It is currently 21 Nov 2017, 07:07

Close

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
Your Progress

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.

Close

Request Expert Reply

Confirm Cancel

Events & Promotions

Events & Promotions in June
Open Detailed Calendar

DS Problem in Magoosh Product

  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics  
Author Message
Intern
Intern
avatar
Joined: 08 Feb 2017
Posts: 4

Kudos [?]: 0 [0], given: 0

DS Problem in Magoosh Product [#permalink]

Show Tags

New post 12 Apr 2017, 22:59
Set K consists of 4 integers. What is the median of K?

(1) The average (arithmetic mean) of K is 3.

(2) The mode of K is 3.

In the video explanation, it is said that since the mode is 3 the set of integers is {3,3,3,3} or {3,3,x,y}. I have a doubt why is the mode a minimum of two values here? Why cant the mode be repeated thrice in the set as follows {3,3,3,x}

Can someone please help?

Kudos [?]: 0 [0], given: 0

Manager
Manager
avatar
S
Joined: 25 Apr 2016
Posts: 53

Kudos [?]: 16 [0], given: 282

Re: DS Problem in Magoosh Product [#permalink]

Show Tags

New post 13 Apr 2017, 00:25
Clearly, statements 1st and 2nd itself are not sufficient. Combining them, we get three different combinations (1,5),(2,4) and (3,3) and, interestingly enough in each of these cases we would get an unique value '3' for the median.

Kudos [?]: 16 [0], given: 282

Intern
Intern
avatar
Joined: 08 Feb 2017
Posts: 4

Kudos [?]: 0 [0], given: 0

Re: DS Problem in Magoosh Product [#permalink]

Show Tags

New post 13 Apr 2017, 03:58
attari92 wrote:
Clearly, statements 1st and 2nd itself are not sufficient.


yes, I got that. However, definition of mode means value which is repeated the most times in a set. Why does the mode have max value of 2 here? and not 3?

Kudos [?]: 0 [0], given: 0

Manager
Manager
avatar
P
Joined: 17 May 2015
Posts: 208

Kudos [?]: 239 [0], given: 73

CAT Tests
Re: DS Problem in Magoosh Product [#permalink]

Show Tags

New post 13 Apr 2017, 04:58
AmitLobo wrote:
Set K consists of 4 integers. What is the median of K?

(1) The average (arithmetic mean) of K is 3.

(2) The mode of K is 3.

In the video explanation, it is said that since the mode is 3 the set of integers is {3,3,3,3} or {3,3,x,y}. I have a doubt why is the mode a minimum of two values here? Why cant the mode be repeated thrice in the set as follows {3,3,3,x}

Can someone please help?


Hi AmitLobo,

The mode can be repeated thrice, no problem. But, notice that in this problem {3,3,3,x} => is same as {3,3,3,3}. x has to be equal to 3 (sum = 12 from st.1).

Hope it helps.

Kudos [?]: 239 [0], given: 73

Senior CR Moderator
User avatar
D
Status: Long way to go!
Joined: 10 Oct 2016
Posts: 1246

Kudos [?]: 1010 [0], given: 61

Location: Viet Nam
GMAT ToolKit User Premium Member CAT Tests
Re: DS Problem in Magoosh Product [#permalink]

Show Tags

New post 13 Apr 2017, 07:08
AmitLobo wrote:
Set K consists of 4 integers. What is the median of K?

(1) The average (arithmetic mean) of K is 3.

(2) The mode of K is 3.

In the video explanation, it is said that since the mode is 3 the set of integers is {3,3,3,3} or {3,3,x,y}. I have a doubt why is the mode a minimum of two values here? Why cant the mode be repeated thrice in the set as follows {3,3,3,x}

Can someone please help?


Nice question. To prove that statement (2) is insufficient, we need to specify that there are 2 cases that satisfy condition (2) but they lead to 2 different result.

Case 1. Set K = {3, 3, 3, 3}. It's clear that the median of K is 3.

Case 2. Set K = {3, 3, 3, x}. No matter what x is, the median of K is still 3. This case has the same result as Case 1, so we could left it out.

Case 3. Set K = {3, 3, x, y}. And now, the median of K could be different. For example, if K = {3, 3, 5, 7} then the median of K is 4.

Hence, we need just 2 cases: case 1 & case 3 to prove that (2) is insufficient. No need to mention case 2 here. That's why the OE lefts out that case.
_________________

Actual LSAT CR bank by Broall

How to solve quadratic equations - Factor quadratic equations
Factor table with sign: The useful tool to solve polynomial inequalities
Applying AM-GM inequality into finding extreme/absolute value

New Error Log with Timer

Kudos [?]: 1010 [0], given: 61

Intern
Intern
avatar
Joined: 08 Feb 2017
Posts: 4

Kudos [?]: 0 [0], given: 0

Re: DS Problem in Magoosh Product [#permalink]

Show Tags

New post 18 Apr 2017, 23:01
nguyendinhtuong wrote:
AmitLobo wrote:
Set K consists of 4 integers. What is the median of K?

(1) The average (arithmetic mean) of K is 3.

(2) The mode of K is 3.

In the video explanation, it is said that since the mode is 3 the set of integers is {3,3,3,3} or {3,3,x,y}. I have a doubt why is the mode a minimum of two values here? Why cant the mode be repeated thrice in the set as follows {3,3,3,x}

Can someone please help?


Nice question. To prove that statement (2) is insufficient, we need to specify that there are 2 cases that satisfy condition (2) but they lead to 2 different result.

Case 1. Set K = {3, 3, 3, 3}. It's clear that the median of K is 3.

Case 2. Set K = {3, 3, 3, x}. No matter what x is, the median of K is still 3. This case has the same result as Case 1, so we could left it out.

Case 3. Set K = {3, 3, x, y}. And now, the median of K could be different. For example, if K = {3, 3, 5, 7} then the median of K is 4.

Hence, we need just 2 cases: case 1 & case 3 to prove that (2) is insufficient. No need to mention case 2 here. That's why the OE lefts out that case.


Thanks all. Understood.

Kudos [?]: 0 [0], given: 0

Expert Post
Magoosh GMAT Instructor
User avatar
G
Joined: 28 Dec 2011
Posts: 4491

Kudos [?]: 8758 [0], given: 105

Re: DS Problem in Magoosh Product [#permalink]

Show Tags

New post 01 Jun 2017, 09:37
AmitLobo wrote:
Set K consists of 4 integers. What is the median of K?

(1) The average (arithmetic mean) of K is 3.

(2) The mode of K is 3.

In the video explanation, it is said that since the mode is 3 the set of integers is {3,3,3,3} or {3,3,x,y}. I have a doubt why is the mode a minimum of two values here? Why cant the mode be repeated thrice in the set as follows {3,3,3,x}

Can someone please help?

Dear AmitLobo,

I'm happy to respond. :-)

First of all, I'm sorry if you have been waiting for a response all this time. This Magoosh subforum on GMAT Club sometimes gets more attention and sometimes less. I assume that you know that, since you are a Magoosh student, you can email the student help team either at help@magoosh.com or by clicking the purple "Help" button in the lower right-hand corner of any Magoosh page. You usually get a response from student help in about 24 hours.

In case you haven't already gotten an answer, I will provide one here. In a GMAT DS question, it's very easy to use picking numbers to prove that individual statements are insufficient--as soon as two different choices of numbers produce two different answers to the prompt question, we know that the statement is insufficient. At that stage of the solution, there is no reason to investigate every possibility.

At that stage, the instructor was evaluating the second statement, "The mode of K is 3," and trying to decide whether it is sufficient.
The choice of {3,3,3,3} produces a definitive answer to the prompt question--the median would be 3
The choice {3, 3, 11, 50} produces another answer to the prompt question--the median would be 7
Right there--BAM! Two different choices consistent with this statement produce two different answers to the prompt question. We are already done. We have determined without a doubt that the second statement, alone and by itself, is not sufficient.

Yes, the set could be {3, 3, 3, 51}, but there's no reason to investigate anything else--we have already determined what we wanted to determine about statement #2 at that stage of the problem, namely, that it is insufficient.

On Data Sufficiency, it's very important to be strategic: know exactly the information you need, and don't spend time exploring mathematical options that don't get you closer to the information you need.

Does all this make sense?
Mike :-)
_________________

Mike McGarry
Magoosh Test Prep

Image

Image

Education is not the filling of a pail, but the lighting of a fire. — William Butler Yeats (1865 – 1939)

Kudos [?]: 8758 [0], given: 105

Re: DS Problem in Magoosh Product   [#permalink] 01 Jun 2017, 09:37
Display posts from previous: Sort by

DS Problem in Magoosh Product

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

Moderator: mikemcgarry



cron

GMAT Club MBA Forum Home| About| Terms and Conditions| GMAT Club Rules| Contact| Sitemap

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®.