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A museum recorded the number of visitors for each of 12 consecutive days. If the visitor counts were all different and the smallest daily visitor count was 27, what was the largest daily visitor count?

(1) The range of the visitor counts for the 12 days was at most 12.
(2) The median visitor count over the 12 days was 33.


12 consective days visitors visited museum..
each day count is different and smallest count is 27
largest daily visitor count

#1
range for 12 days is at most 12
last digit can be either 38 , 39
insufficient
#2
median count is 33
5th & 6th day can be ( 32,34 ) or ( 31,35)
insufficient
from 1 & 2
possible when
27,28,29,30,31,32,34,35,26,37,38,39

OPTION C is correct
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A museum recorded the number of visitors for each of 12 consecutive days.
The visitor counts were all different.
The smallest daily visitor count = 27

What was the largest daily visitor count?

(1) The range of the visitor counts for the 12 days was at most 12.
Largest daily visitor count <= 27 + 12 = 39
Case 1: Number of visitors = {27,28,29,30,31,32,33,34,35,36,37,38}: Largest daily visitor count = 38
Case 2: Number of visitors = {27,28,29,30,31,32,33,34,35,36,37,39}: Largest daily visitor count = 39
Not sufficient

(2) The median visitor count over the 12 days was 33.
Case 1: Number of visitors = {27,28,29,30,31,32,34,35,36,37,38,39}: Largest daily visitor count = 39
Case 2: Number of visitors = {27,28,29,30,31,32,34,35,37,39,41,43}: Largest daily visitor count = 43
Not sufficient

(1) + (2)
(1) The range of the visitor counts for the 12 days was at most 12.
(2) The median visitor count over the 12 days was 33.
Largest daily visitor count <= 27 + 12 = 39
Number of visitors = {27,28,29,30,31,32,33,34,35,36,37,38,39}
Largest daily visitor count = 39
Sufficient

IMO C
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answer is option c

statement 1:range of visitor is atmost 12
so the range can be 27-38 or 27-39 hence there can be 2 possible larger visitor count hence statement 1 is not sufficient.
statement 2: median is 33
we can't find the max value of visitors hence it is also not sufficient it can be more than 100 as well

combining both statement we can find the below possible visitors on the 12 days
27,28,29,30,31,32,34,35,36,37,38,39
since all value are unique

answer is option c
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S1 Means max is at most 39 (27+12) but could as well be 38 given that there are 12 terms between 27 and 39 hence insufficient
S2 Means the 6th and the 7th values add upto 66 which can yield more than one pair including 32,34 and 35,31 hence insufficient
Both statements combined the only possible outcome that meets the constraints is one where middle terms are 34 and 32 hence sufficient
Ans C
Bunuel
A museum recorded the number of visitors for each of 12 consecutive days. If the visitor counts were all different and the smallest daily visitor count was 27, what was the largest daily visitor count?

(1) The range of the visitor counts for the 12 days was at most 12.
(2) The median visitor count over the 12 days was 33.

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it was given in statement 1 that range is atmost 12 - not a definitive number

statement 2 says median value which is not helpful to derive largest daily count even when clubbed with statement 1

both statements are not enough

hence ans is E
Bunuel
A museum recorded the number of visitors for each of 12 consecutive days. If the visitor counts were all different and the smallest daily visitor count was 27, what was the largest daily visitor count?

(1) The range of the visitor counts for the 12 days was at most 12.
(2) The median visitor count over the 12 days was 33.

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there are 12 values, all different (obviously only integers)

(1) not sufficient
the values could be either:
27,28,...,38 -> range = 11 -> max = 38
27,28,...,39 -> range = 12 -> max = 39
Since we cannot determine one unique value for the maximum number of visitors, statement 1 alone is not sufficient.

(2) not sufficient
Knowing the median doesn't give us an indication of the maximum value, only of the two middle values (there is an even number of elements, therefore the median is the arithmetic mean of the 6th and 7th values)
27, ..., 32,34, ..., 200 -> max = 200
27, ..., 32,34, ..., 50 -> max = 50

(1) and (2) sufficient
the only possible set of values is
27,28,29,30,31,32,34,35,36,37,38,39
range = 12
median = 33
max = 39

Answer C Together they are sufficient, alone neither is sufficient
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1. Least is 27. Largest maximum can be 39.
so these two are possible: 27,28,29,30,31,32,33,34,35,36,37,38... OR 27,28,29,30....,37,39...NOT SUFFICIENT

2. Median 33. so 6th & 7 th term sum be 66. 27,...32,34..... Largest term can be anything. NOT SUFFICIENT

Together,
if all numbers are different, then 6th term has to be 32.
only possible : 27,28,29,30,31,32,34,25,36,37,38,39...SUFFICIENT

Ans C
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Ans = A

A museum recorded the number of visitors for each of 12 consecutive days. If the visitor counts were all different and the smallest daily visitor count was 27, what was the largest daily visitor count?

If each visitor count was different, it means the largest daily count would be atleast 27+12 = 39 (if each day count from smallest to largest would be 27, 28, 29, 30 ... 39)

(1) The range of the visitor counts for the 12 days was at most 12.

This statement helps us know that atleast 39 = atmost 39 since the range is at most 12. which means the maximum range in largest and smallest is 12 and hence, the largest would be 27+12 = 39 since it cannot be lesser either (each day has a different count). Hence, Sufficient

(2) The median visitor count over the 12 days was 33.

While the median can be 33, it doesnt tell us anythig about the largest, that could be 35, 40, 50, 70 anything. Not Sufficient
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Bunuel
A museum recorded the number of visitors for each of 12 consecutive days. If the visitor counts were all different and the smallest daily visitor count was 27, what was the largest daily visitor count?

(1) The range of the visitor counts for the 12 days was at most 12.
(2) The median visitor count over the 12 days was 33.

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Stem is asking us to find a definitive value for the largest daily visitor count.

Statement 1: "at most" tells us the maximum, but we have an assortment of numbers between 27 and 39 that could be the maximum. Not a definitive value, therefore insufficient.

Statement 2: We now have the lowest value and values for the 6th-highest and 7th-highest numbers. 12 is an even number, so the median will be the average of 6th place and 7th place. Since 33 is a whole number, this means 6th=32 and 7th=34 (stem tells us that no two days had the same count). However, this does not give us the largest number in the range. Insufficient.

Statement 1 + 2: With all the information in statement 1, 2, and the stem combined, the daily count is forced to be as follows.

27, 28, 29, 30, 31, 32, 34, 35, 36, 37, 38, 39.

We now have a definitive value for the largest number: 39, making this sufficient. Therefore, C is the answer.
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Bunuel
A museum recorded the number of visitors for each of 12 consecutive days. If the visitor counts were all different and the smallest daily visitor count was 27, what was the largest daily visitor count?

(1) The range of the visitor counts for the 12 days was at most 12.
(2) The median visitor count over the 12 days was 33.

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stmnt1-range<=12
max visitor<=12+27= 39
max can be both 38 or 39
Not sufficient
stmnt 2- median = 33
we cannot say anything about the maximum value
both stmnt together also cannot help us narrow down to a single value for max visitor
ans=E
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min value is 27 and all values are unique


Statement1:

we know that

first one is 27, last one can be almost 39 and has to be atleast 38
if last one is 38, then they will be consecutive integers But since last one

couple of possibilities:
ending with 38:
27, 28, 29, 30, 31, 32, |, 33, 34, 35, 36, 37, 38

ending with 39:
27, 28, 29, 30, 31, 32, |, 34, 35, 36, 37, 38, 39

insufficient

Statement 2:

median is 33 meaning, the 6th and 7th ones have to be some value such that their mean is 33.
ex:
27, 28, 29, 30, 31, 32, |, 34, 40, 50, 60, 70, 80
so no limit on what max value can be

insufficient

Combined:
for median to be 33, the 6th and 7th values have to be 32 and 34 in this case since the max range is 12
27, 28, 29, 30, 31, 32, |, 34, 35, 36, 37, 38, 39

so max value will be 39.

Ans: Option C
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All different numbers and minimum was 27

1. Range was at most 12, i.e. max number can be 27 + 12 = 39
But, different visitors can also be 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38
Hence, 1 alone is not sufficient.

2. Median visitor count was 33
Since median is the middle number, this would mean that 6th and 7th number were 32 and 34. There is no limit for the highest number.
Hence, 2 alone is not sufficient.

Combining both statements,
only combination that fits is 27, 28, 29, 30, 31, 32, 34, 35, 36, 37, 38, 39 which satisfy both median value as 33 and range of 12

Hence, both statements together are sufficient
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The smallest daily count is 27. We have to find the largest daily count.
Given that the visitor counts were all different on the 12 days

Evaluating statements
A) The range of visitor counts was atmost 12
Range <= 12
If the visitor count has to be different on all days, then the range can be 11 or 12 as the numbers are distinct.

Among the numbers 27 28 29 30 31 32 33 34 35 36 37 38 39
So largest count can be 38 or 39.
This statement is insufficient

B)Median visitor count is 33
This statement alone cannot help us get to the largest visitor count.
Hence this is insufficient

Combining both statements
If median is 33 with 12 observations, we now know that 33 is the average of 6th and 7th observation.
This happens only when we take the following numbers
27 28 29 30 31 32 34 35 36 37 38 39

Hence largest number is 39.
Hence answer is C
Bunuel
A museum recorded the number of visitors for each of 12 consecutive days. If the visitor counts were all different and the smallest daily visitor count was 27, what was the largest daily visitor count?

(1) The range of the visitor counts for the 12 days was at most 12.
(2) The median visitor count over the 12 days was 33.

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(1) max - min <= 12
=> max <= 12+27 = 39
The maximum visitors was at most 39, but from 27 to 39 we have 13 different numbers. So the maximum visitors can be 38 or 39. NOT SUFFICIENT.
(2) Median = 33 => 6th day = 32, 7th day = 34. However, with only Min and Median, we can't find Max. NOT SUFFICIENT.

(1)+(2) => The set can only be {27,28,29,30,31,32,34,35,36,37,38,39}. SUFFICIENT.

Answer: C
Bunuel
A museum recorded the number of visitors for each of 12 consecutive days. If the visitor counts were all different and the smallest daily visitor count was 27, what was the largest daily visitor count?

(1) The range of the visitor counts for the 12 days was at most 12.
(2) The median visitor count over the 12 days was 33.

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Given that the smallest number is 27, we are required to find the largest count among 12 days. Also, the count is distinct everyday.

Statement 1- The range was a maximum of 12. If count was increasing by 1 everyday, the range would be 11. There can be two cases wherein the maximum count can be 38 or 39 depending on the range being 11 or 12. Not sufficient

Statement 2- If the median was 33, the 6th and 7th highest counts were 32 and 34 respectively. However, it doesn’t say anything about the largest value. Not sufficient.

Combining both the statements, the range has to be 12 and not 11 since we know the 6th and 7th highest counts already differ by 2. There can only be one case for the final value I.e. 39. Therefore, it is sufficient.

Therefore, Option C
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total = 12 days
smallest daily count= 27
largest daily counts= x
everyday its different count. say each day num id increasing.

st 1
range <= 12
x-27 <=12
x <=39
x could be anything.

st 2
median =33
(6rd + 7th/2) = 33
6th + 7th= 66
but this doesnt give much

combine them together

we know x maximum can be 39.
and median is 66.
now there are few options to get 66.
but both 33 cant be done.
if we consider 6th=32, 7th =34
27,28,29,30,31,32,34,35,36,37,38,39.

ans C
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A museum recorded the number of visitors for each of 12 consecutive days. If the visitor counts were all different and the smallest daily visitor count was 27, what was the largest daily visitor count?

(1) The range of the visitor counts for the 12 days was at most 12.
(2) The median visitor count over the 12 days was 33.

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Bunuel
A museum recorded the number of visitors for each of 12 consecutive days. If the visitor counts were all different and the smallest daily visitor count was 27, what was the largest daily visitor count?

(1) The range of the visitor counts for the 12 days was at most 12.
(2) The median visitor count over the 12 days was 33.

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we know each day unique visitor min is 27, need to find max
(1) The range of the visitor counts for the 12 days was at most 12.
This means max-min <= 12
max <= 39
but because of unique constraint max can be either 38 or 39
Insufficient.
(2)
The median visitor count over the 12 days was 33.
As each element is unique, this is only possible if middle elements are 34, 36

but largest element can be 39,40 ....
Insufficient
Combining (1) and (2)
we see only one pattern is common, so 39 will be maximum.
Sufficient.
Correct Answer: C
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