Last year in City X, the range of daily low temperatures, in degrees F

Question

Last year in City X, the range of daily low temperatures, in degrees Fahrenheit, was 20 for the month of June and 25 for the month of July. Which of the following is the smallest possible range of City X's daily low temperatures, in degrees Fahrenheit, for the two-month period of June and July of last year?

A. 5

B. 20

C. 25

D. 30

E. 45

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Screenshot 2023-12-29 232036.png

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nazii · Accepted Answer

ONLY 2 second approach 
Rule: The minimum range of the entire group is the MAXIMUM range of individuals 
Max {20,25}= 25

MartyMurray · Answer

Last year in City X, the range of daily low temperatures, in degrees Fahrenheit, was 20 for the month of June and 25 for the month of July. Which of the following is the smallest possible range of City X's daily low temperatures, in degrees Fahrenheit, for the two-month period of June and July of last year?

A. 5

B. 20

C. 25

D. 30

E. 45

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Attachment:

Screenshot 2023-12-29 232036.png

A. 5

B. 20

C. 25

D. 30

E. 45

The range is the difference between the highest and lowest temperatures during the period in question.

Since the range for July is 25 and July is within the period in question, we know that, during the period in question, there were temperatures that differed by at least 25 degrees. So, the range for the two-month period cannot be less than 25.

So, we can eliminate choices (A) and (B).

Now, the question becomes whether the fact that June is also included in the period means that the range must be even greater than 25.

Since June's range is 20 degrees, it's possible that the June low was higher than the July low and that the June high was lower than the July high.

For example the July low and high could be 50 and 75, and the June low and high could be 52 and 72. In that case, the range would still be 25 since 25 is the difference between the highest and lowest temperatures for the entire period.

The correct answer is (C).

lakshitaj · Answer

This question seems a little bit tricky to think logically. so let's go mathematically.
1) what is range ? - difference between min and max value.
for June: y1-x1
for July : y2-x2
2) Now range for combined two months would depend upon the values of x1,x2 and y1,y2.
-->if smallest and largest value are both from the month of June, then range = y1-x1 =20
-->similarly if both are from July, then range =y2-x2=25
otherwise, the two cases would be
1. x1<x2 and y1<y2 ==> range = y2-x1, now that y2-x2 =25 and x1<x2, we can say that y2-x1>=25
hence, the min value of range is 25.
2. x1>x2 and y1>y2 ==> range = y1-x2, now that y2-x2 =25 and y1>y2, we can say that y1-x2 >=25
hence, min value of range is 25

hence, the answer is 25.

esseeveniet · Answer

Did not get this line? - For example the July low and high could be 50 and 75, and the June low and high could be 52 and 72. In that case, the range would still be 25 since 25 is the difference between the highest and lowest temperatures for the entire period.

What if June's degree is 0(Min)-20(Max)and July's is 1 (Min) 26 (Max)

What if June's degree is 0(Min)-20(Max)and July's is 1 (Min) 26 (Max)

Bunuel · Answer

We are asked to find the  smallest possible  range. Your example gives a bigger range, but the question is asking for the minimum possible. July alone is already 25, and June can be placed fully inside that interval, so the  smallest possible  range is still 25.

luisdicampo · Answer

To find the  smallest possible range  for the combined two-month period, we need to make the temperature sets of June and July  overlap  as much as possible.

Method 1: Logical Reasoning

1.  Definition:  Range =  Maximum - Minimum .
2.  Constraints: 
 * Range of June =  20 
 * Range of July =  25

3.  Concept: 
 The combined range is determined by the  overall highest  temperature and the  overall lowest  temperature recorded across both months.
 Since July alone has a spread of  25  degrees, the combined period must accommodate at least that spread. You cannot "shrink" the existing spread of July by adding June's data.

Therefore, the minimum possible combined range is simply the larger of the two individual ranges. This happens if the range of June is completely "contained" within the range of July.

Rule:   Min(Combined \ Range) = Max(Range_A, Range_B)

Method 2: Picking Numbers (Visualizing the Overlap)

Let's construct a scenario where the ranges overlap perfectly to minimize the total spread.

*  Scenario for July (Range 25): 
 Let the temperatures in July be between  50^\circ  and  75^\circ .
  Range = 75 - 50 = 25 .

*  Scenario for June (Range 20): 
 To minimize the combined range, let's put June's temperatures completely inside July's numbers.
 Let the temperatures in June be between  50^\circ  and  70^\circ .
  Range = 70 - 50 = 20 .

*  Combined Period: 
 * Overall Minimum:  50^\circ  (from both months).
 * Overall Maximum:  75^\circ  (from July).
 *  Combined Range:   75 - 50 = 25 .

It is impossible to get a number lower than 25 because the month of July forces the spread to be at least 25.

Answer: C

Varun291 · Answer

Last year in City X, the range of daily low temperatures, in degrees Fahrenheit, was 20 for the month of June and 25 for the month of July. Which of the following is the smallest possible range of City X's daily low temperatures, in degrees Fahrenheit, for the two-month period of June and July of last year?

A. 5

B. 20

C. 25

D. 30

E. 45

Show Spoiler

Attachment:

Screenshot 2023-12-29 232036.png

A. 5
B. 20
C. 25
D. 30
E. 45

I am slightly confused here. Why does the range of June have to overlap with the the range of July? For example I could have the daily low for June as 10 and 30 degree which gives a range of 20 and a daily low of July as 5 and 30 with a range of 25. Now I can subtract 30-10 which gives me 20. What am I doing wrong?

Bunuel · Answer

The ranges do not  have to  overlap. But the question asks for the smallest  possible  two month range, and the smallest possible range happens when one month’s temperatures sit inside the other month’s range as much as possible. If June’s range is 20 and July’s range is 25, then the two month range cannot be less than 25, because July alone already contains a 25 degree spread.

In your example, once July includes 5, the overall minimum for the two months is 5, and the overall maximum is 30, so the two month range is 30 minus 5, which is 25, not 20. You used June’s low (10) instead of the overall low (5).

HarshG7 · Answer

what if for June we have 20-40 giving us 20 as the range
and for July we have 0-25 giving us 25 as the range
finally giving us 25-20=5 as the range ?

nihilre · Answer

What is the largest possible range  Bunuel   bb   MartyMurray

Bunuel · Answer

Theoretically, there is no limit to the largest possible range, because the two monthly temperature ranges can be placed arbitrarily far apart.

Pablo321 · Answer

If my understanding is correct, the range is the highest value in the two month span minus the lowest value. In your example it would be 40-0= 40. Which would be higher than the minimum of 25.

iaditi · Answer

if the range of July is wider than that of June, how can both nos., the smallest and the largest, be from the month of June?

Last year in City X, the range of daily low temperatures, in degrees F

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