is the median of S an odd number?

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GMATsid2016: Senior | Next Rank: 100 Posts; Posts: 39; Joined: Sun Nov 13, 2016 4:38 am; Thanked: 1 times

by GMATsid2016 » Sat Nov 19, 2016 10:30 pm

If S is a finite set of consecutive even numbers, is the median of S an odd number?

(1) The mean of set S is an even number.

(2) The range of set S is divisible by 4.

OAE

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Source: Beat The GMAT — Data Sufficiency | Sat Nov 19, 2016 10:30 pm

melguy: Master | Next Rank: 500 Posts; Posts: 335; Joined: Mon Mar 21, 2011 11:31 pmFollowed by: 2 members; Location: Australia / India; Thanked: 37 times

by melguy » Sat Nov 19, 2016 11:33 pm

Statement 1

If we know mean is even then median must be even.

Sufficient

Statement 2

Example:
2,4,6,8 (even count) = Range not divisible by 4
2,4,6,8,10 (odd count)= Range divisible by 4

It will always be the case that for odd count of even integers that
- range will be divisible by 4
- median will be even

Sufficient

Answer is D

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MartyMurray: Legendary Member; Posts: 2135; Joined: Mon Feb 03, 2014 9:26 amFollowed by: 140 members; Location: https://martymurraycoaching.com/; Thanked: 955 times; GMAT Score:800

by MartyMurray » Sun Nov 20, 2016 4:15 am

Hey melguy, from the looks of your work, it's starting to look as if you should move that target score higher.

Marty Murray
Perfect Scoring Tutor With Over a Decade of Experience
MartyMurrayCoaching.com
Contact me at [email protected] for a free consultation.

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MartyMurray: Legendary Member; Posts: 2135; Joined: Mon Feb 03, 2014 9:26 amFollowed by: 140 members; Location: https://martymurraycoaching.com/; Thanked: 955 times; GMAT Score:800

by MartyMurray » Sun Nov 20, 2016 4:38 am

Statement 1: The mean of set S is an even number.

For a set of consecutive even numbers, if the number of elements in the set is even, the mean will be the average of the two middle elements, and will always be an odd number. Consider the following set.

{2, 4, 6, 8} The sum of the elements is 20, and the mean is 5.

The median will also be the average of the two middle elements, 4, and 6, which is 5. So the median of such a set will also be odd.

If the number of elements in the set is odd, the mean will always equal the value of the middle element of the set. Consider the following set.

{2, 4, 6, 8, 10}

The mean is 6.

The median is also, 6, which is even.

So if the mean of a set of consecutive even numbers is even, the median is even.

Sufficient.

Statement 2: The range of set S is divisible by 4.

The range is the difference between the highest value and the lowest value in the set.

Consider a set with range 8, which is divisible by 4. {2, 4, 6, 8, 10}

Notice that when 8 is divided by 4, we get 2. So we could say that there are four 2's in 8.

However, set {2, 4, 6, 8}, which has an even number of elements, has a range of only 8 - 2 = 6. To have a range of 8, the set needs an additional element, 10, the addition of which makes the number of elements odd.

It will always be the case that in order for the range of a set of consecutive even numbers to be divisible by 4, the set will have to have that additional element that makes the number of elements odd.

A set made up of an odd number of consecutive even numbers always has an even median, as illustrated in the discussion of Statement 1.

Sufficient.

The correct answer is D.

Marty Murray
Perfect Scoring Tutor With Over a Decade of Experience
MartyMurrayCoaching.com
Contact me at [email protected] for a free consultation.

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melguy: Master | Next Rank: 500 Posts; Posts: 335; Joined: Mon Mar 21, 2011 11:31 pmFollowed by: 2 members; Location: Australia / India; Thanked: 37 times

by melguy » Sun Nov 20, 2016 4:44 am

Marty Murray wrote:Hey melguy, from the looks of your work, it's starting to look as if you should move that target score higher.

Thanks a lot for your compliment Marty

GMAT has been really unpredictable for me in the past. I will give it a shot again January 2017. If i can get over my silly mistakes I think I may have a chance. Lets see how it turns out!

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MartyMurray: Legendary Member; Posts: 2135; Joined: Mon Feb 03, 2014 9:26 amFollowed by: 140 members; Location: https://martymurraycoaching.com/; Thanked: 955 times; GMAT Score:800

by MartyMurray » Sun Nov 20, 2016 5:27 am

melguy wrote:GMAT has been really unpredictable for me in the past. I will give it a shot again January 2017. If i can get over my silly mistakes I think I may have a chance. Lets see how it turns out!

To increase your accuracy you could do some of the following.

For Quant:

When you do practice questions go beyond being satisfied with knowing how to the answer to being satisfied only with correct answers. In other words, make clear to yourself that the goal is not really understanding concepts or using strategies. The end goal is right answers.

I read something once that said something along the lines of "People who score in the 600's are concerned with how to handle questions. People who score in the 700's are concerned with how to get right answers."

Also, become aware of what you tend to do that gets you to wrong answers and seek to catch yourself before you do those things. I, for example, have had a tendency to do things like adding 26 and 26 and getting 56. I am aware of that and can therefore catch myself before I choose a wrong answer or make a misstep in a calculation process.

For Verbal:

Unpredictable verbal results often indicate that there are subtle, or not so subtle flaws in the way a person is getting to answers.

So probably you could stabilize and increase your verbal scores by analyzing your processes for getting to verbal answers and tightening them up. For instance, if you choose the wrong answer to a verbal question, rather than focus on the explanation to that question, ask yourself what YOU DID that got you to that wrong answer. I am guessing that that's what matters most at this point in your training.

Overall, you could meditate on accuracy and even consider why you might be unconsciously choosing wrong answers on purpose. We all have unconscious things going on that cause us to do things that don't seem to make sense. In my case, my inner child loved to see me make crazy mistakes. Once I became aware of that and had an internal conversation, my accuracy quickly increased, as I described in this post.

https://www.beatthegmat.com/rocked-the-g ... 82365.html

I have seen scores SHOOT higher as results of adjustments in perception, attitude and overall approach.

Make it so.

Marty Murray
Perfect Scoring Tutor With Over a Decade of Experience
MartyMurrayCoaching.com
Contact me at [email protected] for a free consultation.

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GMAT/MBA Expert

Brent@GMATPrepNow: GMAT Instructor; Posts: 16207; Joined: Mon Dec 08, 2008 6:26 pmFollowed by: 1268 members; Location: Vancouver, BC; Thanked: 5254 times; GMAT Score:770

by Brent@GMATPrepNow » Sun Nov 20, 2016 5:38 am

melguy wrote: GMAT has been really unpredictable for me in the past. I will give it a shot again January 2017. If i can get over my silly mistakes I think I may have a chance. Lets see how it turns out!

If silly mistakes are hurting your score, then it's important that you identify and categorize these mistakes. Some examples might include:
- sloppy writing causes a 7 to mysteriously turn into a 1
- you forget that a question is an EXCEPT question.
- you fail to notice crucial information such as x is an integer or w < 0.
- you calculate Pat's current age when the question asked for the Pat's age 5 years from now.
- and so on

Once you have identified the types of mistakes that YOU typically make, you will be able to spot situations/questions in which you're prone to making errors.

I write about this and other strategies in the following article: https://www.gmatprepnow.com/articles/avo ... teaks-gmat

Cheers,
Brent

Brent Hanneson - Creator of GMATPrepNow.com

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melguy: Master | Next Rank: 500 Posts; Posts: 335; Joined: Mon Mar 21, 2011 11:31 pmFollowed by: 2 members; Location: Australia / India; Thanked: 37 times

by melguy » Sun Nov 20, 2016 8:43 pm

Thanks both for your inputs

Marty I totally agree with what you said

- People who score in the 600's are concerned with how to handle questions. People who score in the 700's are concerned with how to get right answers. (I can see my approach in the 600 bracket!)
- The GMAT is not a math test testing knowledge of concepts. The GMAT tests skill in getting to answers.
- Make sure on quant you cover basic topics and problem types. You won't see more than a few of certain tough problem types. So if you focus too much studying on those types you may shortchange yourself.

I always took GMAT as a Math test where I try and solve each and every problem with the same approach (this comes back from how we all were taught at high school). Right now where i stand I can see a few ways to increase my score

- Not take GMAT as a Math test and try and think of the shortest / smartest way to solve a problem
- Trying to get my basics strong and learn different approaches rather than focusing on very tough problems.
- Avoid careless errors (which I have started avoiding to a good extend just by double checking my work)

I have time till Jan. Fingers crossed!

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