Pavel made a list of 31 chores he needed to complete over the next 7

Question

Pavel made a list of 31 chores he needed to complete over the next 7 days. On the first 5 days, he completed 3, 5, 7, 2, and 6 of the listed chores, respectively. On the next 2 days, he completed the remaining 8 chores.

Select for  Least possible median  and for  Greatest possible median  values that are consistent with the information provided and give the least and greatest possible values, respectively, for the median of the numbers of the listed chores Pavel completed on each of the 7 days. Make only two selections, one in each column.

ID: 700354

Bunuel · Accepted Answer

Here’s a more precise way to solve this question. The number of chores completed over the first five days, in ascending order: {2, 3, 5 , 6, 7} The median of these values is 5. To minimize the median, we should distribute the remaining 8 chores over the next 2 days so that both days have fewer than 5 chores. The only way to achieve this is by assigning 4 chores to each day: {2, 3, 4, 4 , 5, 6, 7} Thus, the least possible median is 4. To make the median greater than 5, we would need to distribute the remaining 8 chores so both days have more than 5 chores, but this is not possible. Therefore, the next best option is to distribute the chores to maintain the current median of 5. This can be done by assigning fewer than 5 chores to one day and more than 5 to the other. For example: {0, 2, 3, 5 , 6, 7, 8} Thus, the greatest possible median is 5. GMAT-Club-Forum-hp0lmq7e.png

jeet1204 · Answer

list out the number of ways the 8 remaining tasks could have been done in the 2 days.

0,8 - median is 5
1,7 - median is 5
2,6 - median is 5
3,5 - median is 5
4,4 - median is 4

satish_sahoo · Answer

Bunuel

Could you please suggest any quicker approach than manually working out with the division of 8 tasks?

bb · Answer

The trick in this question is to actually plug in 4,4
That's the whole trick of the question and if you do not write out all possible combinations and check for them (should not take you 2 minutes), you will not spot that 4,4 pushes out the median.
P.S. I like this trick

satish_sahoo

Bunuel

Could you please suggest any quicker approach than manually working out with the division of 8 tasks?

MohdZaidKhan · Answer

_ _ 2 _ _3_ _5_ _ 6 _ _ 7_ _
and x+y = 8 .
we have to fill x and y in the blanks x,y could be equal to (0,1,2,3,4,5,6,7,8)

Median now itself is 5 
if one sits before 5 the other will sit after 5 .
So med will not change for any case except when 4,4 which sits on same side of 5 so 5 is one median possible and 4 is another possible median . least of these is 4 and max is 5 .  Answer

Bunuel · Answer

Have you reviewed  this post ? Let me know if you still have any questions.

GMATinsight · Answer

Answer: Options C | D Please check the video explanation here for a detailed approach to the question. SOLUTION: https://www.youtube.com/watch?v=pLRK4oPXnVo Please Like and Subscribe to YouTube channel if you like the video and access 1100+ more FREE videos . Every subscription matters!!! If you like to subscribe to modular courses on Quant and DI then please visit the following link: https://gmatinsight.com/gmat-2/

shwetakoshija · Answer

Given: 
 
 Total chores = 31 
 Chores completed on first 5 days: 3, 5, 7, 2, 6, respectively. 
 Chores completed on last 2 days: remaining 8 chores

To find:  Least and Greatest possible values of the median number of chores completed per day over the 7 days.

Sort known values: 2, 3, 5, 6, 7 
 Let the 2 unknowns be A and B.
 
 Then, A + B = 8

OBSERVE: 
 
 First, note that without the unknowns, median of 2, 3, 5, 6, 7 is  5 .
 
 If we take A and B such that one is less than 5 and the other is more than 5, then the median will not change. It will stay at 5. 
 We will try to see if any other case can reduce it.  
 
 Case 1: Both A and B less than or equal to 5
 
 (A, B): (3, 5), (4, 4), (5, 3).
 
 For (3, 5) or (5, 3), new list becomes 2, 3, 3, 5, 5, 6, 7. Median is still 5. 
 For (4, 4), new list becomes 2, 3, 4, 4, 5, 6, 7. Median is now  4 .

Case 2: Both A and B greater than 5
 
 This case is impossible since the sum of two numbers both greater than 5 cannot be 8.

Column 1: Least possible median 
From the analysis above, we are sure that the least possible median = 4 (for the case where A = B = 4)

Column 2: Greatest possible median 
Since the median = 5 for all other cases, we can infer that the greatest possible median = 5 (> 4)

Correct Answer: Least = 4, Greatest = 5

Pavel made a list of 31 chores he needed to complete over the next 7

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Pavel made a list of 31 chores he needed to complete over the next 7

Prep Toolkit

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My Rewards