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# DS Problem in Magoosh Product

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Intern
Joined: 08 Feb 2017
Posts: 4
DS Problem in Magoosh Product [#permalink]

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12 Apr 2017, 21:59
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}

Manager
Joined: 25 Apr 2016
Posts: 52
Re: DS Problem in Magoosh Product [#permalink]

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12 Apr 2017, 23:25
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.
Intern
Joined: 08 Feb 2017
Posts: 4
Re: DS Problem in Magoosh Product [#permalink]

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13 Apr 2017, 02:58
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?
Manager
Joined: 17 May 2015
Posts: 210
Re: DS Problem in Magoosh Product [#permalink]

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13 Apr 2017, 03:58
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}

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.
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Re: DS Problem in Magoosh Product [#permalink]

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13 Apr 2017, 06:08
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}

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.
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Joined: 08 Feb 2017
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Re: DS Problem in Magoosh Product [#permalink]

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18 Apr 2017, 22:01
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}

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.
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Joined: 28 Dec 2011
Posts: 4680
Re: DS Problem in Magoosh Product [#permalink]

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01 Jun 2017, 08:37
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}

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
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Mike McGarry
Magoosh Test Prep

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

Re: DS Problem in Magoosh Product   [#permalink] 01 Jun 2017, 08:37
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# DS Problem in Magoosh Product

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