Last visit was: 24 Jul 2024, 23:47 It is currently 24 Jul 2024, 23:47
Close
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
Your Progress

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
Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.
Close
Request Expert Reply
Confirm Cancel
SORT BY:
Date
Tags:
Difficulty: Sub 505 Level,   Fractions and Ratios,                           
Show Tags
Hide Tags
Manager
Manager
Joined: 09 Jan 2016
Status:Persevere
Posts: 107
Own Kudos [?]: 3722 [49]
Given Kudos: 94
Location: Hong Kong
GMAT 1: 750 Q50 V41
GPA: 3.52
Send PM
Most Helpful Reply
User avatar
Manager
Manager
Joined: 18 Jan 2010
Posts: 209
Own Kudos [?]: 1014 [13]
Given Kudos: 9
Send PM
General Discussion
Alum
Joined: 12 Aug 2015
Posts: 2270
Own Kudos [?]: 3199 [3]
Given Kudos: 893
GRE 1: Q169 V154
Send PM
avatar
Intern
Intern
Joined: 17 Mar 2017
Posts: 1
Own Kudos [?]: 1 [1]
Given Kudos: 0
Send PM
Re: If the average (arithmetic mean) of x, y, and z is 7x and x ≠ 0 [#permalink]
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.
Manager
Manager
Joined: 06 Dec 2016
Posts: 195
Own Kudos [?]: 59 [2]
Given Kudos: 10
Send PM
Re: If the average (arithmetic mean) of x, y, and z is 7x and x ≠ 0 [#permalink]
2
Kudos
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
Manager
Manager
Joined: 21 Jun 2017
Posts: 60
Own Kudos [?]: 39 [1]
Given Kudos: 3
Send PM
If the average (arithmetic mean) of x, y, and z is 7x and x ≠ 0 [#permalink]
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
Ratio.jpg [ 80.71 KiB | Viewed 34844 times ]

VP
VP
Joined: 09 Mar 2016
Posts: 1142
Own Kudos [?]: 1028 [0]
Given Kudos: 3851
Send PM
If the average (arithmetic mean) of x, y, and z is 7x and x ≠ 0 [#permalink]
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



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

\(x+y+z = 21x\)

\(20x = y+z\)

\(x = \frac{y+z}{20}\)

can anyone tell me if my solution is correct ? :-)
Intern
Intern
Joined: 15 Oct 2016
Posts: 20
Own Kudos [?]: 29 [1]
Given Kudos: 9
Send PM
Re: If the average (arithmetic mean) of x, y, and z is 7x and x ≠ 0 [#permalink]
1
Kudos
dave13 wrote:
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



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

\(x+y+z = 21x\)

\(20x = y+z\)

\(x = \frac{y+z}{20}\)

can anyone tell me if my solution is correct ? :-)


Yes Dave - It is correct.
Director
Director
Joined: 09 Jan 2020
Posts: 953
Own Kudos [?]: 235 [0]
Given Kudos: 432
Location: United States
Send PM
Re: If the average (arithmetic mean) of x, y, and z is 7x and x ≠ 0 [#permalink]
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.
Director
Director
Joined: 14 Jul 2010
Status:No dream is too large, no dreamer is too small
Posts: 958
Own Kudos [?]: 5019 [0]
Given Kudos: 690
Concentration: Accounting
Send PM
If the average (arithmetic mean) of x, y, and z is 7x and x ≠ 0 [#permalink]
Top Contributor
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


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

\(x+y+z=21x\)

\(y+z=20x\)

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

The answer is \(B\)
Board of Directors
Joined: 11 Jun 2011
Status:QA & VA Forum Moderator
Posts: 6047
Own Kudos [?]: 4768 [0]
Given Kudos: 463
Location: India
GPA: 3.5
WE:Business Development (Commercial Banking)
Send PM
Re: If the average (arithmetic mean) of x, y, and z is 7x and x ≠ 0 [#permalink]
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

\(x + y + z = 21x\)

Or, \(y + z = 20x\)

Or, \(\frac{1}{20} = \frac{x}{( y + z )}\) , Answer must be (B)
Intern
Intern
Joined: 08 Feb 2023
Posts: 31
Own Kudos [?]: 1 [0]
Given Kudos: 22
Send PM
If the average (arithmetic mean) of x, y, and z is 7x and x 0 [#permalink]
decotis74 wrote:
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.


wondering exactly the same!
Math Expert
Joined: 02 Sep 2009
Posts: 94609
Own Kudos [?]: 643702 [1]
Given Kudos: 86737
Send PM
Re: If the average (arithmetic mean) of x, y, and z is 7x and x 0 [#permalink]
1
Kudos
Expert Reply
Thib33600 wrote:
decotis74 wrote:
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



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.


wondering exactly the same!


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.
GMAT Club Bot
Re: If the average (arithmetic mean) of x, y, and z is 7x and x 0 [#permalink]
Moderator:
Math Expert
94609 posts