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# Each of the 45 boxes on shelf J weighs less than each of the

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Each of the 45 boxes on shelf J weighs less than each of the  [#permalink]

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02 Sep 2010, 12:45
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Each of the 45 boxes on shelf J weighs less than each of the 44 boxes on shelf K. What is the median weight of the 89 boxes on these shelves?

(1) The heaviest box on shelf J weighs 15 pounds.
(2) The lightest box on shelf K weighs 20 pounds.
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Re: Each of the 45 boxes on shelf J weighs less than each of the  [#permalink]

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02 Sep 2010, 12:58
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udaymathapati wrote:
Each of the 45 boxes on shelf J weighs less than each of the 44 boxes on shelf K. What is
the median weight of the 89 boxes on these shelves?
(1) The heaviest box on shelf J weighs 15 pounds.
(2) The lightest box on shelf K weighs 20 pounds.

If a set has odd number of terms the median of a set is the middle number when arranged in ascending or descending order;
If a set has even number of terms the median of a set is the average of the two middle terms when arranged in ascending or descending order.

Set J+K has 89 terms, which means that the median would be the 45th term, so the heaviest box on shelf J (as each of the 45 boxes on shelf J weighs less than each of the 44 boxes on shelf K, when arranged in ascending order we'll have j1, j2, ..., j45, k1, k2, ..., k44).

(1) The heaviest box on shelf J weighs 15 pounds --> $$j_{45}=15$$--> directly gives us the answer. Sufficient.

(2) The lightest box on shelf K weighs 20 pounds --> $$k_1=20$$ --> just tells us that median is less than 20. Not sufficient.

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Re: Each of the 45 boxes on shelf J weighs less than each of the  [#permalink]

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31 Dec 2014, 12:35
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Hi jhasac,

DS questions on the Official GMAT are often based on patterns/concepts that you know, but are presented in ways that you're not used to thinking about.

If you were told you that there were 89 values in a group and you were asked to find the median of the group, what would you do?

You'd...
1) Put the numbers in order from least to greatest.
2) Look at the 45th number - even if there are duplicates (since that's the one in "the middle")

Those rules don't change, even though the question is worded in a quirky way. Maybe there's a way to figure out the 45th term WITHOUT putting ALL the numbers in a row first though....

We're told that EACH of the 45 boxes on shelf J weigh LESS than EACH of the 44 boxes on shelf K. This means that the 44 boxes on shelf K would be the "heaviest 44" numbers in the group; by extension, the "heaviest" value on shelf J MUST be the median. With that realization, the question is really asking "what is the heaviest value on shelf J?" From here, getting to the correct answer doesn't require much work.

The "take-away" from all of this is that by spending a little bit of time thinking about the "setup" in the prompt and doing some work to "rewrite" the question can make answering the question considerably easier (and save you some time).

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Special Offer: Save $75 + GMAT Club Tests Free Official GMAT Exam Packs + 70 Pt. Improvement Guarantee www.empowergmat.com/ Manager Joined: 11 May 2018 Posts: 90 Location: India GMAT 1: 460 Q42 V14 Re: Each of the 45 boxes on shelf J weighs less than each of the [#permalink] ### Show Tags 30 Jun 2018, 22:02 1 Hey guys please add a tag this is a question from exam pack 1. _________________ If you want to Thank me Give me a KUDOS "I’ve spent months preparing for the day I’d face you. I’ve come a long way, GMAT"- SonGoku Manager Joined: 14 Jun 2010 Posts: 169 Re: Each of the 45 boxes on shelf J weighs less than each of the [#permalink] ### Show Tags 02 Sep 2010, 23:18 Good question.....and an amazing answer from the master....Kudos! Manager Joined: 20 Apr 2010 Posts: 190 Location: Hyderabad WE 1: 4.6 years Exp IT prof Re: Each of the 45 boxes on shelf J weighs less than each of the [#permalink] ### Show Tags 03 Sep 2010, 00:36 Option 1 alone is enough to solve this question but option 2 can't alone resolve this question Hence A is the answer. _________________ I will give a Fight till the End "To dream anything that you want to dream, that is the beauty of the human mind. To do anything that you want to do, that is the strength of the human will. To trust yourself, to test your limits, that is the courage to succeed." - Bernard Edmonds A person who is afraid of Failure can never succeed -- Amneet Padda Don't Forget to give the KUDOS Intern Joined: 20 Aug 2014 Posts: 5 Re: Each of the 45 boxes on shelf J weighs less than each of the [#permalink] ### Show Tags 31 Dec 2014, 00:53 But if the boxes of shelf J is same and each of the boxes in other shelf is different ... will the median still follow the same logic. Math Expert Joined: 02 Sep 2009 Posts: 58099 Re: Each of the 45 boxes on shelf J weighs less than each of the [#permalink] ### Show Tags 31 Dec 2014, 04:38 jhasac wrote: But if the boxes of shelf J is same and each of the boxes in other shelf is different ... will the median still follow the same logic. Yes. {15, 15, 15, 15, ..., 15, j45 = 15, k1=20, k2, = 21, ..., k44 = 63} _________________ Director Joined: 04 Jun 2016 Posts: 558 GMAT 1: 750 Q49 V43 Each of the 45 boxes on shelf J weighs less than each of the [#permalink] ### Show Tags 15 Jul 2016, 10:57 udaymathapati wrote: Each of the 45 boxes on shelf J weighs less than each of the 44 boxes on shelf K. What is the median weight of the 89 boxes on these shelves? (1) The heaviest box on shelf J weighs 15 pounds. (2) The lightest box on shelf K weighs 20 pounds. The important terms to note in this questions are "MEDIAN" and "89 box" The median of a set containing odd numbers of elements is always the mid point in this case it will be the $$45^{th}$$ term (1) The heaviest box on shelf J weighs 15 pounds. Sufficient :- shelf J has 45 box and the 45$$^{th}$$ term is 15 pound Therefore we found the median==>sufficient (2) The lightest box on shelf K weighs 20 pounds. This is the $$46^{th}$$ term and thus not helpful in finding median ==> Insufficient ANSWER IS A _________________ Posting an answer without an explanation is "GOD COMPLEX". The world doesn't need any more gods. Please explain you answers properly. FINAL GOODBYE :- 17th SEPTEMBER 2016. .. 16 March 2017 - I am back but for all purposes please consider me semi-retired. Target Test Prep Representative Status: Head GMAT Instructor Affiliations: Target Test Prep Joined: 04 Mar 2011 Posts: 2819 Re: Each of the 45 boxes on shelf J weighs less than each of the [#permalink] ### Show Tags 14 Sep 2017, 10:45 udaymathapati wrote: Each of the 45 boxes on shelf J weighs less than each of the 44 boxes on shelf K. What is the median weight of the 89 boxes on these shelves? (1) The heaviest box on shelf J weighs 15 pounds. (2) The lightest box on shelf K weighs 20 pounds. We are given that each of the 45 boxes on shelf J weighs less than each of the 44 boxes on shelf K and need to determine the median weight of the 89 boxes. We may recall that when the boxes are ordered from least weight to greatest, the box with the median weight is in the (89 + 1)/2 = 90/2 = 45th position. Thus, the box with the median weight is on shelf J and it is the heaviest box on shelf J. Statement One Alone: The heaviest box on shelf J weighs 15 pounds. Since the heaviest box on shelf J weighs 15 pounds, the 45th box weighs 15 pounds. Since the 45th box is the median of the boxes, the median weight is 15 pounds. Statement one alone is sufficient to answer the question. Statement Two Alone: The lightest box on shelf K weighs 20 pounds. Since the lightest box on shelf K weighs 20 pounds, when the boxes on both shelves are ordered from least to greatest weight, the 46th box weighs 20 pounds. However, we do not have enough information to determine the weight of the 45th box, i.e., the median weight. Answer: A _________________ # Jeffrey Miller Head of GMAT Instruction Jeff@TargetTestPrep.com 122 Reviews 5-star rated online GMAT quant self study course See why Target Test Prep is the top rated GMAT quant course on GMAT Club. Read Our Reviews If you find one of my posts helpful, please take a moment to click on the "Kudos" button. CEO Joined: 12 Sep 2015 Posts: 3961 Location: Canada Re: Each of the 45 boxes on shelf J weighs less than each of the [#permalink] ### Show Tags 16 Sep 2017, 07:22 Top Contributor udaymathapati wrote: Each of the 45 boxes on shelf J weighs less than each of the 44 boxes on shelf K. What is the median weight of the 89 boxes on these shelves? (1) The heaviest box on shelf J weighs 15 pounds. (2) The lightest box on shelf K weighs 20 pounds. Target question: What is the median weight of 89 boxes on these shelves? Given: Each of the 45 boxes on shelf J weighs less than each of the 44 boxes on the shelf K. Let J1 be the weight of the lightest box on shelf J. Let J2 be the weight of the 2nd lightest box on shelf J. . . . Let J45 be the weight of the heaviest box on shelf J. Let K1 be the weight of the lightest box on shelf K. Let K2 be the weight of the 2nd lightest box on shelf K. etc. So, the given information tells us that J1 < J2 < J3 < ... < J45 < K1 < K2 < ...< K44 Since the 89 boxes are now arranged in ascending order (according to weight), the median weight will be the weight of the middle box. That is, the median weight, will be the weight of the 45th box. So, we can REPHRASE the target question.... REPHRASED target question: What is the weight of box J45? Statement 1: The heaviest box on shelf J weighs 15 pounds. PERFECT! Box J45 is the heaviest box on shelf J So, box J45 weighs 15 pounds. Since we can answer the REPHRASED target question with certainty, statement 1 is SUFFICIENT Statement 2: The lightest box on shelf K weighs 20 pounds. This tells us that box K1 weighs 20 pounds. This does not help us find the weight of box J45 Since we cannot answer the REPHRASED target question with certainty, statement 2 is NOT SUFFICIENT Answer: RELATED VIDEO FROM OUR COURSE _________________ Test confidently with gmatprepnow.com EMPOWERgmat Instructor Status: GMAT Assassin/Co-Founder Affiliations: EMPOWERgmat Joined: 19 Dec 2014 Posts: 15015 Location: United States (CA) GMAT 1: 800 Q51 V49 GRE 1: Q170 V170 Re: Each of the 45 boxes on shelf J weighs less than each of the [#permalink] ### Show Tags 20 Dec 2017, 18:40 Hi All, This is a great 'concept' question, meaning that you don't really have to do any math to answer it as long as you understand the concepts involved. We're told that EACH of the 45 boxes on shelf J weighs LESS than EACH of the 44 boxes on shelf K. We're asked for the MEDIAN weight of the 89 boxes. To start, the 'median box' will be the 45th box. Since each of the boxes on shelf J weigh LESS than each of the boxes on shelf K, the 'heaviest' box on shelf J will be the median. If we have that one value, then we can answer the question. 1) The heaviest box on shelf J weighs 15 pounds. This Fact gives us exactly what we need to answer the question. Fact 1 is SUFFICIENT 2) The lightest box on shelf K weighs 20 pounds. Unfortunately, this Fact doesn't tell us anything about the weights of the boxes on shelf J. Maybe the median is 19 pounds, but it could just as easily be 18 pounds, 17 pounds, 16.5 pounds, etc. Fact 2 is INSUFFICIENT 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 *****Select EMPOWERgmat Courses now include ALL 6 Official GMAC CATs!***** # Rich Cohen Co-Founder & GMAT Assassin Special Offer: Save$75 + GMAT Club Tests Free
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Re: Each of the 45 boxes on shelf J weighs less than each of the  [#permalink]

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30 Jun 2018, 23:31
SonGoku wrote:
Hey guys please add a tag this is a question from exam pack 1.

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Done. Thank you.
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Each of the 45 boxes on shelf J weighs less than each of the  [#permalink]

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03 Aug 2019, 12:22
udaymathapati wrote:
Each of the 45 boxes on shelf J weighs less than each of the 44 boxes on shelf K. What is the median weight of the 89 boxes on these shelves?

(1) The heaviest box on shelf J weighs 15 pounds.
(2) The lightest box on shelf K weighs 20 pounds.

If the 89 boxes are arranged in an ascending order , 45th box 's weight will be the median weight.
45th box is the heaviest in the shelf J.

Statement 1 is sufficient.

Statement 2 does give any information regarding the 45th box.

Each of the 45 boxes on shelf J weighs less than each of the   [#permalink] 03 Aug 2019, 12:22
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