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

officiisestyad

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26 Dec 2025, 21:49

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Arrange the details:
55% < 140 min
69% > 90 mins
21% = 90 mins
As all are 7% arranging it into descending order.
7% = 140 mins
7% = 138 mins
7% = 115 mins
7% = 92 mins

As 7% = 140 mins is the median of the entire list. Ans E

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26 Dec 2025, 22:38

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Given 55% <140m, 69% > 90m, 21% = 90m, 7% = 92m, 7% = 115m, 7% = 138m, 7% = 140m

Now for median we need the value exactly at between or at 50% like what's value been there.

Now, We Know

45% >= 140 Therefore the option is definitely not E.

31% <= 90m, Therefore option is definitely not A.

only 24% lies between 90 and 140
and we know the exact 21% where it belongs only uncertain is about 3%.

Now we know 7% at 138m...so if we look from right..

so more than 50% population lies >= 138 and we know 45 % have >= 140

So if we assume 3% that was uncertain was 139 then also it would be 48% and answer would be 138 and so for any case 50% would lie for 138m

Hence answer (D) 138m

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26 Dec 2025, 23:13

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This is a really challenging one, given the overlaps and intricacies of the information. Exactly why it's better to go through the information step-by-step.

55% employees reported spending less than 140 minutes per day communicating. This means, 45% employees spent 140 minutes or more commuting.

69% employees spend more than 90 minutes per day commuting. This means, 31% employees spend 90 minutes or less commuting. This also means that, out of the 69% who spent 91 minutes and more commuting, 24% (69 - 45) spend between 91 and 139 minutes, inclusive.

21% employees spent exactly 90 minutes commuting. This means, out of the 31% who spent 90 minutes or less commuting, 21% spent exactly 90 minutes. That leaves us with 10% employees who spent less than 90 minutes.

7% employees spent exactly 92 minutes commuting. This means, out of the 24% who spent between 91 and 139 minutes, inclusive, 7% spent 92 minutes. Leaving us 17% employees who spent 91 minutes and between 93 and 139 minutes, inclusive.

7% employees spent exactly 115 minutes commuting. This means, out of the 17% who spent 91 minutes and between 93 and 139 minutes inclusive, 7% spent 115 minutes. Leaving 10% employees who spent 91 minutes, between 93 and 114 minutes, and between 116 and 139 minutes.

7% employees spent exactly 138 minutes commuting. This means, out of the 10% who spent 91 minutes, 91 - 114 minutes, 116 - 139 minutes, 7% spent 138 minutes.

This leaves 3% who spent either 91 minutes, between 91 and 114 minutes, between 116 and 137 minutes, and 139 minutes.

Now, 7% employees spent exactly 140 minutes commuting. This means, out of the 45% employees who spent 140 minutes or more commuting, 7% spent 140 minutes, leaving 38% employees who spent more than 140 minutes commuting.

With all this information given, and considering this is percentage values that will be relative to each other, we can define the median effectively:

For the sake of clarity, let's assume we're looking at 100 employees. The Median, naturally, will be where the 50th and the 51st employees are present.

Based on all the information above, this is what we have:

10 employees: Less than 90 minutes commuting.
21 employees: 90 minutes commuting (we're up to 31 employees now)
7 employees: 92 minutes commuting (we're up to 38 employees now)
7 employees: 115 minutes commuting (we're up to 45 employees now)
7 employees: 138 minutes commuting (we're up to 52 employees now, covering the range including 50 and 51 employees)
7 employees: 140 minutes commuting (that takes things up to 59 employees)
38 employees: more than 140 minutes commuting (that takes things up to 97 employees).

We do have the 3% not accounted for, which can either be 91 minutes, anywhere between 91 and 114 minutes, anywhere between 116 and 139 minutes, or 139 minutes. But, remember, even if this range lies below the 138-minute mark, it will only take the range of 138 minutes up from 46 - 52 employees, to 49 - 55 employees, within which we also see the 50% and 51% employees, exist, so the median will NOT be impacted.

Hence, we have 138 minutes as the median value.

Bunuel

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26 Dec 2025, 23:41

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Bunuel

It’s good to solve this sum, by visualise it on the number line. Moreover, assume the total value as 100.

69 members have value greater than 90. ( That’s from 91 onwards).

Any value less than or equal to 90, has a value of 100- 69 = 31.

Exactly 90 = 21

Then, less than 90 equals = 31-21 = 10.

Exactly at 92 , there are 7 members.

Exactly at 115, there are 7 members.

Exactly at 138, there are 7 members.

So, let’s write everything in sequence to visualise it much better.

Less than 90, we have 10 values.

Exactly at 90, we have 21 values.

Exactly at 92, we have 7 values.

Exactly at 115, we have 7 values.

Exactly at 138, we have 7 values.

Sum of all values = (10+21+7+7+7) = 52

This has crossed the median value, as we have taken the total count of 100.

Median value lies around the value position of 138.

Median position = 138.

Option D

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27 Dec 2025, 00:46

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If we add up all the individual percentages, we get 49% (21+4*7).
The median will be at 50%. Now, we know that under 140 minutes takes up 55%. So the median is definitely less than 140 minutes.
And it can't be less than 138 minutes, because the remaining add up to 42%, and we could say the rest add up to 8% and get the median as less than 138 minutes. But then 138 minutes takes up 7%, so if the rest take other minutes, take 8%, then the total would go above 55%, which is the percentage less than 140 minutes.
So it has to be greater than 138 and less than 140.
But since we don't have such an option, we choose 138. We for sure can't choose 140. 138 is possible, if the rest take up 1%, and then one's above 138 and below 140 take up 5%.

Option D.

Bunuel

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27 Dec 2025, 01:07

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Given that:
55%<140
69%>90
21%=90
7%=92
7%=115
7%=138
7%=140
Meaning <90 = 100%-69%-21%= 10%
Meaning >140 = 100%-55%-7%= 38%
Arrange them in cumulative form from the <90 and add them until you get to where 50% falls:
<90 90 92 115 138
Thus 10+21+7+7+7= 52
50% falls within the 138 minutes

Bunuel

thuckhang

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27 Dec 2025, 01:23

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Use Cumulative Distribution
69% spend more than 90 min => 31% spend < 90min, 21% exactly 90 min => 10% < 90min
Times --- % at that time --- Cumulative
<90min---10%---10%
=90min---21%---31%
=92min---7%---38%
=115min---7%---45%
=138min---7%---52%
=140min---7%---59%
Hence, the median is around 138min. D

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27 Dec 2025, 02:03

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We have the first 31% people reporting less than or equal to 90 minutes, since 69% people report more than 90%.

The next 7% report 92 minutes, the next 7% 115 minutes. We have covered 31+14=45% so far. We are also given that 7% cover 138 minutes. Since by now, we cross the 50% mark (45+7=52%), the median has to be 138 minutes.

Therefore, Option D imo

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27 Dec 2025, 02:12

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To find the median we need to estimate the number at around 50th percentile

69% spend more than 90 min => 31% spend exact 90 and below
7% spend exact 92, 7% spend exact 115 and 7% spend exact 138 min => 31+7+7+7=52% ~ 55% spend less than 140 min
Hence the median must around 138.

Answer: D

Bunuel

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27 Dec 2025, 02:38

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Median = the value where you first reach 50%
The median will be less than 140 because 55% is already below 140
Exactly 90 min is 21%
Exactly 92 min is 7%, Total 21+7= 28%
Exactly 115 min is 7%, Total value 28+7=35%
Exactly 138 min is 7% total = 35+7= 42%
Median not reached yet but since if we add the remaining unaccounted group the total will be more than 50, then our median is 138minutes

Correct Answer is 138 minutes

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27 Dec 2025, 02:42

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let's take 100 total. we need to find median minutes -> which will lie 50 and 51st position
55 less than 140 min // within 140 our median will lie
69 is more than 90 hence 31 will be less than & equal to 90.
21 is exactly 90 -> less then 90 is 31-21 = 10
exactly 92 -> 7
exactly 115 -> 7
exactly 138 -> 7
exactly 140 -> 7
if we sum till 138 -> we get 31+7+7+7 = 52 hence median lies at 138.

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27 Dec 2025, 02:52

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Question is asking MEDIAN = (Total quantity+1) /2

If Q=100%, median is (100+1)/2 = between percentile 50th and 51th

We can draw a line between 90 and 140

quantity of <90 = 100-69 = 31
quantity of 90 = 21

31+21 =52

Hence, the 50th-51st percentile lies in Q90.

Answer A 90 minutes.

Bunuel

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27 Dec 2025, 03:22

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To find the median, we need to find the value at the 50th percentile.
Finding the starting point:
First, we determine how many people commute for less than 90 minutes:
69% commute more than 90 mins.
21% commute exactly 90 mins.
Remaining: 100% - (69% + 21%)
= 10% commute less than 90 mins.

Now calculating the cumulative percentages,
Adding the percentages in order of time to see where we hit 50%:

Commute Time	Group %	Cumulative percentage
<90 mins	10%	10%
90 mins	21%	31%
92 mins	7%	38%
115 mins	7%	45%
138 mins	7%	52% (50% mark hits here)

So the answer should be D. 138 mins.

Bunuel

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27 Dec 2025, 03:44

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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?

To find the median from shortest commute to longest commute, the median is the time where we croos 50%.

69% reported spending more than 90 minutes. Hence, (100-69=31%) spend 90 minutes or less
Also, 21% spend exactly 90 minutes
So, people who spend less than 90 minutes= 31%-21% =10%

55% reported spending less than 140 minutes. Hence, 45% spend 140 minutes or more.
Also, 7% spend exactly 140 minutes
So people who spend more than 140 minutes = 45%-7%= 38%

Now we list everything from smallest to largest, adding percentages as we go to find the median.
Time....% employees....cumulative%
<90 ........10..........10
90..........21...........31
92..........7............38
115.........7............45
138.........7............52
140.........7............59
>140........38...........97

The median is the value where the cumulative% first reaches 50%
At 115 minutes, cumulative% = 45%
At 138 minutes, cumulative% = 52%

the median daily commuting time for the employees in the survey= 138 minutes

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27 Dec 2025, 04:50

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Given, 69% people commute for more than 90 minutes which means 31% spend less than 90 minutes.

Also, since 21% spend exactly 90 minutes, 31-21 = 10% spend<90 mins

We know, the median will lie around 50% of cumulative population,

Check in which range does this 50% fall,

Time Cumulative distribution
<90 - 10%
=90 - +21% = 31%
=92 +7% = 38%
=115 +7% = 45%
=138 +7% = 52%

So, the median will be the time at which cumulative percentage first reaches or exceeds 50% which happens at 138 mins

Option D

Bunuel