Twenty-five adults reported the amount of time each spent studying

Question

https://gmatclub.com/forum/download/file.php?id=81427 Twenty-five adults reported the amount of time each spent exercising during a particular week. The results are summarized in the graph as follows: 5 respondents reported exercising for less than 1 hour, 3 respondents reported exercising for at least 1 hour but less than 2, and so on. Based on the given information, use the drop-down menus to most accurately complete the following statements. The least possible value for the mean of the numbers of hours of exercise reported for the week is GRAPH_1_PLACEHOLDER . The number of respondents who exercised on average less than one-half hour per day during the week is between GRAPH_2_PLACEHOLDER , inclusive. ID: 100406 IR 4.docx Table.jpg GMAT-Club-Forum-1lb3qdzu.png

srcc25anu · Accepted Answer

1. To find the least possible mean the sum of all hours exercised must be the minimum.
For 0-1 hours lets assume all 5 exercised the minimum possible of just over 0 hours and same for all bars.
so SUM of hours exercised = 0*5 + 1*3+2*2+3*3+4*4+5*5+0+0+8*1+0+10*0 = 78
# respondents = 25
average = 78/25 = 3.12

2. # respondents who exercised on average <0.5 hours per day
If Avg hours exercised = 0.5 hours per day the Total hours exercised during the week will be 0.5*7 OR 3.5 hours/week
We need to count respondents who exercise below 3.5 hours per week.
That will include all in 0-1 hour, 1-2 hr, 2-3 hour and since 3.5 lies in between 3-4 band, we can take 2 cases: 
CAse 1: where we assume all 4 in 3-4 years exercise MORE than 3.5 hours
Total # respondednts in that case = 5 + 3 + 2 + 4 = 14 (this is the maximum)
CAse 2: where we assume all 4 in 3-4 years exercise LESS than 3.5 hours
Total # respondednts in that case = 5 + 3 + 2 = 10 (this is the minimum)
Range od 10-14 respondents

rajatjain14 · Answer

Hi Ashsim, Part 1 Solution: Sum of = 5*0 + 3*1 + 2*2 + 4*3 + 4*4 + 5*5 + 1*8 + 1*10 = 78 Average = \frac{78}{25} = 3.12 Part 2 Solution: Less than 0.5 hr per day = less than 3.5 hr per week Minimum number = 5 + 3 + 2 + 0 = 10 (When respondents spending time between 3 and 4 have values greater than 3.5) Maximum Number = 5 + 3 + 2 + 4 = 14 (When respondents spending time between 3 and 4 have values less than 3.5) I hope it could be solved in 2 mins :lol:

Rgds, Rajat

Sajjad1994 · Answer

Official Explanation

The least possible value for the mean of the numbers of hours of exercise reported for the week is.

Explanation

The least possible mean corresponds to the case where each individual reported the minimum amount of time for their category (i.e., 5 people exercised 0 hours, 3 people exercised 1 hour, and so on). The mean in this case would be

\frac{5(0)+3(1)+2(2)+4(3)+4(4)+5(5)+1(8)+1(10)}{5+3+2+4+4+5+1+1}=\frac{78}{25}=3.12

The correct answer is 3.12.

The number of respondents who exercised on average less than one-half hour per day during the week is between________, inclusive.

Explanation

A respondent who averaged less than one-half hour of exercise per day would have reported less than 3.5 hours of exercise for the week. There were 10 respondents who reported exercising less than 3 hours per week: those respondents necessarily averaged less than one-half hour of exercise per day. There were 11 respondents who reported exercising more than 4 hours for the week: those respondents necessarily averaged more than one-half hour of exercise per day. There were 4 respondents who reported exercising at least 3 hours but no more than 4 hours for the week. It is possible that all 4 of these respondents reported more than 3.5 hours of exercise, in which case only 10 respondents would have averaged less than one-half hour of exercise per day. It is also possible, however, that 1 or more of these 4 respondents reported fewer than 3.5 hours, in which case, up to 14 respondents would have averaged less than one-half hour of exercise per day.

The correct answer is 10 and 14.

astinashler · Answer

I don't understand the second question. Does "one-half hour per day" means 1.5 hour per day?

Catman · Answer

No, one-half =1/2
This means 1/2 hour per day which corresponds to 3.5 hour per week.

Sid7210 · Answer

why not just say half then? such an annoying way of wording a question. smh

chetan2u · Answer

one-half is a valid word for 0.5, even if it is not soothing to the ear. If one has to write 1.5, it is one and a half. One-half of the population or one-half of the pizza. It is also used in official questions, so we should get used to it. one-half the previous term https://gmatclub.com/forum/in-a-certain ... l#p1690040

Lizshadehdg · Answer

Why the least possible average is not 3?

chetan2u · Answer

Least possible average is the least sum divided by the total number. 
Hence 78/25 or 3.12

Why do you think it should be 3?

DhruvBadaya · Answer

There is a whole lot of mistakes in this question. "studying" should be replaced by "exercising". Only then will this question makes sense.

NPProb · Answer

Oh, sh*t, I thought "one-half" hour means "one and a half" hour. LMAO.

bumpbot · Answer

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Twenty-five adults reported the amount of time each spent studying

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