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

 It is currently 22 Sep 2018, 14:34

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

Show Tags

25 Jun 2018, 05:02
00:00

Difficulty:

5% (low)

Question Stats:

81% (01:20) correct 19% (01:28) wrong based on 306 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 7-week period? A.$64

B. $70 C.$73

D. $74 E.$85

NEW question from GMAT® Official Guide 2019

(PS07369)

_________________
e-GMAT Representative
Joined: 04 Jan 2015
Posts: 2007
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 7-week period

Approach and Working:
• Smith’s total bill amount over the 7-week 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.

_________________

Number Properties | Algebra |Quant Workshop

Success Stories
Guillermo's Success Story | Carrie's Success Story

Ace GMAT quant
Articles and Question to reach Q51 | Question of the week

Number Properties – Even Odd | LCM GCD | Statistics-1 | Statistics-2
Word Problems – Percentage 1 | Percentage 2 | Time and Work 1 | Time and Work 2 | Time, Speed and Distance 1 | Time, Speed and Distance 2
Advanced Topics- Permutation and Combination 1 | Permutation and Combination 2 | Permutation and Combination 3 | Probability
Geometry- Triangles 1 | Triangles 2 | Triangles 3 | Common Mistakes in Geometry
Algebra- Wavy line | Inequalities

Practice Questions
Number Properties 1 | Number Properties 2 | Algebra 1 | Geometry | Prime Numbers | Absolute value equations | Sets

| '4 out of Top 5' Instructors on gmatclub | 70 point improvement guarantee | www.e-gmat.com

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

Show Tags

27 Jun 2018, 18:28
1
1
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 7-week period? A.$64

B. $70 C.$73

D. $74 E.$85

NEW question from GMAT® Official Guide 2019

(PS07369)

I took the approach described by Iakovos1995 (second method) +1.

I do not want to attempt crunching these numbers.

Finding the mean as a balance point with numbers this large is faster.

The arithmetic mean can be viewed as a balancing point of a scale or seesaw.

The mean is the point at which the total distance of numbers below the mean is equal to the total distance above the mean

VeritasPrepKarishma explains the theory and method in The Meaning of Arithmetic Mean, here, here, and here (important!)

This "balancing" method makes finding the average of a lot of large numbers much easier.

We have 64, 64, 69, 74, 77, 79, 84

74 is the median. The lowest and highest data values (64 and 84) are both 10 away from the median, so the list is not heavily skewed.

We make an educated guess about the mean: 74 is the middle number, and the center of the range.

Now measure distance from (difference from) the middle value. At the mean, the totals on each side will be equal. [74] is NOT the mean -- it is a number that is probably very close to the mean.

64, 64, 69, [74] 77, 79, 84

64 is 10 less than 74
64 is 10 less than 74
69 is 5 less than 74

Total: 25 below the middle

VeritasPrepKarishma calls this total the "overall shortfall."

77 is 3 more than 74
79 is 5 more than 74
84 is 10 more than 74

Total: 18 above the middle
This is called "overall excess."

Shortfall must balance out excess. Not true here, so the scale is not balanced. The overall shortfall is greater than the overall excess by 7: (25 - 18) = 7

This shortfall of 7 needs to be distributed evenly. There are a total of 7 numbers. So the mean must decrease (because we have a shortfall) by $$\frac{7}{7}=1$$.
(74 - 1) = 73

_________________

In the depths of winter, I finally learned
that within me there lay an invincible summer.

Target Test Prep Representative
Status: Founder & CEO
Affiliations: Target Test Prep
Joined: 14 Oct 2015
Posts: 3515
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 1 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 7-week 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 _________________ Scott Woodbury-Stewart Founder and CEO GMAT Quant Self-Study Course 500+ lessons 3000+ practice problems 800+ HD solutions Intern Joined: 14 Apr 2017 Posts: 1 Location: Hungary GMAT 1: 690 Q50 V34 GMAT 2: 760 Q50 V42 Re: Over the past 7 weeks, the Smith family had weekly grocery bills of$7  [#permalink]

Show Tags

29 Jun 2018, 06:58
2
2
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

Intern
Joined: 11 Jun 2011
Posts: 8
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 7-week 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 Manager Joined: 20 Oct 2016 Posts: 69 Re: Over the past 7 weeks, the Smith family had weekly grocery bills of$7  [#permalink]

Show Tags

10 Sep 2018, 01:08
https://youtu.be/laNkexjIN2Y
_________________

Founder, GMAT Mantra
One to One Live Online GMAT Coaching
8860616050
http://www.gmatmantra.com

Board of Directors
Status: QA & VA Forum Moderator
Joined: 11 Jun 2011
Posts: 4033
Location: India
GPA: 3.5
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 7-week 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) _________________ Thanks and Regards Abhishek.... PLEASE FOLLOW THE RULES FOR POSTING IN QA AND VA FORUM AND USE SEARCH FUNCTION BEFORE POSTING NEW QUESTIONS How to use Search Function in GMAT Club | Rules for Posting in QA forum | Writing Mathematical Formulas |Rules for Posting in VA forum | Request Expert's Reply ( VA Forum Only ) Intern Joined: 02 May 2018 Posts: 11 GMAT 1: 620 Q46 V29 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
Re: Over the past 7 weeks, the Smith family had weekly grocery bills of $7 &nbs [#permalink] 10 Sep 2018, 07:46 Display posts from previous: Sort by Over the past 7 weeks, the Smith family had weekly grocery bills of$7

Events & Promotions

 Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne Kindly note that the GMAT® test is a registered trademark of the Graduate Management Admission Council®, and this site has neither been reviewed nor endorsed by GMAC®.