GMAT Practice Question: If the average (arithmetic mean) of x, y, and z is 7x and x...
Question
If the average (arithmetic mean) of x, y, and z is 7x and x is not equal to 0, what is the ratio of x to the sum of y and z ?
- 1: 21
- 1: 20
- 1: 6
- 6: 1
- 20: 1
Topics: linear equations, ratios, mean
Solution
Step 1
We first translate \textbf{\text{"average (arithmetic mean) of x, y, and z is 7x"}} into an equation.
\frac{x+y+z}{3} = 7x
Step 2
We multiply both sides by 3 and then subtract x from both sides to isolate y+z.
x+y+z = 21x y+z = 21x - x y+z = 20x
Step 3
We then find the ratio of x to y+z by expressing \frac{x}{y+z} and simplifying the fraction.
\frac{x}{y+z} = \frac{x}{20x} \frac{x}{20x} = \frac{\cancel{x}}{\cancel{x}\times20} \frac{1}{20} \text{ratio of }x\text{ to }y+z = 1:20
Answer
1:20
