grandh01 wrote:4x=5y=10z, what is the value of x+y+z?

1) x-y=6
2) y+z=36

OA is D

1) x - y = 6 implies x = y + 6
So, 4x = 5y implies 4(y + 6) = 5y or 4y + 24 = 5y or y = 24
5y = 10z implies 5 * 24 = 10z or z = 12
We know the values of y and z, so we can find the value of x and hence can fine the value of x + y + z; SUFFICIENT.

2) y + z = 36 implies y = 36 - z
So, 5y = 10z implies 5(36 - z) = 10z or 180 = 15z or z = 12
y = 36 - 12 = 24
We know the values of y and z, so we can find the value of x and hence can fine the value of x + y + z; SUFFICIENT.

The correct answer is D.

grandh01 wrote:4x=5y=10z, what is the value of x+y+z?
1) x-y=6
2) y+z=36

This is a nice question because the target question asks us to find the sum of 3 variables, and when it comes to solving systems with three variables, we typically need 3 different equations. At first glance, it appears that we are given only 1 equation (4x=5y=10z) when, in fact, there are 3 different equations here:
1) 4x=5y
2) 5y=10z
3) 4x=10z
If we make the mistake of believing that 4x=5y=10z is a single equation with 3 variables, we may erroneously conclude that we need two more equations to answer the target question. If we make this mistake, we will incorrectly conclude that each statement on its own is insufficient.

That's all I wanted to say about that.

Mitch and Anurag already provided great explanations (as always). I just wanted to make that observation.

Cheers,
Brent