If the average (arithmetic mean) of x, y, and z is 7x and x ≠ 0

Question

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

adiagr · Accepted Answer

\frac{x+y+z}{3}  = 7x

y+z= 20x.

Important: ratio of x to the sum of y and z, has been asked

\frac{x}{y+z}  =  \frac{1}{20}

Answer: B

stonecold · Answer

Nice Official Question.
Here is my Solution to this one =>

Using  Mean = \frac{Sum}{#}

x+y+z=21x 
Hence  y+z=20x 
 \frac{x}{y+z}=1/20 
Hence the Required Ratio=1:20

Hence B

decotis74 · Answer

I feel a little stupid for asking, but how do we know to divide both sides by 20(y+z)? I can see how we get the answer from this method, but don't understand how we get there.

matthewsmith_89 · Answer

decotis74

(x+y+z)/3 = 7x
x + y + z = 21x
y + z = 20 x

y + z is twenty times x

Therefore the ratio is
x - 1
y + z - 20

1:20 which is answer B

CyberStein · Answer

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.

dave13 · Answer

\frac{x+y+z}{3} = 7x x+y+z = 21x 20x = y+z x = \frac{y+z}{20} can anyone tell me if my solution is correct ?

vineet6316 · Answer

Yes Dave - It is correct.

Basshead · Answer

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?

\frac{x + y + z }{ 3 }= 7x

x + y + z = 21x

y + z = 20x

y + z = \frac{20}{1}

Answer is B.

MHIKER · Answer

\frac{x+y+z}{3}=7x

x+y+z=21x

y+z=20x

Now, \ \frac{x}{y+z}=\frac{x}{20x}=\frac{1}{20}

The answer is  B

Abhishek009 · Answer

x + y + z = 21x

Or,  y + z = 20x

Or,  \frac{1}{20} = \frac{x}{( y + z )}  , Answer must be (B)

Thib33600 · Answer

wondering exactly the same!

Bunuel · Answer

We get  y + z = 20x , and are asked to find  \frac{x}{y+z} . Since  y + z = 20x , then  \frac{x}{y+z}=\frac{x}{20x}=\frac{1}{20} .

Hoppe it's clear.

bumpbot · Answer

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If the average (arithmetic mean) of x, y, and z is 7x and x ≠ 0

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