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# If two elements are dropped from set X {-10, -8, 0, 6, 7}

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If two elements are dropped from set X {-10, -8, 0, 6, 7}  [#permalink]

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Updated on: 02 Dec 2016, 05:03
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If two elements are dropped from set X {-10, -8, 0, 6, 7}, what will be the percentage change in its mean?

(1) The median of the set will remain the same
(2) The range of the set will decrease by 3

I don't have an OA but this is how I solved this.

Statement 1 - Median is 0 so the set can be $${-8,0,6}, {-10, 0, 6}$$. Therefore it will give different values of percentage change and hence insufficient to answer the question.

Statement 2 - The range of X {$$-10, -8, 0, 6, 7$$}is $$17$$. The new range is given as $$14$$ [ The range of the set will decrease by 3]. This can only be possible when we drop -10 and 7 from the set. Therefore, the new set will look like $${-8,0,6}$$. No we can calculate mean and the percentage change and therefore sufficient.

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Originally posted by enigma123 on 08 Mar 2012, 15:11.
Last edited by abhimahna on 02 Dec 2016, 05:03, edited 2 times in total.
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Re: If two elements are dropped from set X {-10, -8, 0, 6, 7}  [#permalink]

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08 Mar 2012, 15:19
2
enigma123 wrote:
If two elements are dropped from set X {$$-10, -8, 0, 6, 7$$}, what will be the percentage change in its mean?

(1) The median of the set will remain the same
(2) The range of the set will decrease by 3

I don't have an OA but this is how I solved this.

Statement 1 - Median is 0 so the set can be $${-8,0,6}, {-10, 0, 6}$$. Therefore it will give different values of percentage change and hence insufficient to answer the question.

Statement 2 - The range of X {$$-10, -8, 0, 6, 7$$}is $$17$$. The new range is given as $$14$$ [ The range of the set will decrease by 3]. This can only be possible when we drop -10 and 7 from the set. Therefore, the new set will look like $${-8,0,6}$$. No we can calculate mean and the percentage change and therefore sufficient.

The correct answer is B indeed, have nothing else to add. Perfect analyzes. + 1.
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Re: If two elements are dropped from set X {-10, -8, 0, 6, 7}  [#permalink]

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05 Jan 2015, 23:24
enigma123 wrote:
If two elements are dropped from set X {-10, -8, 0, 6, 7}, what will be the percentage change in its mean?

(1) The median of the set will remain the same
(2) The range of the set will decrease by 3

I don't have an OA but this is how I solved this.

Statement 1 - Median is 0 so the set can be $${-8,0,6}, {-10, 0, 6}$$. Therefore it will give different values of percentage change and hence insufficient to answer the question.

Statement 2 - The range of X {$$-10, -8, 0, 6, 7$$}is $$17$$. The new range is given as $$14$$ [ The range of the set will decrease by 3]. This can only be possible when we drop -10 and 7 from the set. Therefore, the new set will look like $${-8,0,6}$$. No we can calculate mean and the percentage change and therefore sufficient.

Hi Brunel
Statement 1: we will have new set (-10, 0, 6 ) and (-8, 0, 6) with the same median 0 as the old set does. So the percentage change is 100%. Please help to clarify this case
Thanks a lot
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Re: If two elements are dropped from set X {-10, -8, 0, 6, 7}  [#permalink]

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06 Jan 2015, 02:29
HuongShashi wrote:
enigma123 wrote:
If two elements are dropped from set X {-10, -8, 0, 6, 7}, what will be the percentage change in its mean?

(1) The median of the set will remain the same
(2) The range of the set will decrease by 3

I don't have an OA but this is how I solved this.

Statement 1 - Median is 0 so the set can be $${-8,0,6}, {-10, 0, 6}$$. Therefore it will give different values of percentage change and hence insufficient to answer the question.

Statement 2 - The range of X {$$-10, -8, 0, 6, 7$$}is $$17$$. The new range is given as $$14$$ [ The range of the set will decrease by 3]. This can only be possible when we drop -10 and 7 from the set. Therefore, the new set will look like $${-8,0,6}$$. No we can calculate mean and the percentage change and therefore sufficient.

Hi Brunel
Statement 1: we will have new set (-10, 0, 6 ) and (-8, 0, 6) with the same median 0 as the old set does. So the percentage change is 100%. Please help to clarify this case
Thanks a lot

The question asks about the percentage change between the old mean and the mean of the new set. How is the change 100%?
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Re: If two elements are dropped from set X {-10, -8, 0, 6, 7}  [#permalink]

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06 Jan 2015, 11:46
1
Hi HuongShashi,

I think that you're confusing the 'MEDIAN' with the 'MEAN'...

While you're correct that the MEDIAN (0) will stay the same in both groups, the question does NOT ask about the change in median, it asks about the percentage change in the MEAN.

The groups (-10, 0, 6) and (-8, 0, 6) have DIFFERENT averages/means, so the percentage change from the original mean will be DIFFERENT. By extension, this gives us two different answers to the question and Fact 1 is INSUFFICIENT.

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Special Offer: Save $75 + GMAT Club Tests Free Official GMAT Exam Packs + 70 Pt. Improvement Guarantee www.empowergmat.com/ *****Select EMPOWERgmat Courses now include ALL 6 Official GMAC CATs!***** Current Student Joined: 18 Oct 2014 Posts: 856 Location: United States GMAT 1: 660 Q49 V31 GPA: 3.98 Re: If two elements are dropped from set X {-10, -8, 0, 6, 7} [#permalink] ### Show Tags 20 May 2016, 09:48 enigma123 wrote: If two elements are dropped from set X {-10, -8, 0, 6, 7}, what will be the percentage change in its mean? (1) The median of the set will remain the same (2) The range of the set will decrease by 3 Given Information- two elements are dropped from set X {-10, -8, 0, 6, 7} Question asked- percentage change in its mean? Inference:- We need to know those two numbers in order to find % drop in mean (1) The median of the set will remain the same Median will remain '0'. That means one number from -10, -8 is dropped and one number from 6,7 is dropped. This doesn't give us exact numbers. Hence, Insufficient (2) The range of the set will decrease by 3 Current range = 7- (-10)= 17 New range= 14 Out of given numbers only 6 and -8 will yield the desired range. Hence, the dropped out numbers are -10 and 7. We can find % drop now B is the answer _________________ I welcome critical analysis of my post!! That will help me reach 700+ Intern Joined: 24 Jan 2016 Posts: 18 Re: If two elements are dropped from set X {-10, -8, 0, 6, 7} [#permalink] ### Show Tags 10 Nov 2016, 13:14 Answer:B If two elements are dropped from set X {-10, -8, 0, 6, 7}, what will be the percentage change in its mean? (1) The median of the set will remain the same (2) The range of the set will decrease by 3 1- The median will remain the same ⇒ one number before 0 (-10, or -8) and one number after 0 (6 or 8) should be removed. As long as we have 4 different variations of numbers that can be removed, we cannot have a single answer -- INSUFFICIENT 2- The range of X is 17. the new range will be 17-3=14 ⇒ -10 and 7 should be removed. we have just one answer for the new mean -- SUFFICIENT Director Joined: 26 Oct 2016 Posts: 642 Location: United States Concentration: Marketing, International Business Schools: HBS '19 GMAT 1: 770 Q51 V44 GPA: 4 WE: Education (Education) If two elements are dropped from set X {-10, -8, 0, 6, 7}, what will b [#permalink] ### Show Tags 11 Dec 2016, 17:51 If two elements are dropped from set X {-10, -8, 0, 6, 7}, what will be the percentage change in its mean? (1) The median of the set will remain the same. (2) The range of the set will decrease by 3. Please help with above problem. _________________ Thanks & Regards, Anaira Mitch Senior CR Moderator Status: Long way to go! Joined: 10 Oct 2016 Posts: 1381 Location: Viet Nam Re: If two elements are dropped from set X {-10, -8, 0, 6, 7}, what will b [#permalink] ### Show Tags 11 Dec 2016, 19:29 1 anairamitch1804 wrote: If two elements are dropped from set X {-10, -8, 0, 6, 7}, what will be the percentage change in its mean? (1) The median of the set will remain the same. (2) The range of the set will decrease by 3. Please help with above problem. The average (mean) of set X is $$\frac{-10-8+6+7}{5}=\frac{-5}{5}=-1$$ (1) The median of set X will remain the same. This means that two elements that are dropped from X, one will be in {-10, -8} and one will be in {6, 7} so that the median of X will be 0. If we drop -10 and 7, new set X'={-8, 0, 6} and the average is $$\frac{-8+6}{3}=\frac{-2}{3}$$. The average changes. If we drop -8 and 6, new set X''={-10, 0, 7} and the average is $$\frac{-10+7}{3}=\frac{-3}{3}=-1$$. The average remains the same. Insufficient. (2) The range of X is $$7-(-10)=17$$. The range of new set (or X') decrease by 3, or $$17-3=14$$. In set X = {-10, -8, 0, 6, 7}, there are only 2 elements that one is 14 greater than another: -8 and 6. Hence, we must drop -10 and 7 so X' = {-8, 0, 6} will have the range 14. Now, if we know what new set is, we'll know the percentage change in its mean, does't matter how many. Sufficient. The answer is B _________________ EMPOWERgmat Instructor Status: GMAT Assassin/Co-Founder Affiliations: EMPOWERgmat Joined: 19 Dec 2014 Posts: 12694 Location: United States (CA) GMAT 1: 800 Q51 V49 GRE 1: Q170 V170 Re: If two elements are dropped from set X {-10, -8, 0, 6, 7}, what will b [#permalink] ### Show Tags 11 Dec 2016, 21:30 1 Hi anairamitch1804, From the prompt, we can calculate the MEAN of the original 5 values... -5/5 = -1. We're asked for the percentage change in the MEAN after we remove two of the numbers from the original set: {-10,-8, 0, 6, 7} 1) The median of the set will remain the same. The current median is 0. If the median remains the same after removing the two values, then we could end up with a four different groups: {-10, 0, 6] Avg = -4/3 {-10, 0, 7} Avg = -3/3 = -1 {-8, 0, 6} Avg = -2/3 {-8, 0, 7} Avg = -1/3 Each of these groups has a different average, so the percentage change would be different for each. Fact 1 is INSUFFICIENT 2) The range of the set will decrease by 3. The current range is 7 - (-10) = 17. If we decrease that value by 3, we'll end up with a range of 14. With the set of numbers that we're working with, there's only one sub-group that can occur: {-8, 0 , 6} Fact 2 is SUFFICIENT Final Answer: GMAT assassins aren't born, they're made, Rich _________________ 760+: Learn What GMAT Assassins Do to Score at the Highest Levels Contact Rich at: Rich.C@empowergmat.com # Rich Cohen Co-Founder & GMAT Assassin Special Offer: Save$75 + GMAT Club Tests Free
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Re: If two elements are dropped from set X {-10, -8, 0, 6, 7}  [#permalink]

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11 Dec 2016, 22:57
anairamitch1804 wrote:
If two elements are dropped from set X {-10, -8, 0, 6, 7}, what will be the percentage change in its mean?
(1) The median of the set will remain the same.
(2) The range of the set will decrease by 3.

Merging topics. Please search before posting.
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Re: If two elements are dropped from set X {-10, -8, 0, 6, 7}  [#permalink]

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Re: If two elements are dropped from set X {-10, -8, 0, 6, 7} &nbs [#permalink] 23 Apr 2018, 12:04
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