GMAT Question of the Day - Daily to your Mailbox; hard ones only

 It is currently 22 Oct 2019, 09:31 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

Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.  The average (arithmetic mean) of y numbers is x. If 30 is added to the

 new topic post reply Question banks Downloads My Bookmarks Reviews Important topics
Author Message
TAGS:

Hide Tags

Math Expert V
Joined: 02 Sep 2009
Posts: 58421
The average (arithmetic mean) of y numbers is x. If 30 is added to the  [#permalink]

Show Tags

2
2 00:00

Difficulty:   25% (medium)

Question Stats: 80% (02:00) correct 20% (01:59) wrong based on 108 sessions

HideShow timer Statistics

The average (arithmetic mean) of y numbers is x. If 30 is added to the set of numbers, then the average will be x - 5. What is the value of y in terms of x ?

A. x/6 - 6
B. x/6 - 5
C. x/7 - 5
D. x/5 - 7
E. x/5 - 6

_________________
Current Student P
Joined: 02 Jul 2017
Posts: 289
Concentration: Entrepreneurship, Technology
GMAT 1: 730 Q50 V38 Re: The average (arithmetic mean) of y numbers is x. If 30 is added to the  [#permalink]

Show Tags

2
Let sum of y numbers by S(y)

$$So Average = \frac{S(y)}{y}= x => S(y) = x*y$$

Now 30 is added to the list.
=> Sum = S(y)+30
No. of terms = y+1

$$So average = \frac{S(y) +30}{y+1}= x-5$$
=> S(y)+30 = (x-5)(y+1)
=> xy+30 = xy+x-5y-5
=> x-5y=35
=>5y=x-35
=>$$y= \frac{x}{5} -7$$

Current Student S
Joined: 25 Jul 2011
Posts: 57
Location: India
Concentration: Strategy, Operations
GMAT 1: 740 Q49 V41 GPA: 3.5
WE: Engineering (Energy and Utilities)
Re: The average (arithmetic mean) of y numbers is x. If 30 is added to the  [#permalink]

Show Tags

Bunuel wrote:
The average (arithmetic mean) of y numbers is x. If 30 is added to the set of numbers, then the average will be x - 5. What is the value of y in terms of x ?

A. x/6 - 6
B. x/6 - 5
C. x/7 - 5
D. x/5 - 7
E. x/5 - 6

Since mean of "y" numbers is "x"...sum of these no. = mean (or average)* number of nos=x*y
again..if a no 30 is added..sum will be (xy+30) and no of numbers will be y+1;

reapplying same formula... (xy+30)=(x-5)(y+1) as new mean is (x-5) as per question stem;

so...solving we get (xy+30)=xy+x-5y-5
35=x-5y
5y=x-35
or y=x/5-7 hence (D)

hit kudos if this was helpful _________________
Please hit kudos button below if you found my post helpful..TIA
Math Expert V
Joined: 02 Aug 2009
Posts: 8006
Re: The average (arithmetic mean) of y numbers is x. If 30 is added to the  [#permalink]

Show Tags

Bunuel wrote:
The average (arithmetic mean) of y numbers is x. If 30 is added to the set of numbers, then the average will be x - 5. What is the value of y in terms of x ?

A. x/6 - 6
B. x/6 - 5
C. x/7 - 5
D. x/5 - 7
E. x/5 - 6

AVG of y Numbers is x, so SUM is yx..
Add 30 to it yx+30..
So new avg = $$\frac{yx+30}{1+y}=x-5.....yx+30=x-5+xy-5y.....35=x-5y......y=\frac{x-35}{5}=\frac{x}{5}-7$$

D
_________________
Manager  B
Joined: 19 Jul 2017
Posts: 82
Location: India
Concentration: General Management, Strategy
GPA: 3.5
Re: The average (arithmetic mean) of y numbers is x. If 30 is added to the  [#permalink]

Show Tags

Bunuel wrote:
The average (arithmetic mean) of y numbers is x. If 30 is added to the set of numbers, then the average will be x - 5. What is the value of y in terms of x ?

A. x/6 - 6
B. x/6 - 5
C. x/7 - 5
D. x/5 - 7
E. x/5 - 6

Sum =Average *Number
Sum of y numbers is xy
Sum of y+1= (x-5)*y+1

xy+30 =(x-5)*(y+1)
xy+30=xy-5y+x-5
30+5=x-5y
x=5(y+7);
y=x/5-7

So Ans:D
Senior SC Moderator V
Joined: 22 May 2016
Posts: 3574
The average (arithmetic mean) of y numbers is x. If 30 is added to the  [#permalink]

Show Tags

Bunuel wrote:
The average (arithmetic mean) of y numbers is x. If 30 is added to the set of numbers, then the average will be x - 5. What is the value of y in terms of x ?

A. x/6 - 6
B. x/6 - 5
C. x/7 - 5
D. x/5 - 7
E. x/5 - 6

If the equation is hard to set up, a simple A*n = S table can help.

The key is that one occurrence of a numeric value added or subtracted to the set of numbers gets its own row; then add column "n" to get total number and column "S" to get total sum (averages CANNOT be added).

__A__|__n__|___S____|
__x__|__y__|___xy____|
_30__|__1__|___30___|
-------|_y+1_|_xy+30__|

The new average is (x - 5). That doesn't get written in the table anywhere. It's the RHS of the equation.

LHS = $$\frac{Total Sum}{Total Number}$$

$$\frac{(xy + 30)}{(y+1)} = (x - 5)$$

$$xy + 30 = (x - 5)(y + 1)$$
$$xy + 30 = xy + x - 5y - 5$$
$$5y = x - 35$$

$$y = \frac{x}{5} - 7$$

_________________
SC Butler has resumed! Get two SC questions to practice, whose links you can find by date, here.

Instructions for living a life. Pay attention. Be astonished. Tell about it. -- Mary Oliver
Non-Human User Joined: 09 Sep 2013
Posts: 13409
Re: The average (arithmetic mean) of y numbers is x. If 30 is added to the  [#permalink]

Show Tags

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: The average (arithmetic mean) of y numbers is x. If 30 is added to the   [#permalink] 01 Jan 2019, 04:41
Display posts from previous: Sort by

The average (arithmetic mean) of y numbers is x. If 30 is added to the

 new topic post reply Question banks Downloads My Bookmarks Reviews Important topics

 Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne  