Hospital H conducted a survey of two groups of patients who were enrol

Answer D

We know there are 21 people in a group we know the least is 5 in one group and the average is 13 but we cant find the the number of days of the max and min individuals(except the given one which is not enough)

Hospital H conducted a survey of two groups of patients who were enrolled in an exercise rehabilitation program last month. Was the range of the numbers of days that the patients in the first group exercised last month equal to the range of the numbers of days that the patients in the second group exercised last month?

(1) For each group, the number of patients enrolled was 21 and the least number of days that a patient exercised last month was 5.

(2) For each group, the average (arithmetic mean) number of days that the patients exercised last month was 13.

statement 1:
The number of patients in each group = 21
minimum number of days that a patient exercised in each group = 5
but we do not know the maximum number of days that a patient in each group exercised.
not sufficient

statement 2:
lets consider the number of patients in each group be x.
for each group, total number of days that all patients exercised = 13*x
but this does not gives us minimum or maximum number of days that a patient exercised.
not sufficient

combining both statements,
total number of days that all patients exercised in each group = 13*21 = 273
but still do not know maximum number of days that a patient in each group exercised?

Ans: E

Answer is supposedly E
Statement 1: at least 5 days of exercise. It doesn't state the highest no. Of exercising days to calculate range. ( Not sufficient)

Statement 2: average is 13 days. But highest and lower no. Can always vary ( Not Sufficient)

Both: the least no. Is 5 and average is 13.
Let, group A and B did exercise for maximum 26 days. Given the average.
But the lowest no. Can still vary. X>=5
So range can't be identified again (Not Sufficient)

Answer should be E

Posted from my mobile device
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(1) For each group, the number of patients enrolled was 21 and the least number of days that a patient exercised last month was 5.
We don't have the maximum number of days that a patient exercised last month for each group.
NOT SUFFICIENT

(2) For each group, the average (arithmetic mean) number of days that the patients exercised last month was 13.
We don't have the minimum and the maximum number of days that a patient exercised last month for each group.
NOT SUFFICIENT

(1)+(2)
Even with the combined information, we cannot deduce the maximum number of days that a patient exercised last month for each group.
NOT SUFFICIENT

FINAL ANSWER IS (E)

Posted from my mobile device

E

As we cannot determine the largest value by 1 statement .

It is not possible by both the statements again as we still cannot find the range

range=greatest-least num of days

(1) insufic
we don't know the greatest num of days

(2) insufic
we don't know the greatest or least num of days

(1/2) insufic
we don't know the greatest num of days

Ans (E)

1) n=21, and least value is 5, the max value is unknown
2) mean = 13, no smallest and largest value on both groups to find the range
1+2
from 21, the least value is 5 for both groups, but the highest can be anything greater than 13, but dont know
HEnce E

Hospital H conducted a survey of two groups of patients who were enrolled in an exercise rehabilitation program last month. Was the range of the numbers of days that the patients in the first group exercised last month equal to the range of the numbers of days that the patients in the second group exercised last month?

Range1 = Range2?

(1) For each group, the number of patients enrolled was 21 and the least number of days that a patient exercised last month was 5.
Least number is available but Largest number can vary for both groups.

INSUFFICIENT.

(2) For each group, the average (arithmetic mean) number of days that the patients exercised last month was 13.
Since number of people can vary in both groups, the least and the largest number can also vary leading to either case - range may or may no be equal.

INSUFFICIENT.

Together 1 and 2
\(\frac{G1 + G2 + G3 .... G20 + 5 }{ 21} = \frac{g1 +g2 + g3 .... g20 + 5 }{ 21}\)
Here again G1 = g1 OR G1 ≠ g1 (G1 and g1 being the largest number in their respective group)

INSUFFICIENT.

Answer E.
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Hi Bunuel,

This is a prep ques. Can you please mark the same?

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Done. Thank you.
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Can you explain your logic why you felt safe after doing that? I understand the 268 is sum (Statement 1: # of patients = 21, Statement 2: average of patients = 13, so therefore 21 * 13 = 273, then subtract the minimum number 5 given in Statement 1 = 268 and /20 = 13.4), but what exactly does that confirm?

To Find: Was Range Group 1= Range Group 2 ( Range= Maximum no of days exercised- minimum no of day)
1. No. of observations in each group= 21, Min values=5
Max not known could be any value, range could be anything. Equal or not
say Case A: maximum number of days patients exercised in both group 1 &2 = 25 then RangeGroup1=RangeGroup2=20
Case B:
Maximum number of days patients exercised in group 1 = 20 then RangeGroup1= 15 &
Maximum number of days patients exercised in group 2 = 10 then RangeGroup2= 5; RangeGroup1 not equal to RangeGroup2

2. Average= 13; could be 13, 13,13,…Range=0 for all patients or 3 (Min).. And 23 ( max ) such that average is 13 but range=20; Not sufficient.

Combining:
Total 13*21=273 with Min 5, now we do not know no. of observation of 5,
say only one 5 and rest 20 observations are other values so that total is 273 or
20 5's and 1 large value such that range is higher than former case; Not sufficient

Correct: E