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

 It is currently 08 Dec 2019, 13:29 ### 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.  # At a certain restaurant, the average (arithmetic mean) number of custo

Author Message
TAGS:

### Hide Tags

Math Expert V
Joined: 02 Sep 2009
Posts: 59590
At a certain restaurant, the average (arithmetic mean) number of custo  [#permalink]

### Show Tags

1
3 00:00

Difficulty:   15% (low)

Question Stats: 82% (01:37) correct 18% (02:25) wrong based on 137 sessions

### HideShow timer Statistics

At a certain restaurant, the average (arithmetic mean) number of customers served for the past x days was 75. If the restaurant serves 120 customers today, raising the average to 90 customers per day, what is the value of x?

A. 2
B. 5
C. 9
D. 15
E. 30

Kudos for a correct solution.

_________________
CEO  S
Joined: 20 Mar 2014
Posts: 2561
Concentration: Finance, Strategy
Schools: Kellogg '18 (M)
GMAT 1: 750 Q49 V44 GPA: 3.7
WE: Engineering (Aerospace and Defense)
Re: At a certain restaurant, the average (arithmetic mean) number of custo  [#permalink]

### Show Tags

1
Bunuel wrote:
At a certain restaurant, the average (arithmetic mean) number of customers served for the past x days was 75. If the restaurant serves 120 customers today, raising the average to 90 customers per day, what is the value of x?

A. 2
B. 5
C. 9
D. 15
E. 30

Kudos for a correct solution.

Per the question,

$$\frac{75x+120}{x+1}$$ =90 ---> x =2. A is the correct answer.
Director  P
Joined: 21 May 2013
Posts: 633
Re: At a certain restaurant, the average (arithmetic mean) number of custo  [#permalink]

### Show Tags

1
Bunuel wrote:
At a certain restaurant, the average (arithmetic mean) number of customers served for the past x days was 75. If the restaurant serves 120 customers today, raising the average to 90 customers per day, what is the value of x?

A. 2
B. 5
C. 9
D. 15
E. 30

Kudos for a correct solution.

No of customers/No of days=75
C/x=75
C=75x
Now, C+120/x+1=90
Put C=75x from the earlier equation,
15x=30
x=2
Senior Manager  G
Joined: 21 Jan 2015
Posts: 454
Location: India
Concentration: Strategy, Marketing
GMAT 1: 620 Q48 V28 GMAT 2: 690 Q49 V35 WE: Sales (Consumer Products)
Re: At a certain restaurant, the average (arithmetic mean) number of custo  [#permalink]

### Show Tags

Bunuel wrote:
At a certain restaurant, the average (arithmetic mean) number of customers served for the past x days was 75. If the restaurant serves 120 customers today, raising the average to 90 customers per day, what is the value of x?

A. 2
B. 5
C. 9
D. 15
E. 30

Ans: A
Solution: from the given info we can say if N is the total number of people served in x says then avg 75=N/x = N=75x
and after todayavg 90= (N+120)/(x+1); puttine the value of N we get the x=2
_________________
--------------------------------------------------------------------
The Mind is Everything, What we Think we Become.
Director  G
Joined: 23 Jan 2013
Posts: 522
Schools: Cambridge'16
At a certain restaurant, the average (arithmetic mean) number of custo  [#permalink]

### Show Tags

1
Algebraic:

y/x=75
(y+120)/(x+1)=90
75x+120=90x+90
30=15x => x=2

Backsolving:

take 9 (C) 75*9=675+120=795/10=79.5, too low average so should take less days
take 5 (B) 75*5=375+120=495/6=82.5, low again but going up, so must be 2

A
Manager  Joined: 09 Jan 2013
Posts: 68
Concentration: Entrepreneurship, Sustainability
GMAT 1: 650 Q45 V34 GMAT 2: 740 Q51 V39 GRE 1: Q790 V650 GPA: 3.76
WE: Other (Pharmaceuticals and Biotech)
Re: At a certain restaurant, the average (arithmetic mean) number of custo  [#permalink]

### Show Tags

1
Equating total number of customers served
75x+120 = 90(x+1)
=> 15x = 30
x=2

Manager  B
Joined: 06 Jan 2014
Posts: 52
Re: At a certain restaurant, the average (arithmetic mean) number of custo  [#permalink]

### Show Tags

1
Total Customers Served in X days = 75x

Total customers served after today 75x+120

New Average (75x+120)/x+1 = 90

Solving X =2 ( Option A)
Manager  Joined: 10 Jun 2015
Posts: 110
Re: At a certain restaurant, the average (arithmetic mean) number of custo  [#permalink]

### Show Tags

1
Bunuel wrote:
At a certain restaurant, the average (arithmetic mean) number of customers served for the past x days was 75. If the restaurant serves 120 customers today, raising the average to 90 customers per day, what is the value of x?

A. 2
B. 5
C. 9
D. 15
E. 30

Kudos for a correct solution.

the increase in average is 15
the increase in customers from the mean is 45
45/15 = 3 is x+1
Therefore, x=2
Math Expert V
Joined: 02 Sep 2009
Posts: 59590
Re: At a certain restaurant, the average (arithmetic mean) number of custo  [#permalink]

### Show Tags

1
1
Bunuel wrote:
At a certain restaurant, the average (arithmetic mean) number of customers served for the past x days was 75. If the restaurant serves 120 customers today, raising the average to 90 customers per day, what is the value of x?

A. 2
B. 5
C. 9
D. 15
E. 30

Kudos for a correct solution.

GROCKIT OFFICIAL SOLUTION:

WITHOUT using the formula, we can see that today the restaurant served 30 customers above the average. The total amount ABOVE the average must equal total amount BELOW the average. This additional 30 customers must offset the “deficit” below the average of 90 created on the x days the restaurant served only 75 customers per day.

30/15 = 2 days. Choice (A).

WITH the formula, we can set up the following:

90 = (75x + 120)/(x + 1)

90x + 90 = 75x + 120

15x = 30

x = 2 Answer Choice (A)

Use whichever makes more sense to you!
_________________
Intern  Joined: 30 Sep 2013
Posts: 20
Re: At a certain restaurant, the average (arithmetic mean) number of custo  [#permalink]

### Show Tags

HI Bunnel,

If you could you explain more elaborately, that would be very helpful.
Senior Manager  Joined: 15 Sep 2011
Posts: 305
Location: United States
WE: Corporate Finance (Manufacturing)
Re: At a certain restaurant, the average (arithmetic mean) number of custo  [#permalink]

### Show Tags

riteshgmat wrote:
HI Bunnel,

If you could you explain more elaborately, that would be very helpful.

Hi riteshgmat

Perhaps I can be of assistance. He means, whatever the residual is, it must be spread across the days equally, one part below and another above. The residual here is 30 days ($$120 - 90 = 30$$) and so to have the new average be 90, it must have been split into two $$15$$s and therefore, the number of days is $$2$$.

Kr,
Ron
Current Student D
Joined: 12 Aug 2015
Posts: 2549
Schools: Boston U '20 (M)
GRE 1: Q169 V154 Re: At a certain restaurant, the average (arithmetic mean) number of custo  [#permalink]

### Show Tags

Nice Question
Here is my solution to this one =>

$$Using Mean = \frac{Sum}{#}$$

Sum(x)=75x

Sum(x+1)=75x+120

As pre Question => 75x+120/x+1=90
Hence x=2

Alternately,
75+15(x+1)=120
x=2

Hence A

_________________
Non-Human User Joined: 09 Sep 2013
Posts: 13726
Re: At a certain restaurant, the average (arithmetic mean) number of custo  [#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: At a certain restaurant, the average (arithmetic mean) number of custo   [#permalink] 05 Oct 2018, 05:06
Display posts from previous: Sort by

# At a certain restaurant, the average (arithmetic mean) number of custo  