nalinnair wrote:
If the average (arithmetic mean) of x, y, and z is 7x and x ≠ 0, what is the ratio of x to the sum of y and z?
(A) 1:21
(B) 1:20
(C) 1:6
(D) 6:1
(E) 20:1
1. (X + Y + Z) / 3 = 7x
2. You want to isolate (X + Y + Z); therefore, multiple both sides of the equation by 3. Multiplying 1/3 by 3 neutralizes the denominator.
3. (X + Y + Z) = 21x
"what is the ratio of x to the sum of y and z?" given this, we want to isolate Y + Z; therefore, we subtract X from both sides of the equation.
4. Y + Z = 21X - 1X (remember the coefficients when add/subtracting variables)
4.1 Y + Z = 20x
5. divide by X: doing this will help you visualize the ratio as fraction --> Y+Z / X = 20/1 or see Attached:
Meaning, for every sum of Y and Z there is 20, and for every sum of Y and Z there is exactly 1 X
Therefore, The Answer is (B) 1:20 As for a roundabout method, Let X = 1, Y = 14, Z = 6
(1) + (14) + (6) / 3 = 7(1)
21 / 3 = 7
The five steps I posted first is a little quicker.
This Question is Q 100 on
OG 2017.
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