It is currently 21 Nov 2017, 22:39

### 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 and y is 60 and the av

Author Message
TAGS:

### Hide Tags

Manager
Joined: 08 Sep 2006
Posts: 51

Kudos [?]: 37 [1], given: 0

If the average (arithmetic mean) of x and y is 60 and the av [#permalink]

### Show Tags

23 Jul 2007, 19:33
1
KUDOS
1
This post was
BOOKMARKED
00:00

Difficulty:

5% (low)

Question Stats:

86% (00:41) correct 14% (00:52) wrong based on 276 sessions

### HideShow timer Statistics

If the average (arithmetic mean) of x and y is 60 and the average (arithmetic mean) of y and z is 80, what is the value of z-x?.

A. 70
B. 40
C. 20
D. 10
E. It cannot be determined from the information.
[Reveal] Spoiler: OA

Kudos [?]: 37 [1], given: 0

GMAT Club Legend
Joined: 07 Jul 2004
Posts: 5032

Kudos [?]: 453 [0], given: 0

Location: Singapore

### Show Tags

23 Jul 2007, 19:37
(x+y)/2 = 60
x+y = 120 ---[1]

(y+z)/2 = 80
y+z = 160 ---[2]

[2]-[1]
z-x = 40

Kudos [?]: 453 [0], given: 0

Manager
Joined: 08 Sep 2006
Posts: 51

Kudos [?]: 37 [0], given: 0

### Show Tags

23 Jul 2007, 19:39
Can you explain why you are subtracting [2] - [1] ?

Kudos [?]: 37 [0], given: 0

GMAT Club Legend
Joined: 07 Jul 2004
Posts: 5032

Kudos [?]: 453 [0], given: 0

Location: Singapore

### Show Tags

23 Jul 2007, 19:42
tinman1412 wrote:
Can you explain why you are subtracting [2] - [1] ?

The question is looking for z-x. If you substract equation 2 from eqaution 1, then you will get z-x on the left hand side of the equation.

Kudos [?]: 453 [0], given: 0

Manager
Joined: 08 Jul 2007
Posts: 173

Kudos [?]: 11 [0], given: 0

### Show Tags

23 Jul 2007, 19:47
Just to expand on the explanation.

x+y=120 means x=120-y
y+z=160 means z=160-y

Thus, z-x=(160-y)-(120-y)=40-y+y=40

Kudos [?]: 11 [0], given: 0

Senior Manager
Joined: 21 Jun 2006
Posts: 282

Kudos [?]: 144 [0], given: 0

### Show Tags

23 Jul 2007, 22:23
x+y/2 = 60
x+y=120
similarly, y+z=160

y+z-x-y=40
z-x=40

Kudos [?]: 144 [0], given: 0

Intern
Joined: 08 Sep 2006
Posts: 34

Kudos [?]: [0], given: 0

### Show Tags

24 Jul 2007, 07:48
tinman1412 wrote:
If the average (arithmetic mean) of x and y is 60 and the average (arithmetic mean) of y and z is 80, what is the value of z-x?.

a)70
b)40
c)20
d)10
e)It cannot be determined from the information.

This question is from the OG 10, but I do not understand their explanation. Hopefully someone can give me their approach.

Thanks,

I did this problem a couple of ways but it is essential the same as other posters.

(x+y)/2 = 60 (from avg formula)
(y+z)/2 = 80 (from avg formula)

set both equal to each other but we need to subtract 20 from 2nd equation to ensure they are equal (60):

(x+y)/2 = (y+z)/2 - 20 ->
x+y = y+z - 40 ->
z - x = 40

Kudos [?]: [0], given: 0

Intern
Joined: 08 Jan 2013
Posts: 39

Kudos [?]: 25 [0], given: 5

### Show Tags

15 Jun 2013, 17:45
briks123 wrote:
Just to expand on the explanation.

x+y=120 means x=120-y
y+z=160 means z=160-y

Thus, z-x=(160-y)-(120-y)=40-y+y=40

Doh! In the absence of multiplication, my feeble eyes discarded the brackets, and I came to the same answer by the wrong route (finding x, y and z).

Substituting equations:
$$z-x = 40-2y; y = 160-z$$
$$z+x = 280$$

Combining equations:
$$(x+y)/2 + (y+z)/2 = 140$$
$$2y+x+z = 280$$

Compare scribbles:
$$y = 0; z = 160; x = 120$$
$$z-x = 40$$

If, like me, you find yourself wandering down the dark tunnel... there can still be luck. I didn't finish the section on time though

Kudos [?]: 25 [0], given: 5

Verbal Forum Moderator
Joined: 10 Oct 2012
Posts: 627

Kudos [?]: 1388 [2], given: 136

Re: If the average (arithmetic mean) of x and y is 60 and the av [#permalink]

### Show Tags

16 Jun 2013, 01:13
2
KUDOS
tinman1412 wrote:
If the average (arithmetic mean) of x and y is 60 and the average (arithmetic mean) of y and z is 80, what is the value of z-x?.

A. 70
B. 40
C. 20
D. 10
E. It cannot be determined from the information.

10 second approach :

Mean of x and y is 60. We can assume both x = y = 60. Again, mean of y and z is 80; We can keep the value of y = 60 and assume the value of z = 100. Thus, z-x = 100-60 = 40.

B.
_________________

Kudos [?]: 1388 [2], given: 136

Intern
Joined: 08 Jan 2013
Posts: 39

Kudos [?]: 25 [0], given: 5

Re: If the average (arithmetic mean) of x and y is 60 and the av [#permalink]

### Show Tags

16 Jun 2013, 02:04
That's brilliant Mau5. Do you know of a guide with general speed tips?

Kudos [?]: 25 [0], given: 5

Verbal Forum Moderator
Joined: 10 Oct 2012
Posts: 627

Kudos [?]: 1388 [0], given: 136

Re: If the average (arithmetic mean) of x and y is 60 and the av [#permalink]

### Show Tags

16 Jun 2013, 02:26
stormbind wrote:
That's brilliant Mau5. Do you know of a guide with general speed tips?

As for general speed tips, as it is with everyone on gmatclub, I have learnt a lot by just observing Bunuel's solutions! In this case particularly, what I did is just one of the many ways of interpreting averages,i.e. if average of 2 things is X, then each of them can be assumed to be X.
_________________

Kudos [?]: 1388 [0], given: 136

Director
Joined: 04 Jun 2016
Posts: 647

Kudos [?]: 379 [0], given: 36

GMAT 1: 750 Q49 V43
If the average (arithmetic mean) of x and y is 60 and the av [#permalink]

### Show Tags

23 Jul 2016, 07:43
tinman1412 wrote:
If the average (arithmetic mean) of x and y is 60 and the average (arithmetic mean) of y and z is 80, what is the value of z-x?.

A. 70
B. 40
C. 20
D. 10
E. It cannot be determined from the information.

$$\frac{X+Y}{2}=60 ; X+Y=120$$

$$\frac{Y+Z}{2}=80 ; Y+Z=160$$

$$(Y+Z)-(X+Y)= 160-120$$

$$Y+Z-X-Y=40$$ (+Y AND -Y CANCELS EACH OTHER)

$$Z-X=40$$

_________________

Posting an answer without an explanation is "GOD COMPLEX". The world doesn't need any more gods. Please explain you answers properly.
FINAL GOODBYE :- 17th SEPTEMBER 2016. .. 16 March 2017 - I am back but for all purposes please consider me semi-retired.

Kudos [?]: 379 [0], given: 36

Retired Moderator
Joined: 12 Aug 2015
Posts: 2213

Kudos [?]: 876 [0], given: 602

Re: If the average (arithmetic mean) of x and y is 60 and the av [#permalink]

### Show Tags

29 Jul 2016, 15:19
X+Y=120
Y+Z=160
Equation 2 - Equation 1
=> Z-X=40
Smash B
_________________

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

Kudos [?]: 876 [0], given: 602

Senior Manager
Status: DONE!
Joined: 05 Sep 2016
Posts: 408

Kudos [?]: 25 [0], given: 283

Re: If the average (arithmetic mean) of x and y is 60 and the av [#permalink]

### Show Tags

13 Oct 2016, 16:28
y+z - x - y = 160-120
z-x = 40

Kudos [?]: 25 [0], given: 283

Target Test Prep Representative
Status: Founder & CEO
Affiliations: Target Test Prep
Joined: 14 Oct 2015
Posts: 1821

Kudos [?]: 939 [1], given: 3

Location: United States (CA)
Re: If the average (arithmetic mean) of x and y is 60 and the av [#permalink]

### Show Tags

16 Oct 2016, 18:20
1
KUDOS
Expert's post
tinman1412 wrote:
If the average (arithmetic mean) of x and y is 60 and the average (arithmetic mean) of y and z is 80, what is the value of z-x?.

A. 70
B. 40
C. 20
D. 10
E. It cannot be determined from the information.

We are given that the average (arithmetic mean) of x and y is 60 and the average (arithmetic mean) of y and z is 80. We can create the following equations:

Equation 1:

(x + y)/2 = 60

x + y = 120

y = 120 - x

Equation 2:

(y + z)/2 = 80

y + z = 160

y = 160 - z

Since y = 120 - x and y = 160 - z, we can equate the two expressions.

120 - x = 160 - z

z - x = 40

_________________

Scott Woodbury-Stewart
Founder and CEO

GMAT Quant Self-Study Course
500+ lessons 3000+ practice problems 800+ HD solutions

Kudos [?]: 939 [1], given: 3

Intern
Joined: 31 Oct 2016
Posts: 3

Kudos [?]: [0], given: 11

Re: If the average (arithmetic mean) of x and y is 60 and the av [#permalink]

### Show Tags

18 Oct 2017, 11:46
x+y/2= 60 = 120
y+z/2=80 = 160
x= 120-y
z= 160-y
therefore
z-x= 160-y -( 120-y)
= 40

Kudos [?]: [0], given: 11

Re: If the average (arithmetic mean) of x and y is 60 and the av   [#permalink] 18 Oct 2017, 11:46
Display posts from previous: Sort by