It is currently 23 Jan 2018, 23:43

### GMAT Club Daily Prep

#### Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History

# Events & Promotions

###### Events & Promotions in June
Open Detailed Calendar

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

Author Message
TAGS:

### Hide Tags

Manager
Status: Persevere
Joined: 08 Jan 2016
Posts: 123
Location: Hong Kong
GMAT 1: 750 Q50 V41
GPA: 3.52
If the average (arithmetic mean) of x, y, and z is 7x and x ≠ 0 [#permalink]

### Show Tags

26 May 2016, 20:17
2
This post was
BOOKMARKED
00:00

Difficulty:

5% (low)

Question Stats:

82% (00:41) correct 18% (00:41) wrong based on 206 sessions

### HideShow timer Statistics

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
[Reveal] Spoiler: OA
Senior Manager
Joined: 18 Jan 2010
Posts: 257
Re: If the average (arithmetic mean) of x, y, and z is 7x and x ≠ 0 [#permalink]

### Show Tags

26 May 2016, 21:32
1
KUDOS
$$\frac{x+y+z}{3}$$ = 7x

y+z= 20x.

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

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

Retired Moderator
Joined: 12 Aug 2015
Posts: 2344
GRE 1: 323 Q169 V154
If the average (arithmetic mean) of x, y, and z is 7x and x ≠ 0 [#permalink]

### Show Tags

17 Dec 2016, 18:41
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

_________________

Give me a hell yeah ...!!!!!

Intern
Joined: 17 Mar 2017
Posts: 1
Re: If the average (arithmetic mean) of x, y, and z is 7x and x ≠ 0 [#permalink]

### Show Tags

17 Mar 2017, 19:27
1
KUDOS
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.
Senior Manager
Joined: 06 Dec 2016
Posts: 253
Re: If the average (arithmetic mean) of x, y, and z is 7x and x ≠ 0 [#permalink]

### Show Tags

18 Mar 2017, 11:09
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

Manager
Joined: 21 Jun 2017
Posts: 77
If the average (arithmetic mean) of x, y, and z is 7x and x ≠ 0 [#permalink]

### Show Tags

22 Aug 2017, 11:09
1
KUDOS
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.
Attachments

Ratio.jpg [ 80.71 KiB | Viewed 1026 times ]

If the average (arithmetic mean) of x, y, and z is 7x and x ≠ 0   [#permalink] 22 Aug 2017, 11:09
Display posts from previous: Sort by