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

 It is currently 21 Feb 2019, 14:41

### 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

## Events & Promotions

###### Events & Promotions in February
PrevNext
SuMoTuWeThFrSa
272829303112
3456789
10111213141516
17181920212223
242526272812
Open Detailed Calendar
• ### Online GMAT boot camp for FREE

February 21, 2019

February 21, 2019

10:00 PM PST

11:00 PM PST

Kick off your 2019 GMAT prep with a free 7-day boot camp that includes free online lessons, webinars, and a full GMAT course access. Limited for the first 99 registrants! Feb. 21st until the 27th.
• ### Free GMAT RC Webinar

February 23, 2019

February 23, 2019

07:00 AM PST

09:00 AM PST

Learn reading strategies that can help even non-voracious reader to master GMAT RC. Saturday, February 23rd at 7 AM PT

# A cafeteria offers seven types of sandwiches, each with a fixed price

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

### Hide Tags

Math Expert
Joined: 02 Sep 2009
Posts: 53063
A cafeteria offers seven types of sandwiches, each with a fixed price  [#permalink]

### Show Tags

08 Feb 2017, 00:51
1
6
00:00

Difficulty:

85% (hard)

Question Stats:

48% (02:28) correct 52% (02:25) wrong based on 133 sessions

### HideShow timer Statistics

A cafeteria offers seven types of sandwiches, each with a fixed price and a fixed set of ingredients (no additions or substitutions). If the average price among the seven sandwiches is $2.25 do any sandwiches cost less than$1.75?

(1) The maximum price of a sandwich is $2.70. (2) The median price of a sandwich is$2.70.

_________________
CEO
Joined: 11 Sep 2015
Posts: 3445
Re: A cafeteria offers seven types of sandwiches, each with a fixed price  [#permalink]

### Show Tags

08 Feb 2017, 08:21
Top Contributor
Bunuel wrote:
A cafeteria offers seven types of sandwiches, each with a fixed price and a fixed set of ingredients (no additions or substitutions). If the average price among the seven sandwiches is $2.25 do any sandwiches cost less than$1.75?

(1) The maximum price of a sandwich is $2.70. (2) The median price of a sandwich is$2.70.

Great question!

Target question: Do any sandwiches cost less than $1.75? Given: The average price among the seven sandwiches is$2.25
So, (TOTAL cost of all 7 sandwiches)/7 = $2.25 So, TOTAL cost of all 7 sandwiches = (7)($2.25) = $15.75 Statement 1: The maximum price of a sandwich is$2.70
This statement doesn't FEEL sufficient, so I'll TEST some values.
There are several scenarios that satisfy statement 1 and the given information (that the TOTAL cost of all 7 sandwiches = $15.75). Here are two: Case a: the sandwich prices numbers are {$1.00, $1.25,$2.70, $2.70,$2.70, $2.70,$2.70}, in which case there IS a sandwich that costs less than $1.75 Case b: the sandwich prices numbers are {$2.05, $2.20,$2.20, $2.20,$2.20, $2.20,$2.70}, in which case NO sandwich costs less than $1.75 Since we cannot answer the target question with certainty, statement 1 is NOT SUFFICIENT Aside: For more on this idea of plugging in values when a statement doesn't feel sufficient, you can read my article: http://www.gmatprepnow.com/articles/dat ... lug-values Statement 2: The median price of a sandwich is$2.70
Notice that, in our analysis of statement 1, we came up with a scenario that happens to meet the condition set out in statement 1.
That is, {$1.00,$1.25, $2.70,$2.70, $2.70,$2.70, $2.70} meets the condition that the median price of a sandwich is$2.70. So, we can see that it IS POSSIBLE to have a situation in which there IS a sandwich that costs less than $1.75 Is it also possible to have a situation in which there are NO sandwiches that cost less than$1.75?
Let's find out.
Let's arrange the 7 sandwich prices in ASCENDING order with a median price of $2.70. We get: _ _ _$2.70 _ _ _

We're trying to create a scenario in which there are NO sandwiches that cost less than $1.75. This means we're trying to MAXIMIZE the values to the LEFT of the median. To do this, we must MINIMIZE the values to the RIGHT of the median. Since the values to the RIGHT of the median must be$2.70 or greater, we can MINIMIZE these values by making them all $2.70. We get: _ _ _$2.70 $2.70$2.70 $2.70 4 x$2.70 = $10.80, so we have already accounted for$10.80 of the total $15.75$15.75 - $10.80 =$4.95, so the remaining 3 prices must add to $4.95 At this point, we might recognize that it is IMPOSSIBLE to achieve our goal of creating a scenario in which there are NO sandwiches that cost less than$1.75
Here's why.
If all 3 remaining prices were $1.75, then we would need$5.25 (3 x $1.75 =$5.25). However, we only have $4.95 left. So, at least one of the 3 remaining prices will be LESS THAN$1.75

So, statement 2 guarantees that there IS a sandwich that costs less than \$1.75
Since we can answer the target question with certainty, statement 2 is SUFFICIENT

RELATED VIDEO FROM OUR COURSE

_________________

Test confidently with gmatprepnow.com

Senior SC Moderator
Joined: 14 Nov 2016
Posts: 1321
Location: Malaysia
A cafeteria offers seven types of sandwiches, each with a fixed price  [#permalink]

### Show Tags

17 Feb 2017, 16:31
Bunuel wrote:
A cafeteria offers seven types of sandwiches, each with a fixed price and a fixed set of ingredients (no additions or substitutions). If the average price among the seven sandwiches is $$2.25$$ do any sandwiches cost less than $$1.75$$?

(1) The maximum price of a sandwich is $$2.70$$.

(2) The median price of a sandwich is $$2.70$$.

Official solution from Veritas Prep.

B. In this Min/Max Data Sufficiency problem, it's important to remember the threshold for sufficiency: if the answer is "only yes" the information is sufficient; if the answer is "only no" the information is sufficient; and if the answer is "yes or no" the information is not sufficient. So your goal should be to use each statement to see if you can get both a "yes" and a "no" - Min/Max Data Sufficiency is almost always about "prove insufficiency".

In this case, statement 1 allows for multiple answers. You could certainly have one sandwich at $$2.70$$, one at $$1.80$$ (the min and max averaging out to $$2.25$$), and the rest all at $$2.25$$ (for an answer of "no"). Or you could set the low price at $$1.70$$ ("yes"), the high at $$2.70$$, and slightly shift one of the middle values to average out to $$2.25$$. Statement 1 should quickly prove to be insufficient.

Statement 2 is somewhat "sneaky sufficient" alone. If you try to maximize the value of the lowest-priced sandwich to see if it can be above $$1.74$$, you should see that your goal, then, is to minimize the value of the higher-priced sandwiches. That would mean that four sandwiches are priced at $$2.70$$ (to keep the median price $$2.70$$ but leave as much of the $$7(2.25)$$ average for the lowest priced sandwich) and similarly minimize the other two sandwiches that are below the median (again, saving as much of that value as possible for the lowest-priced item to see if you can get it to $$1.75$$). If you do that, then, all the lowest-priced items would have the same value, so you'd have the equation:

$$3x + 4(2.70) = 7(2.25)$$

$$3x + 10.80 = 15.75$$

$$3x = 4.95$$

$$x = 1.65$$, meaning that even at its highest price, the lowest priced sandwich is less than $$1.75$$.

This makes statement 2 sufficient, and the answer $$B$$.
_________________

"Be challenged at EVERY MOMENT."

“Strength doesn’t come from what you can do. It comes from overcoming the things you once thought you couldn’t.”

"Each stage of the journey is crucial to attaining new heights of knowledge."

Rules for posting in verbal forum | Please DO NOT post short answer in your post!

Non-Human User
Joined: 09 Sep 2013
Posts: 9879
Re: A cafeteria offers seven types of sandwiches, each with a fixed price  [#permalink]

### Show Tags

10 Oct 2018, 14:18
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: A cafeteria offers seven types of sandwiches, each with a fixed price   [#permalink] 10 Oct 2018, 14:18
Display posts from previous: Sort by

# A cafeteria offers seven types of sandwiches, each with a fixed price

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

 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®.