SimaQ
If 4x = 5y = 10z, what is the value of x + y + z ?
(1) x - y = 6
(2) y + z = 36
The way I approached this is actually through ratios:
We know that 4X = 5Y = 10Z
So what are the values of X, Y and Z that satisfy the equation?
First iteration is 4X = 5Y = 10Z.. these 3 equations "meet" at 20
4(5) = 5(4) = 10(2)
So x = 5 , y = 4 , z = 2
And since you already got the ratio, it's all about multiplying them to get the pattern
First iteration (multiplying everything by 1): x = 5 | y = 4 | z = 2
Second iteration (multiplying everything by 2): x = 10 | y = 8 | z = 2
Third iteration (multiplying everything by 3): x = 15 | y = 12 | z = 6
Now, if check out the pattern. As we proceed to more iterations.. the difference between X and Y increases:
First iteration: x = 5, y = 4 so difference is 5 - 4 = 1
Second iteration: x = 10 y = 8 so difference is 10 - 8 = 2
Third iteration: x = 15 y = 12 so difference is 15 - 12 = 3
That's the relationship between X and Y
How about the relationship between Y and Z?
First iteration: y = 4, z = 2 so sum of the two is 6
Second iteration: y = 8, z = 4 so sum is 12
Third iteration: y = 12, z = 8 so sum is 24
So we could already do a pre-thinking (like CR question) that we just need X = Y to determine what is Z
Statement (1) gives it to us:
X - Y = 6
This happens in the next iterations.. specifically the Sixth Iteration: x = 30 y = 24 (difference is 30 - 24 = 6) so z = 12
Statement (2) also gives it to us:
Y + Z = 36
This happens in the next iterations.. specifically the Sixth iteration: x = 30 y = 24 z = 12 (sum is 24 + 12 = 36) so z must be 12
If this makes sense please kudos!