Join us for MBA Spotlight – The Top 20 MBA Fair      Schedule of Events | Register

 It is currently 07 Jun 2020, 02:55

### 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

# There are x numbers in list L, where x is a positive integer

Author Message
TAGS:

### Hide Tags

Senior Manager
Joined: 21 Oct 2013
Posts: 409
There are x numbers in list L, where x is a positive integer  [#permalink]

### Show Tags

Updated on: 14 Jan 2014, 04:15
4
00:00

Difficulty:

35% (medium)

Question Stats:

76% (02:34) correct 24% (02:51) wrong based on 185 sessions

### HideShow timer Statistics

There are x numbers in list L, where x is a positive integer, and there are y numbers in list M, where y is a positive integer. The average (arithmetic mean) of the numbers in list L is p, and the average of all the numbers in both lists L and M is q. Which of the following expressions is the average of the numbers in list M?

A. (qy - px) / x
B. (qy - px) / y
C. (p + q)x / y
D. [(q - p)x - py] / (x + y)
E. [(q - p)x + qy] / y

OE
Sum = (Average × Number of terms)
Average of all (x + y) numbers in both lists L and M = q
Sum of all numbers in both lists L and M = q(x + y)
Average of x numbers in list L = p, sum of numbers in list L = px
Sum of all (x + y) numbers in both lists L and M = q(x + y)
Sum of x numbers in list L = px
If subtract sum of x numbers in list L from sum of (x + y) numbers in both lists L and M, we will be left with sum of y numbers in list M. → Sum of y numbers in list M = [q(x + y) – px]
Average of y numbers in list M = [q(x + y) – px] / y
Rewriting numerator q(x + y) − px → q(x + y) − px = (qx + qy − px = qx − px + qy) = (q − p)x + qy
→ q(x + y) − px = [(q − p)x + qy]
M = [(q − p)x + qy] / y

Originally posted by goodyear2013 on 14 Jan 2014, 04:05.
Last edited by Bunuel on 14 Jan 2014, 04:15, edited 1 time in total.
Edited the question.
Math Expert
Joined: 02 Sep 2009
Posts: 64322
Re: There are x numbers in list L, where x is a positive integer  [#permalink]

### Show Tags

14 Jan 2014, 04:23
3
goodyear2013 wrote:
There are x numbers in list L, where x is a positive integer, and there are y numbers in list M, where y is a positive integer. The average (arithmetic mean) of the numbers in list L is p, and the average of all the numbers in both lists L and M is q. Which of the following expressions is the average of the numbers in list M?

A. (qy - px) / x
B. (qy - px) / y
C. (p + q)x / y
D. [(q - p)x - py] / (x + y)
E. [(q - p)x + qy] / y

OE
Sum = (Average × Number of terms)
Average of all (x + y) numbers in both lists L and M = q
Sum of all numbers in both lists L and M = q(x + y)
Average of x numbers in list L = p, sum of numbers in list L = px
Sum of all (x + y) numbers in both lists L and M = q(x + y)
Sum of x numbers in list L = px
If subtract sum of x numbers in list L from sum of (x + y) numbers in both lists L and M, we will be left with sum of y numbers in list M. → Sum of y numbers in list M = [q(x + y) – px]
Average of y numbers in list M = [q(x + y) – px] / y
Rewriting numerator q(x + y) − px → q(x + y) − px = (qx + qy − px = qx − px + qy) = (q − p)x + qy
→ q(x + y) − px = [(q − p)x + qy]
M = [(q − p)x + qy] / y

There are x numbers in list L and the average is p --> the sum of the numbers in list L is (average)*(number of terms) = $$px$$.

There are x+y numbers in lists L and M and the average is q --> the sum of the numbers in lists L and M is (average)*(number of terms) = $$q(x+y)$$.

The above implies that the sum of the numbers in list M is $$q(x+y) - px=(q-p)x+qy$$.

Therefore the average of list M is (sum)/(number of terms) = $$\frac{(q-p)x+qy}{y}$$.

_________________
EMPOWERgmat Instructor
Status: GMAT Assassin/Co-Founder
Affiliations: EMPOWERgmat
Joined: 19 Dec 2014
Posts: 16797
Location: United States (CA)
GMAT 1: 800 Q51 V49
GRE 1: Q170 V170
Re: There are x numbers in list L, where x is a positive integer  [#permalink]

### Show Tags

12 Feb 2015, 12:40
Hi All,

While this question certainly looks "crazy", it can be solved rather easily by TESTing VALUES, staying organized and looking for logical patterns.

We're told that there are 2 lists of numbers (List L and List M), but we're NOT told ANYTHING about the lists. We can make them as simple of complex as we choose. I choose to make them SIMPLE....

List L: {2, 2} Average = 2, number of terms = 2
List M: {3, 3, 3} Average = 3, number of terms = 3

The prompt assigns a number of variables to different terms:
X = # of terms in List L
Y = # of terms in List M
P = Average of List L
Q = Average of ALL the terms in Lists L and M.

Using the above 2 lists as reference:
X = 2
Y = 3
P = 2
Q = 13/5 = 2.6

We're asked for the AVERAGE of LIST M. Before you jump into the answer choices, think about what you're asked for....The AVERAGE of List M.....Since list M has 3 terms, we will eventually divide a sum by 3. Now, look at the answer choices.....which answers do NOT do that.... You can eliminate Answer A (it divides by 2) and Answer D (it divides by 5). Now, we just have to check 3 answers; we're looking for an answer that is the AVERAGE of List M, so we're looking for the number 3.

Answer B: (QY-PX)/Y = (7.8 - 4)/3 = 3.8/3 This is clearly too small. Eliminate B.

Answer C: (P+Q)X/Y = (4.6)(2)/3 = 9.2/3 This is too big. Eliminate C.

Answer E is all that's left, but I'll check it just to be sure....

Answer E: [(Q-P)X +QY]/Y = [(0.6)(2) +7.8]/3 = 9/3 = 3. This is a MATCH.

GMAT assassins aren't born, they're made,
Rich
_________________
Contact Rich at: Rich.C@empowergmat.com

The Course Used By GMAT Club Moderators To Earn 750+

souvik101990 Score: 760 Q50 V42 ★★★★★
ENGRTOMBA2018 Score: 750 Q49 V44 ★★★★★
Director
Joined: 02 Sep 2016
Posts: 625
Re: There are x numbers in list L, where x is a positive integer  [#permalink]

### Show Tags

02 Apr 2017, 23:44
Total for list L= xp
Total for List M=ay (Let 'a' be the average here)
Total average for two lists= q
So the total sum for two lists= q(x+y)

q(x+y)- xp= ay
a= [x(q-p)+qy]/ y
Target Test Prep Representative
Status: Founder & CEO
Affiliations: Target Test Prep
Joined: 14 Oct 2015
Posts: 10683
Location: United States (CA)
Re: There are x numbers in list L, where x is a positive integer  [#permalink]

### Show Tags

06 Apr 2017, 08:37
goodyear2013 wrote:
There are x numbers in list L, where x is a positive integer, and there are y numbers in list M, where y is a positive integer. The average (arithmetic mean) of the numbers in list L is p, and the average of all the numbers in both lists L and M is q. Which of the following expressions is the average of the numbers in list M?

A. (qy - px) / x
B. (qy - px) / y
C. (p + q)x / y
D. [(q - p)x - py] / (x + y)
E. [(q - p)x + qy] / y

Let’s use the average formula: average = sum/number. An equivalent equation is (average) x (number) = sum.

Since the average of the numbers in list L is p and there are x numbers in L, the sum of the numbers in L is px. Since the average of all of the numbers in both lists L and M is q and there are x + y numbers in both lists, the sum of all of the numbers in the two lists is q(x + y). Thus, the sum of the numbers in list M is
q(x + y) - px, and since there are y numbers in M, the average of the numbers in M is:

[q(x + y) - px]/y

(qx + qy - px)/y

(qx - px + qy)/y

[x(q - p) + qy]/y

[(q - p)x + qy]/y

_________________

# Scott Woodbury-Stewart

Founder and CEO

Scott@TargetTestPrep.com
202 Reviews

5-star rated online GMAT quant
self study course

See why Target Test Prep is the top rated GMAT quant course on GMAT Club. Read Our Reviews

If you find one of my posts helpful, please take a moment to click on the "Kudos" button.

Non-Human User
Joined: 09 Sep 2013
Posts: 15108
Re: There are x numbers in list L, where x is a positive integer  [#permalink]

### Show Tags

21 Mar 2020, 09:18
Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
_________________
Re: There are x numbers in list L, where x is a positive integer   [#permalink] 21 Mar 2020, 09:18