Last visit was: 14 Jun 2024, 01:18 It is currently 14 Jun 2024, 01:18
Toolkit
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.

# Last year, in a certain housing development, the average (arithmetic m

SORT BY:
Tags:
Show Tags
Hide Tags
Math Expert
Joined: 02 Sep 2009
Posts: 93700
Own Kudos [?]: 631612 [110]
Given Kudos: 82302
examPAL Representative
Joined: 07 Dec 2017
Posts: 1050
Own Kudos [?]: 1790 [36]
Given Kudos: 26
Target Test Prep Representative
Joined: 04 Mar 2011
Affiliations: Target Test Prep
Posts: 3042
Own Kudos [?]: 6449 [21]
Given Kudos: 1646
General Discussion
e-GMAT Representative
Joined: 04 Jan 2015
Posts: 3717
Own Kudos [?]: 17134 [8]
Given Kudos: 165
Re: Last year, in a certain housing development, the average (arithmetic m [#permalink]
2
Kudos
6
Bookmarks

Solution

Given:

• We are given that the average price of 20 houses is \$160,000.
To find:

• We need to find if the price of 9 of the 20 houses is less than the average price i.e \$160,000 or not.

Approach and Working:

Statement 1: Last year the greatest price of one of the 20 houses was \$219,000.
This does not give us any information about the pricing of remaining 19 houses. Thus, we cannot say whether 9 of the 20 houses are priced less than \$160,000 or not.

Statement 2: Last year the median of the prices of the 20 houses was \$150,000.
In a set of 20 numbers, the median is the 10th and 11th term or median = 10th term + 11th term/2

Thus, we can get median= \$150,000 in two cases:
• When the values of both, 10th and 11th term is \$150,000.
• Or, when 10th term is as less from \$150,000 as 11th term is greater than \$150,000.

However, in both the cases at least 10 terms will be less than \$150,000.

Hence, statement 2 is sufficient to get the answer.

CEO
Joined: 23 Feb 2015
Posts: 2512
Own Kudos [?]: 2118 [0]
Given Kudos: 1976
Concentration: Finance, Technology
Re: Last year, in a certain housing development, the average (arithmetic m [#permalink]
DavidTutorexamPAL wrote:
Bunuel wrote:
Last year, in a certain housing development, the average (arithmetic mean) price of 20 new houses was \$160,000. Did more than 9 of the 20 houses have prices that were less than the average price last year?

(1) Last year the greatest price of one of the 20 houses was \$219,000.
(2) Last year the median of the prices of the 20 houses was \$150,000.

NEW question from GMAT® Official Guide 2019

(DS05269)

Questions dealing with average, mean, and std can often be solved with logic, without explicit calculations.
We'll look for such an answer, a Logical approach.

(1) Knowing only one of the 20 values isn't enough, we can, for example, use one house to balance out the \$219,000 and divide the rest however we like. They could all be exactly \$160,00 (answering the question with NO) or could have more than 9 be a bit less than \$160,000 and the rest a bit more than \$160,000) (giving YES)
Insufficient.

(2) If the median was \$150,000 then either 10 or 11 houses cost less than or equal to \$150,000 (depending on if the two middle values were equal or not) meaning the answer to our question must be YES - at least 9 houses had less than \$160,000.

DavidTutorexamPAL
Quote:
at least 9 houses had less than \$160,000.

Is it at least 9 or 10?
It seems that it should be at least 10 houses had less than \$160,000.
Am I missing anything?
Thanks__
CEO
Joined: 23 Feb 2015
Posts: 2512
Own Kudos [?]: 2118 [0]
Given Kudos: 1976
Concentration: Finance, Technology
Re: Last year, in a certain housing development, the average (arithmetic m [#permalink]
Bunuel wrote:
Last year, in a certain housing development, the average (arithmetic mean) price of 20 new houses was \$160,000. Did more than 9 of the 20 houses have prices that were less than the average price last year?

(1) Last year the greatest price of one of the 20 houses was \$219,000.

Hello Experts,
EMPOWERgmatRichC, VeritasKarishma, IanStewart, Bunuel, chetan2u, ArvindCrackVerbal, GMATGuruNY, AaronPond, GMATinsight, ccooley, RonPurewal
The wording of the statement 1 does not make sense to me. Could you help me, please?
Which one from the following could be better version?

a) Last year the greatest price of one of the 20 houses was \$219,000
VS
b) Last year the greatest price of one of the 20 houses was \$219,000
Quote:
a) Last year the greatest price of one of the 20 houses was \$219,000

Doesn't version a) mean ''there are more than 1 houses which carry highest prices''? How can more than one house be highest at a time?
Thanks__
Tutor
Joined: 04 Aug 2010
Posts: 1324
Own Kudos [?]: 3188 [0]
Given Kudos: 9
Schools:Dartmouth College
Re: Last year, in a certain housing development, the average (arithmetic m [#permalink]
How can more than one house be highest at a time?
Thanks__

Consider five houses with the following prices:
{100, 150, 200, 200, 200}
Of the three prices in the set above -- 100, 150, and 200 -- 200 is the greatest.
Three of the five houses have the greatest price (200).
Thus, it is possible for more than one house to have the greatest price.

Originally posted by GMATGuruNY on 02 May 2020, 03:18.
Last edited by GMATGuruNY on 02 May 2020, 08:49, edited 1 time in total.
GMAT Tutor
Joined: 24 Jun 2008
Posts: 4128
Own Kudos [?]: 9360 [1]
Given Kudos: 91
Q51  V47
Re: Last year, in a certain housing development, the average (arithmetic m [#permalink]
1
Kudos
The wording of the statement 1 does not make sense to me. Could you help me, please?
Which one from the following could be better version?

a) Last year the greatest price of one of the 20 houses was \$219,000
VS
b) Last year the greatest price of one of the 20 houses was \$219,000
Quote:
a) Last year the greatest price of one of the 20 houses was \$219,000

Doesn't version a) mean ''there are more than 1 houses which carry highest prices''? How can more than one house be highest at a time?
Thanks__

I agree that the wording of Statement 1 is not ideal, since it seems to be talking about just one house in the group, and what the greatest price of that one house was, as if the house was sold several times at different prices and \$219,000 was the highest price at which it sold. It would be better if it read "Last year the greatest price of any of the 20 houses was \$219,000". But it's still clear what Statement 1 means.

I don't agree with the post above that suggests Statement 1 implies that exactly one house sold for \$219,000. It simply conveys that no house sold for more than \$219,000.
GMAT Club Legend
Joined: 08 Jul 2010
Status:GMAT/GRE Tutor l Admission Consultant l On-Demand Course creator
Posts: 6012
Own Kudos [?]: 13613 [0]
Given Kudos: 124
Location: India
GMAT: QUANT+DI EXPERT
Schools: IIM (A) ISB '24
GMAT 1: 750 Q51 V41
WE:Education (Education)
Re: Last year, in a certain housing development, the average (arithmetic m [#permalink]
Bunuel wrote:
Last year, in a certain housing development, the average (arithmetic mean) price of 20 new houses was \$160,000. Did more than 9 of the 20 houses have prices that were less than the average price last year?

(1) Last year the greatest price of one of the 20 houses was \$219,000.

Hello Experts,
The wording of the statement 1 does not make sense to me. Could you help me, please?
Which one from the following could be better version?

a) Last year the greatest price of one of the 20 houses was \$219,000
VS
b) Last year the greatest price of one of the 20 houses was \$219,000
Quote:
a) Last year the greatest price of one of the 20 houses was \$219,000

Doesn't version a) mean ''there are more than 1 houses which carry highest prices''? How can more than one house be highest at a time?
Thanks__

The language of the statement as mentioned in Question is apt.

The question clearly intends to tell you that one of the 20 houses which is marked at highest price was 219000

I think it's more of a SC doubt than Quant Doubt. just kidding.

But yeah, the language as mentioned is perfect.
CEO
Joined: 23 Feb 2015
Posts: 2512
Own Kudos [?]: 2118 [0]
Given Kudos: 1976
Concentration: Finance, Technology
Re: Last year, in a certain housing development, the average (arithmetic m [#permalink]
IanStewart wrote:
The wording of the statement 1 does not make sense to me. Could you help me, please?
Which one from the following could be better version?

a) Last year the greatest price of one of the 20 houses was \$219,000
VS
b) Last year the greatest price of one of the 20 houses was \$219,000
Quote:
a) Last year the greatest price of one of the 20 houses was \$219,000

Doesn't version a) mean ''there are more than 1 houses which carry highest prices''? How can more than one house be highest at a time?
Thanks__

I agree that the wording of Statement 1 is not ideal, since it seems to be talking about just one house in the group, and what the greatest price of that one house was, as if the house was sold several times at different prices and \$219,000 was the highest price at which it sold. It would be better if it read "Last year the greatest price of any of the 20 houses was \$219,000". But it's still clear what Statement 1 means.

I don't agree with the post above that suggests Statement 1 implies that exactly one house sold for \$219,000. It simply conveys that no house sold for more than \$219,000.

IanStewart
So, do you want to mean that ''in these 20, the two prices (19th house and 20th house prices) could be \$219,000 and \$219,000, respectively''?
Thanks Ian...
GMAT Club Legend
Joined: 03 Oct 2013
Affiliations: CrackVerbal
Posts: 4940
Own Kudos [?]: 7732 [1]
Given Kudos: 216
Location: India
Re: Last year, in a certain housing development, the average (arithmetic m [#permalink]
1
Kudos
Bunuel wrote:
Last year, in a certain housing development, the average (arithmetic mean) price of 20 new houses was \$160,000. Did more than 9 of the 20 houses have prices that were less than the average price last year?

(1) Last year the greatest price of one of the 20 houses was \$219,000.

Hello Experts,
EMPOWERgmatRichC, VeritasKarishma, IanStewart, Bunuel, chetan2u, ArvindCrackVerbal, GMATGuruNY, AaronPond, GMATinsight, ccooley, RonPurewal
The wording of the statement 1 does not make sense to me. Could you help me, please?
Which one from the following could be better version?

a) Last year the greatest price of one of the 20 houses was \$219,000
VS
b) Last year the greatest price of one of the 20 houses was \$219,000
Quote:
a) Last year the greatest price of one of the 20 houses was \$219,000

Doesn't version a) mean ''there are more than 1 houses which carry highest prices''? How can more than one house be highest at a time?
Thanks__

Statement I is probably intended to be confusing. We are all used to the idea of the superlative being ONE value and that’s probably what this statement uses in a way to make the statement sound confusing.

My 2 cents on this - imagine that there are 20 students in a class and you say the “the greatest height of one of the students is 160cm”. This means that there is a possibility that there are more than one students who are 160cm tall. The GREATEST height is 160 cm, so there cannot be a number greater than 160 that represents the height; there can be more than one student who has this number as his/her height.

On the other hand, if you say “The tallest of the 20 students is 170 cm tall”, this means that there is ONE unique student who is 170 cm tall.

So, it really depends on what the adjective “greatest” modifies, in such questions. As GMATinsight has mentioned, there’s a small element of SC involved here that can lead to better comprehension of the statement.
Hope that helps!
Tutor
Joined: 16 Oct 2010
Posts: 14950
Own Kudos [?]: 65900 [2]
Given Kudos: 433
Location: Pune, India
Re: Last year, in a certain housing development, the average (arithmetic m [#permalink]
2
Kudos
Bunuel wrote:
Last year, in a certain housing development, the average (arithmetic mean) price of 20 new houses was \$160,000. Did more than 9 of the 20 houses have prices that were less than the average price last year?

(1) Last year the greatest price of one of the 20 houses was \$219,000.

Hello Experts,
EMPOWERgmatRichC, VeritasKarishma, IanStewart, Bunuel, chetan2u, ArvindCrackVerbal, GMATGuruNY, AaronPond, GMATinsight, ccooley, RonPurewal
The wording of the statement 1 does not make sense to me. Could you help me, please?
Which one from the following could be better version?

a) Last year the greatest price of one of the 20 houses was \$219,000
VS
b) Last year the greatest price of one of the 20 houses was \$219,000
Quote:
a) Last year the greatest price of one of the 20 houses was \$219,000

Doesn't version a) mean ''there are more than 1 houses which carry highest prices''? How can more than one house be highest at a time?
Thanks__

Yeah, not a fan of the wording.

(1) Last year the greatest price of one of the 20 houses was \$219,000

We are talking about one of the houses. Looks like the price keeps fluctuating. So the greatest price last year that it reached was \$219,000.
Doesn't look like we are comparing prices of different houses.

To do that, it has to be "any of the houses".

Taking the whole question into consideration, I understand that they are talking about one price point in the year for each house. So perhaps what they mean to say is that there was a house with price = 219k and no other house had a price more than this. In any case, it is obvious that stmnt 1 is not sufficient.
Thankfully, stmnt 2 is sufficient alone.
Intern
Joined: 30 Mar 2018
Posts: 30
Own Kudos [?]: 25 [0]
Given Kudos: 116
Location: United Kingdom
GMAT 1: 660 Q42 V38
GPA: 4
Re: Last year, in a certain housing development, the average (arithmetic m [#permalink]
Hi

Could anyone please advise of an efficient way of testing statement 1? I found that it took me awfully long to come up with the bookend scenarios: 1 house priced less than average and 19 houses priced less than average. EMPOWERgmatRichC could you please advise?

Thanks
GMAT Club Legend
Joined: 19 Dec 2014
Status:GMAT Assassin/Co-Founder
Affiliations: EMPOWERgmat
Posts: 21843
Own Kudos [?]: 11720 [3]
Given Kudos: 450
Location: United States (CA)
GMAT 1: 800 Q51 V49
GRE 1: Q170 V170
Re: Last year, in a certain housing development, the average (arithmetic m [#permalink]
2
Kudos
1
Bookmarks
silverprince wrote:
Hi

Could anyone please advise of an efficient way of testing statement 1? I found that it took me awfully long to come up with the bookend scenarios: 1 house priced less than average and 19 houses priced less than average. EMPOWERgmatRichC could you please advise?

Thanks

Hi silverprince,

We're told that last year, in a certain housing development, the AVERAGE (arithmetic mean) price of 20 new houses was \$160,000. We're asked if MORE than 9 of the 20 houses have prices that were LESS than the average price last year. This question can be solved with a bit of Arithmetic and TESTing VALUES (although you don't have to do much math to get to the solution).

To start, since the average price of the 20 houses was \$160,000, we know that the SUM of those 20 prices is (20)(\$160,000) = \$3,200,000. We're ultimately looking to see how we can distribute that total sum to see if more than 9.... OR exactly 9 or less than 9 of the houses are below the \$160,000 threshold. I want to reiterate that you DO NOT need to be doing lots of math - as long as you understand how the 20 values "relate" to the \$160,000 average.

(1) Last year the greatest price of one of the 20 houses was \$219,000.

With Fact 1, we know that the HIGHEST PRICE was \$59,000 more than the average... but what about the other 19 prices? To bring the average down to \$160,000.....

-We could 'distribute' that \$59,000 overage equally to the remaining 19 houses and make ALL 19 below average in price... and the answer to the question is YES.
-We could 'distribute' that \$59,000 overage equally to 8 of the 19 houses and make those 8 below average in price...and keep the other 11 AT the exact average price... and the answer to the question is NO.
Fact 1 is INSUFFICIENT

(2) Last year the median of the prices of the 20 houses was \$150,000.

With Fact 2, we're dealing with the MEDIAN of the group. If we put the prices of the 20 houses in order from least to greatest, the median would be the AVERAGE of the two "middle prices" (re: the 10th and 11th prices). Since the median price is BELOW the AVERAGE price, we know that 1 OR both of the 10th and 11th prices are BELOW the average.

For example,
-IF the two prices were \$150,000 and \$150,000, then they are BOTH below the average
-IF the two prices were \$130,000 and \$170,000, then ONE price is below the average and one is above the average
-IF the two prices were \$140,000 and \$160,000, then ONE price is below the average and one IS the average

In ALL THREE situations, since we're dealing with the MEDIAN, we know that there are 9 other prices that are equal to (or below) the lower price of that pair (remember, we had to put the numbers in order from least to greatest before we got the median). Thus, we KNOW that those 9 prices are below the average AND we have 1 or 2 additional prices that are below the average (depending on the prices that you chose for the two 'median' houses). Thus, there will ALWAYS be either 10 or 11 houses that are below the average... so the answer to the question is ALWAYS YES.
Fact 2 is SUFFICIENT

GMAT assassins aren't born, they're made,
Rich
Intern
Joined: 30 Mar 2018
Posts: 30
Own Kudos [?]: 25 [1]
Given Kudos: 116
Location: United Kingdom
GMAT 1: 660 Q42 V38
GPA: 4
Re: Last year, in a certain housing development, the average (arithmetic m [#permalink]
1
Kudos
EMPOWERgmatRichC wrote:
silverprince wrote:
Hi

Could anyone please advise of an efficient way of testing statement 1? I found that it took me awfully long to come up with the bookend scenarios: 1 house priced less than average and 19 houses priced less than average. EMPOWERgmatRichC could you please advise?

Thanks

Hi silverprince,

We're told that last year, in a certain housing development, the AVERAGE (arithmetic mean) price of 20 new houses was \$160,000. We're asked if MORE than 9 of the 20 houses have prices that were LESS than the average price last year. This question can be solved with a bit of Arithmetic and TESTing VALUES (although you don't have to do much math to get to the solution).

To start, since the average price of the 20 houses was \$160,000, we know that the SUM of those 20 prices is (20)(\$160,000) = \$3,200,000. We're ultimately looking to see how we can distribute that total sum to see if more than 9.... OR exactly 9 or less than 9 of the houses are below the \$160,000 threshold. I want to reiterate that you DO NOT need to be doing lots of math - as long as you understand how the 20 values "relate" to the \$160,000 average.

(1) Last year the greatest price of one of the 20 houses was \$219,000.

With Fact 1, we know that the HIGHEST PRICE was \$59,000 more than the average... but what about the other 19 prices? To bring the average down to \$160,000.....

-We could 'distribute' that \$59,000 overage equally to the remaining 19 houses and make ALL 19 below average in price... and the answer to the question is YES.
-We could 'distribute' that \$59,000 overage equally to 8 of the 19 houses and make those 8 below average in price...and keep the other 11 AT the exact average price... and the answer to the question is NO.
Fact 1 is INSUFFICIENT

(2) Last year the median of the prices of the 20 houses was \$150,000.

With Fact 2, we're dealing with the MEDIAN of the group. If we put the prices of the 20 houses in order from least to greatest, the median would be the AVERAGE of the two "middle prices" (re: the 10th and 11th prices). Since the median price is BELOW the AVERAGE price, we know that 1 OR both of the 10th and 11th prices are BELOW the average.

For example,
-IF the two prices were \$150,000 and \$150,000, then they are BOTH below the average
-IF the two prices were \$130,000 and \$170,000, then ONE price is below the average and one is above the average
-IF the two prices were \$140,000 and \$160,000, then ONE price is below the average and one IS the average

In ALL THREE situations, since we're dealing with the MEDIAN, we know that there are 9 other prices that are equal to (or below) the lower price of that pair (remember, we had to put the numbers in order from least to greatest before we got the median). Thus, we KNOW that those 9 prices are below the average AND we have 1 or 2 additional prices that are below the average (depending on the prices that you chose for the two 'median' houses). Thus, there will ALWAYS be either 10 or 11 houses that are below the average... so the answer to the question is ALWAYS YES.
Fact 2 is SUFFICIENT

GMAT assassins aren't born, they're made,
Rich

Thanks EMPOWERgmatRichC this is very helpful and shows that actually we don't actually need to calculate the possible prices for the bookend scenarios in statement 1, we just need to understand the logic of how the prices of the houses relate to the average.

For anyone looking at this thread, I would highly recommend searching for replies / posts by [b]EMPOWERgmatRichC[/b]. In my experience, they have consistently provided the best approach to solving problems and have taught me a completely new way of thinking about the GMAT.
Intern
Joined: 18 Mar 2019
Posts: 8
Own Kudos [?]: 3 [0]
Given Kudos: 265
Re: Last year, in a certain housing development, the average (arithmetic m [#permalink]
For those who, like me, are super confused with Statement A, here is an approach I used that finally satisfied me:

Keeping the question in mind:
"Did more than 9 of the 20 houses have prices that were less than the average price last year"

Given the highest value that can be taken is \$219k, let's take two cases:
1. Finding the maximum price of the first 8 (a number less than 9) houses (arranged in increasing order of price), and
2. Finding the maximum price of the first 10 (a number greater than 9) houses
If both these values are lower than \$160k, we can be sure that Statement 1 can't get a definite answer.

Case 1:
Price of 1st 8 = x each
Price of next 12 = 219 each (a value certainly more than the average \$160)
8*x+219*12=20*160
=> x = 400-219*12/8 ~400-220*12/8 ~400-330 ~70
=> x= 70 (approx)

Case 2:
Price of 1st 10 = x each
Price of next 8 = 219 each
10*x+219*8=20*160
=> x =320-219*8/10 ~320-220*8/10 ~320-176 ~154
=> x = 154 (approx)

Case 1 and 2 shows that values lower than the average (\$160) can occur both less than and more than 9 times.
Hence, reject A.

I struggled hard with this 600 level question that 76% folks did correctly. Phew!

P.S.: I tried using the logic used in solution of this Official question: https://gmatclub.com/forum/last-month-1 ... 28477.html
Director
Joined: 14 Jul 2010
Status:No dream is too large, no dreamer is too small
Posts: 966
Own Kudos [?]: 4987 [0]
Given Kudos: 690
Concentration: Accounting
Re: Last year, in a certain housing development, the average (arithmetic m [#permalink]
Top Contributor
Bunuel wrote:
Last year, in a certain housing development, the average (arithmetic mean) price of 20 new houses was \$160,000. Did more than 9 of the 20 houses have prices that were less than the average price last year?

(1) Last year the greatest price of one of the 20 houses was \$219,000.
(2) Last year the median of the prices of the 20 houses was \$150,000.

NEW question from GMAT® Official Guide 2019

(DS05269)

(1) The highest value of the 20 houses is 219,000. From this information, it is tough to know other distributions of numbers. Insufficient.

(2) The median is 150,000 so surely the first 9 houses have prices less than or equal to 150,000 prices and sum of the 10th and 11th prices are 300,000. As to get median numbers are arranged in ascending order so the 10th number (price) will also be 150,000.

Option 2 is sufficient.

Ans. B
VP
Joined: 11 Aug 2020
Posts: 1255
Own Kudos [?]: 204 [0]
Given Kudos: 332
Re: Last year, in a certain housing development, the average (arithmetic m [#permalink]
So for statement 2, the conclusion is YES, more than 9 houses had a price less than the median?

Since the first 9 are definitely below.

10th + 11th = 300K which means at minimum an additional house costs below 160k and possibly even both of them (in the event that they are both 150K)
GMAT Club Legend
Joined: 08 Jul 2010
Status:GMAT/GRE Tutor l Admission Consultant l On-Demand Course creator
Posts: 6012
Own Kudos [?]: 13613 [1]
Given Kudos: 124
Location: India
GMAT: QUANT+DI EXPERT
Schools: IIM (A) ISB '24
GMAT 1: 750 Q51 V41
WE:Education (Education)
Re: Last year, in a certain housing development, the average (arithmetic m [#permalink]
1
Kudos
Bunuel wrote:
Last year, in a certain housing development, the average (arithmetic mean) price of 20 new houses was \$160,000. Did more than 9 of the 20 houses have prices that were less than the average price last year?

(1) Last year the greatest price of one of the 20 houses was \$219,000.
(2) Last year the median of the prices of the 20 houses was \$150,000.

NEW question from GMAT® Official Guide 2019

(DS05269)

Solve the Official Questions more productively

Click here and solve 1000+ Official Questions with Video solutions as Timed Sectional Tests
and Dedicated Data Sufficiency (DS) Course

Video solution by GMATinsight

Get TOPICWISE: Concept Videos | Practice Qns 100+ | Official Qns 50+ | 100% Video solution CLICK.
Two MUST join YouTube channels : GMATinsight (1000+ FREE Videos) and GMATclub
Non-Human User
Joined: 09 Sep 2013
Posts: 33551
Own Kudos [?]: 837 [0]
Given Kudos: 0
Re: Last year, in a certain housing development, the average (arithmetic m [#permalink]
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: Last year, in a certain housing development, the average (arithmetic m [#permalink]
Moderator:
Math Expert
93700 posts