12 Days of Christmas GMAT Competition 2025 - Day 10: In a survey of

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Bunuel

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26 Dec 2025, 10:00

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Bunuel

GMAT Club Official Explanation:

Think of 100 employees.

69 spend more than 90 minutes, so 31 spend ≤90 minutes.

55 spend less than 140 minutes, so 45 spend ≥140 minutes.

Since 69 spend more than 90 minutes and 55 spend less than 140 minutes, (69 + 55) - 100 = 24 employees spend more than 90 minutes but less than 140 minutes: 90 minutes < (times of 24 employees) < 140 minutes.

The median would be the average of the 50th and 51st commuting times when times are arranged in ascending or descending order.

Notice that the 21 who commute exactly 90 minutes are already part of the 31 who spend 90 minutes or less, so they do not affect the top end where the median will land. Similarly, the 7 who commute exactly 140 minutes are already part of the 45 who spend 140 minutes or more, so they also do not matter.

Next, 7 exactly 92 minutes + 7 exactly 115 minutes + 7 exactly 138 minutes = 21 employees, so there are 3 employees remaining who also fall into 90 < and < 140 range.

However, 45 who spend 140 minutes or more plus 7 who spend exactly 138 minutes already account for 52 of the greatest commuting times. Even if the remaining 3 are assigned as 139 minutes, 138 minutes would still be the 50th and 51st greatest values.

Thus, the median is 138 minutes.

Answer: D.

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Xdsa

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26 Dec 2025, 09:20

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55% reported less than 140 mins
69% reported more than 90 mins
21% reported 90 mins
7% reported each of 92,115,138,140 mins
8% reported less than 90 mins
21+8+7+7+7=50% which is 138 mins
median will be 138 mins
option d is correct

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26 Dec 2025, 09:23

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On simplification,

Time	%/Cumulative
<90	=(100-69)-21 = 10; 10
90	21; 31
92	7; 38
115	7; 45
138	7; 52
140	7
>140	=45-7=38

Median is at 138

Bunuel

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26 Dec 2025, 09:31

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Bunuel

Lets solve this question:

69% commute > 90 => so that gives 31% commute <= 90
Since 21% are exactly 90, we have 31-21=10% are <90

55% commute < 140. Below 140 you already have: 10 + 21 + 7 + 7 + 7 = 52%
so the "other times" between 90 and 140 total 55-52 = 3%

Even if that whole 3% is <= 115, cumulative <=115 is at most 31 + 7 + 7 + 3 = 48% < 50%
so median >115

Even if that whole 3% is > 138, cumulative <=138 is still 31 + 7 + 7 + 7 = 52% >= 50%
so median is 138

Option D

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26 Dec 2025, 09:43

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Bunuel

<= 90 would be 100 -69 = 31%
and =90 is 21 , so <90 =10%

wrting commulative frequency in ()

<90	=90	=92	=115	=138
10	21(31)	7(38)	7(45)	7(52)

50% lie on 138
hence answer is 138

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26 Dec 2025, 09:56

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say total = 100x
<140 min= 55x
>90 min = 21x
exact 90 min = 21x
92 min= 7x
115 min= 7x
138 min= 7x
140 min= 7x

we can find that < 90 min= 10x

we need 50th and 51st to find median.
now if we arrange them in ascending order, those two people fall in 138 min category

BunuelIn 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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26 Dec 2025, 10:03

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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

>90 mins is 69%
less than <90 mins is 31%
exactly 92 mins 7%
exactly 115 mins 7%
exactly 138 mins 7%
exactly 140 mins 7%
less than 140 mins is 55%

between 90 & 140 mins
55-31 ; 24%
less than 115 mins
7(92)+31 (<90)+ 7(115) = 45% ; this is less than 50% not median
at 138 mins
45% + 7% ; 52%
option D ; 138 mins is correct

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26 Dec 2025, 10:05

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Bunuel

Let's assume that there are 100 employees

< 90 = 10
91 = 21
92 = 7
115 = 7
138 = 7
140 = 7
> 140 = 38

The median term is the average of the 50th and 51st term

Both the 50th and 51st term have a value of 138

Hence, the average = 158

Option D

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26 Dec 2025, 10:14

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Given that

69% spend more than 90 minutes
So, 31% spend less than or equal to 90 minutes
Since 21% spend exactly 90 minutes
10% spend less than 90 minutes

7% spend 92 minutes
7% spend 115 minutes
7% spend 138 minutes
7% spend 140 minutes.

The median commuting time is when the cumulative percentage crosses 50%
Upto 90 minutes - 31%
Upto 92 minutes - 31% + 7% = 38%
Upto 115 minutes - 31% + 7% + 7% = 45%
Upto 138 minutes - 31% + 7% + 7% + 7% = 52%

138 minutes is the median per day commuting.

Bunuel

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26 Dec 2025, 10:20

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55% reported spending less than 140 minutes per day commuting
7% reported spending exactly 140 minutes per day commuting
100%-55%-7% = 38% reported spending more than 140 minutes per day commuting

69% reported spending more than 90 minutes per day commuting
21% reported spending exactly 90 minutes per day commuting
100%-69%-21% = 10% reported spending less than 90 minutes per day commuting

10% reported spending less than 90 minutes per commuting; Cumulative 10%
21% reported spending exactly 90 minutes per day commuting; Cumulative 31%
7% reported spending exactly 92 minutes per day commuting; Cumulative 38%
7% reported spending exactly 115 minutes per day commuting; Cumulative 45%
7% reported spending exactly 138 minutes per day commuting; Cumulative 52%
7% reported spending exactly 140 minutes per day commuting
38% reported spending more than 140 minutes per day commuting

Because median 50% lies in 138 minutes per day

Median = 138 minutes

IMO D

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26 Dec 2025, 10:26

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P(T<140)=55%
P(T>90)=69%
P(T=90)=21%
P(T=92)=7%
P(T=115)=7%
P(T=138)=7%
P(T=140)=7%

69% commute more than 90 mins & 21% commute exactly 90 mins, so remaining who commute less than 90 mins=100-69-21=10%
Less than 90 (10% employees) and cumulative%= 10%
90 ; (21% employess) & cumulative%=31%
92 ; (7% employees) & cumulative% =38%
115 ; (7% employees) & cumulative% =45%
138 ; (7% employees) & cumulative% = 52%
140 ; (7% employees) & cumulative% =59%
The first time we cross 50% is at 138 minutes
Median daily commuting time = 138 mins

D

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26 Dec 2025, 11:17

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55% < 140 minutes

then, >= 140 minutes is 45%

So median has to be < 140 minutes (since median is 50th percentile)

69% >90 minutes
then, <= 90 minutes will be 31%

so median has to be between 90 and 140 minutes (excluding the ends)

100% - 31% - 45% = 100% - 76% = 24%

out of this 24%, we know that 7% (92 minutes), 7%(115 minutes) and 7%(138 minutes) exist.
24% - (7% + 7% + 7%) = 3%

This 3% we don't know where it is between 90 and 140 (excluding the ends)

Let's assume two cases:

case1: 3% is at the fag end like > 138 minutes

then 31% (<= 90 minutes) + 7% (from 92 minutes) + 7%(from 115 minutes)
= 45% and then 7% of 138 minutes is there making the median 138 minutes

case 2: 3% is at the left most possible i.e. say 91 minutes

then 31% (<=90 minutes) + 3% (91 minutes) + 7% (from 92 minutes) + 7%(from 115 minutes)
= 48%, and then 7% of 138 minutes is there making the median again 138 minutes

Ans: option D (138 minutes)

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26 Dec 2025, 11:28

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let, Total 100 employees. Median= average of 50th & 51st term
More than 90=69
So less than 90=31
so less than 90, 31-21=10
less than 140= 55
more than 140 = 100-(55+7)=38
so greater than 90 but less than 140 =3
whatever may be these 3 values, 50th & 51th value is 138.

Ans 138

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26 Dec 2025, 11:36

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Let's extrapolate some info from the data:

55% commutes less than 140 min ==> 45% >= 140 min
69% commutes more than 90 min ==> 31% <= 90 min

Now we know that 21% takes exactly 90 min, hence 10 % will take less than 90 min
Moreover 7% takes exactly 140 min ==> 38% takes more than 140

Now we have all the ingredients:

10 % less than 90
21% exactly 90
7% takes 92
7% takes 115
7% takes 138
7% takes 140
38% more than 140

From this we can easily see that the median falls inside the 138 min bucket,
hence IMO D!

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26 Dec 2025, 11:42

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assume there are 100 people. the median is the average of the 50th and 51st person, so you need to find those two values.

55 are <140min
69 are >90min
x people are between 90 and 140min (non inclusive)
(use the formula for overlapping sets -> total = people in one set + people in the other set - people in both)
100 = 55 + 69 - x -> x = 24

using this information and the other data given in the problem you can determine
21 are <90min -> 55 - 34 = 21
7 are =92min -> 21+7=28 <92min
7 are =115min -> 28+7=45 <115min
7 are =138 -> 45+7=52 <138min

the 46th, 47th, ..., 50th and 51st people commute 138 min

Answer D. 138

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26 Dec 2025, 11:43

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Bunuel

Let's assume 100 people for easy math, since we're given percentages, making a 1:1 ratio between a percentage point and person.

To find the median, we need to find person 50 and 51, if the commute times were arranged in ascending order.

We're given that 69 people commute more than 90 minutes, which means 31 commute 90 minutes or less. Let's not worry about anyone who commuted exactly 90 minutes or less, they're all included in this 31 figure.

Moving on, we are given brackets of exact commute times. We just keep adding each bracket until we hit persons 50 and 51.

Exactly 92 minutes: $31+7=38$
Exactly 115 minutes: $38+7=45$
Exactly 138 minutes: $45+7=52$

Perfect! Both #50 and #51 are contained within this last bracket. That means the median is D, 138 minutes.

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26 Dec 2025, 11:59

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given 55% --less than 140 mins./day and 69%--greater than 90 mins/day
so 31%--less than or equal to 90 mins/day, which will also include 21%--who commute exactly 90mins/day

%age of the people	31%	7%	7%	7%	7%
time commuted in mins/day	less than or equal to 90 mins/day	exactly 92 mins/day	exactly 115 mins/day	exactly 138 mins/day	exactly 140 mins/day

from the table above its clear that the employee who commutes median time will lie in the 5th column
as 31+7+7+7=52%
so the employee with the median commute time per day commutes 138 mins/day
D

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26 Dec 2025, 13:24

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Bunuel

Ok office employees spending less than 140 min is 55 %

Median is 50% of the data

so Median is less than 140.

Also, given <= 90 min is 31%.

92 min , 115 min, & 138 min = 7%

31 + 7 + 7 + 7 = 52; so 138 lies in 48 - 55 region, so 138 is the median.

Ans - D

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26 Dec 2025, 14:43

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Bunuel