos please

TheUltimateWinner · Answer

Hello  Bunuel 
It seems that we can solve the question without using 2nd equation. So, may i know why the 2nd equation has been used here? 
Thanks__

For the system of equations given, what is the value of z?

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