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Bunuel
In a survey of office employees, 55% reported spending less than 140 minutes per day commuting, while 69% reported spending more than 90 minutes per day commuting. If 21% reported commuting exactly 90 minutes, 7% exactly 92 minutes, 7% exactly 115 minutes, 7% exactly 138 minutes, and 7% exactly 140 minutes, what is the median daily commuting time for the employees in the survey?

A. 90 minutes
B. 92 minutes
C. 115 minutes
D. 138 minutes
E. 140 minutes

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Answer is D. 138 minutes. I needed to use a number line to depict the stem. Came to figure out that when the numbers are arranged in ascending order, the 50th percentile is at 138.
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69+55=124 -> means that 24% are between 90 and 140 (not inclusive).

55%-24%=31% -> means that 31% are less than or equal to 90.

between 90 and 140:
+ 7% of 92 min
+ 7% of 115 min
+ 7% of 138 min

7%+7%+7%=21%, but between 90 and 140 there are 24% -> 24%-21%=3% that can have any value between 90 and 140 (not inclusive).

31%+7% of 92 min = 38%
38%+7% of 115 min = 45%
45%+7% of 138 min = 52%, that is greater than 50%, so median is 138

If the value of the 3% is less than 138, the answer is also 138 because percentage would reach 48%, that is less than 50%.

The answer is D
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Bunuel
In a survey of office employees, 55% reported spending less than 140 minutes per day commuting, while 69% reported spending more than 90 minutes per day commuting. If 21% reported commuting exactly 90 minutes, 7% exactly 92 minutes, 7% exactly 115 minutes, 7% exactly 138 minutes, and 7% exactly 140 minutes, what is the median daily commuting time for the employees in the survey?

A. 90 minutes
B. 92 minutes
C. 115 minutes
D. 138 minutes
E. 140 minutes

[12daysgclub2025]
[/12daysgclub2025
Commute time % Cum
< 90 min10%10%
= 90 min21%31%
90-115 (other)≤3%≤34%
= 92 min7%≤41%
= 115 min7%≤48%
115-138 (other)remaining<50%
= 138 min7%52-55%
= 140 min7%~62%
> 140 min38%100%

Since the cumulative percentage before 138 minutes <= 48% (less than 50%), and the cumulative percentage at 138 minutes reaches >= 52% (crosses 50%), the median falls at 138 minutes.
Correct Answer: D
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The percentage that intersects the two intervals (less than 140 and greater than 90) is 69+55-100=24%.
Of this 24%, there are known percentages for 3 values: 92, 115 and 138, which makes a total of 21%.
24-21=3% can have a value greater than 90 and less than 140, but not equal to 92, 115 or 138. It can be one value or several.

The percentage of the interval less than or equal to 90 is 55-24=31% (this percentage includes equal to 90)

Median daily commuting time will the time when the cumulative percentage reaches 50%.
The cumulative percentage is:
31% (less than or equal to 90)
31+7=38% (less than or equal to 92)
38+7=45% (less than or equal to 115)
45+7=52% (less than or equal to 138) -> 50% reached.

Considering the value (or values) of the 3% undetermined, the answer is 138 too because, in the worst case, percentage including up to 138 (not included) would be 45+3=48%<50%.

median daily commuting time=138

Answer D
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Given that =>
1. 55% commute less than 140 mins => 45% spend less than 140 mins
2.69% spend more than 90 mins => 31% spend less than 90 mins
3. 21 % = 90 mins
4. 7% = 92,115,138,140 mins

Using 2 and 4 => <90 mins = 10 %

Now => 31+7 = 38% spend less than or equal to 92 mins
=> 38+7 = 45% => spend less than or equal to 115 mins
=>45+7 =52% => spend less than or equal to 138 mins
=> At 138 mins we just exceed 50%

This is also consistent with 55% being less than 140 minutes.

Hence answer is D => 138 minutes.
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Median = 50th percentile

We are given two strong boundary facts :

55% commute less than 140 minutes.
So the 50th person is definitely below 140
69% commute more than 90 minutes
so only 31% are ≤ 90
The Median cannot be 90
Remaining choices
92,115,138

Using the exact percentages near the middle
90 - 21%
92-7%
115-7%
138-7%

So moving upward from 90
Up to 90 - 21%
Up to 92 - 7%
Up to 115 - 35%
Up to 138 - 42%

Even after including 138 , we are still below 50% unless we count additional unknown

55% are below 140
only 42% are accounted somewhere below 140
between 115 and 138
Once those 13% are added.
42+13 = 55
This pushes the 50th person into 138 minute block. ✅
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55% reported <140
69% reported >90

From this we can deduce that 55+69-100 = 24% in the interval 90<x<140.
From this 24% we only know data of 92 minutes, 115 minutes and 138 minutes, which add up to 21%. So there is an unknown 3%.
We can also deduce that 55-24 = 31% reported in the interval x<=90.

We add up percentages in the interval 90<x<140 until we reach 50%, which will give us the median.
Note that 90 is not in this interval.
And note also that we must take into account the unknown 3%.

31+7(92 minutes)=38%
38+7(115 minutes)=45%
up to 137 minutes: 45%, even with an additional 3% we don't reach 50%
45+7(138 minutes)=52% > 50%

So 138 es in answer

IMO D
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answer 138 D

want to find the mediun or when number passes 50%

we know 69% spend more than 90 minutes. 31% must spend 90 or less. 21% spend exactly 90minutes so 10% spend less than 90

puting in order

<90 10% total 10
90 21% 31
92 7% 38
115 7% 45
138 7% 52

first passes 50% at 138 minutes

Bunuel
In a survey of office employees, 55% reported spending less than 140 minutes per day commuting, while 69% reported spending more than 90 minutes per day commuting. If 21% reported commuting exactly 90 minutes, 7% exactly 92 minutes, 7% exactly 115 minutes, 7% exactly 138 minutes, and 7% exactly 140 minutes, what is the median daily commuting time for the employees in the survey?

A. 90 minutes
B. 92 minutes
C. 115 minutes
D. 138 minutes
E. 140 minutes

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This question is part of our holiday event
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