Jul 16 03:00 PM PDT  04:00 PM PDT Join a free live webinar and find out which skills will get you to the top, and what you can do to develop them. Save your spot today! Tuesday, July 16th at 3 pm PST Jul 16 08:00 PM EDT  09:00 PM EDT Strategies and techniques for approaching featured GMAT topics. Tuesday, July 16th at 8 pm EDT Jul 19 08:00 AM PDT  09:00 AM PDT The Competition Continues  Game of Timers is a teambased competition based on solving GMAT questions to win epic prizes! Starting July 1st, compete to win prep materials while studying for GMAT! Registration is Open! Ends July 26th Jul 20 07:00 AM PDT  09:00 AM PDT Attend this webinar and master GMAT SC in 10 days by learning how meaning and logic can help you tackle 700+ level SC questions with ease. Jul 21 07:00 AM PDT  09:00 AM PDT Attend this webinar to learn a structured approach to solve 700+ Number Properties question in less than 2 minutes
Author 
Message 
TAGS:

Hide Tags

Math Expert
Joined: 02 Sep 2009
Posts: 56244

Over the past 7 weeks, the Smith family had weekly grocery bills of $7
[#permalink]
Show Tags
25 Jun 2018, 05:02
Question Stats:
82% (01:40) correct 18% (01:48) wrong based on 884 sessions
HideShow timer Statistics
Over the past 7 weeks, the Smith family had weekly grocery bills of $74, $69, $64, $79, $64, $84, and $77. What was the Smiths' average (arithmetic mean) weekly grocery bill over the 7week period? A. $64 B. $70 C. $73 D. $74 E. $85 NEW question from GMAT® Official Guide 2019 (PS07369)
Official Answer and Stats are available only to registered users. Register/ Login.
_________________




Senior SC Moderator
Joined: 22 May 2016
Posts: 3063

Over the past 7 weeks, the Smith family had weekly grocery bills of $7
[#permalink]
Show Tags
27 Jun 2018, 18:28
Bunuel wrote: Over the past 7 weeks, the Smith family had weekly grocery bills of $74, $69, $64 $79, $64, $84, and $77. What was the Smiths' average (arithmetic mean) weekly grocery bill over the 7week period? A. $64 B. $70 C. $73 D. $74 E. $85 NEW question from GMAT® Official Guide 2019 (PS07369) I do not want to crunch these numbers. With numbers this large, find the mean as if it were a balancing point of a scale or seesaw.*The mean is the point at which the total distance of numbers below the mean (the total "weight" on a "scale") is equal to the total distance ("weight") above the mean. We have 64, 64, 69, 74, 77, 79, 84 Just make an educated guess about a number that is probably very close to the mean: 74 is good. It's the median and exactly halfway between 64 and 84. Now measure distance from (difference from) the chosen number. At the mean, the totals on each side will be equal. 64, 64, 69, [74] 77, 79, 84 Overall shortfall? Find the difference between 74 and each number to the left of 74. Sum the answers. 64 is 10 less than 74 64 is 10 less than 74 69 is 5 less than 74  Overall shortfall is (10+10+5) = 25 total on the left of (below) the middle Overall excess?Same process, but to the right of the chosen number: (7774) + (7974) + (8474) = (3+5+10) = 18 total above the middle Find the balance point, which is the mean Overall shortfall and overall excess must be equal at the balancing point. There is too much shortfall. Redistribute that extra amount evenly. \(\frac{(Shortfall  Excess)}{7}=\frac{(2518)}{7}=\frac{7}{7}=1\) Because the extra is shortfall, each list number must decrease by 1. To find the exact mean, we need to adjust only that rough number that we chose. The mean is (74  1) = 73 Answer C *An explanation can be found in The Meaning of Arithmetic Mean, here, here, and here.
_________________
SC Butler has resumed!Get two SC questions to practice, whose links you can find by date, here.Tell me, what is it you plan to do with your one wild and precious life?  Mary Oliver




Intern
Joined: 14 Apr 2017
Posts: 45
Location: Hungary
GMAT 1: 690 Q50 V34 GMAT 2: 760 Q50 V42 GMAT 3: 700 Q50 V33
WE: Education (Education)

Re: Over the past 7 weeks, the Smith family had weekly grocery bills of $7
[#permalink]
Show Tags
29 Jun 2018, 06:58
First, choose a nice, round number, such as 70, within the range of values. Then calculate the average with the following formula: Average = Nice number + Average of differences from the nice number Average = 70 + (4  1  6 + 9  6 + 14 + 7)/7 = 70 + 21/7 =73 Answer: C
_________________




eGMAT Representative
Joined: 04 Jan 2015
Posts: 2942

Re: Over the past 7 weeks, the Smith family had weekly grocery bills of $7
[#permalink]
Show Tags
25 Jun 2018, 05:10
Solution Given:• Over the past 7 weeks, the Smith family had weekly grocery bills of $74, $69, $64, $79, $64, $84, and $77 To find:• Smith’s average weekly grocery bill over the 7week period Approach and Working:• Smith’s total bill amount over the 7week period = (74 + 69 + 64 + 79 + 64 + 84 + 77) = 511 • Therefore, Smith’s average bill amount over the same period = \(\frac{511}{7}\) = 73 Hence, the correct answer is option C. Answer: C
_________________



Intern
Joined: 08 Jul 2017
Posts: 17
Location: Greece
GPA: 3.31

Over the past 7 weeks, the Smith family had weekly grocery bills of $7
[#permalink]
Show Tags
25 Jun 2018, 05:28
The first way to find the average weekly grossery bill is to find the sum of the bills and to divide it with seven. In this case we have that: Average=[64+64+69+74+77+79+84][/7]=[511][/7]=73.
An another quickest way is to arrange the seven values in ascending order. The arrengement is: 64 64 69 74 77 79 84 The median value is 74 but the three smaller values have a total difference of 25 from the median (7464=10, 7464=10, 7469=5 so 10+10+5=25). The three bigger values have a total difference of 18 from the median (7774=3, 7974=5, 8474=10 so 3+5+10=18). So clearly, the average weekly grossery bill has to be a little smaller from the median. The next smaller value from the median is 73.
In my opinion, if it is possible to make simple calculations without wasting a lot of time (as is the case in this problem), the first way is preferable. But if we have many different values and especially if the given numbers are difficult to handle, the second way can be really helpful.
In both cases, the correct answer is C.



Target Test Prep Representative
Status: Founder & CEO
Affiliations: Target Test Prep
Joined: 14 Oct 2015
Posts: 6923
Location: United States (CA)

Re: Over the past 7 weeks, the Smith family had weekly grocery bills of $7
[#permalink]
Show Tags
28 Jun 2018, 18:07
Bunuel wrote: Over the past 7 weeks, the Smith family had weekly grocery bills of $74, $69, $64, $79, $64, $84, and $77. What was the Smiths' average (arithmetic mean) weekly grocery bill over the 7week period? A. $64 B. $70 C. $73 D. $74 E. $85 We can determine the average using the formula: average = sum / number: average = (74 + 69 + 64 + 79 + 64 + 84 + 77)/7 = 511/7 = 73 Answer: C
_________________
5star 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.



Intern
Joined: 11 Jun 2011
Posts: 9

Re: Over the past 7 weeks, the Smith family had weekly grocery bills of $7
[#permalink]
Show Tags
28 Aug 2018, 03:42
Bunuel wrote: Over the past 7 weeks, the Smith family had weekly grocery bills of $74, $69, $64, $79, $64, $84, and $77. What was the Smiths' average (arithmetic mean) weekly grocery bill over the 7week period? A. $64 B. $70 C. $73 D. $74 E. $85 NEW question from GMAT® Official Guide 2019 (PS07369) Easy way out is consider avg 70  so diff for all terms is 4, 1 , 6, 9 , 6,14, 7 = sum is 21 = divided by 7 = equal to 3 so 70 +3 = 73 avg



Board of Directors
Status: QA & VA Forum Moderator
Joined: 11 Jun 2011
Posts: 4511
Location: India
GPA: 3.5
WE: Business Development (Commercial Banking)

Re: Over the past 7 weeks, the Smith family had weekly grocery bills of $7
[#permalink]
Show Tags
10 Sep 2018, 07:34
Bunuel wrote: Over the past 7 weeks, the Smith family had weekly grocery bills of $74, $69, $64, $79, $64, $84, and $77. What was the Smiths' average (arithmetic mean) weekly grocery bill over the 7week period? A. $64 B. $70 C. $73 D. $74 E. $85 NEW question from GMAT® Official Guide 2019 (PS07369) \(\frac{( 70 + 4 ) + ( 70  1 ) + ( 60 + 4 ) + ( 80  1 ) + ( 60 + 4 ) + ( 80 + 4 ) + ( 70 + 7 )}{7}\) = \(\frac{( 70 + 70 + 60 + 80 + 60 + 80 + 70 ) + ( 4  1 + 4  1 + 4 + 4 + 7 )}{7}\) = \(\frac{490 + 21}{7}\) = \(\frac{490}{7} + \frac{21}{7}\) = \(70 + 3\) = \(73\), Answer must be (C)
_________________



Intern
Joined: 02 May 2018
Posts: 14

Re: Over the past 7 weeks, the Smith family had weekly grocery bills of $7
[#permalink]
Show Tags
10 Sep 2018, 07:46
We can rule out 64, 74 and 85 as they are the extreme numbers. That leaves just two choices to choose from 70 and 73.
Only 3 values in the 60s and therefore less likely for 70.
73 is the most likely choice. Confirm 73 by taking difference and summing it up



Intern
Joined: 22 Jul 2018
Posts: 22
Location: Indonesia
GPA: 3.24

Over the past 7 weeks, the Smith family had weekly grocery bills of $7
[#permalink]
Show Tags
02 Oct 2018, 00:09
This solution might be too blunt for some people. Sum the unit digits and you will have 41. Now there are 7 numbers, which mean if x multiply by 7 must will result a number with unit digit of 1, so the x is 3. The only answer with 3 as its unit digit is C.



Director
Joined: 14 Feb 2017
Posts: 688
Location: Australia
Concentration: Technology, Strategy
GMAT 1: 560 Q41 V26 GMAT 2: 550 Q43 V23 GMAT 3: 650 Q47 V33
GPA: 2.61
WE: Management Consulting (Consulting)

Re: Over the past 7 weeks, the Smith family had weekly grocery bills of $7
[#permalink]
Show Tags
19 Nov 2018, 16:13
Admittedly I made a stupid mistake and I organised the numbers in ascending order then selected the median (74) instead of solving Sum/# Terms The method I used is only for consecutive integers and the punishment answer D is there for suckers like me.
_________________
Goal: Q49, V41
+1 Kudos if you like my post pls!




Re: Over the past 7 weeks, the Smith family had weekly grocery bills of $7
[#permalink]
19 Nov 2018, 16:13






