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805+ (Hard)|   Math Related|         
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GMAT Club World Cup 2026 (Day 5): The cockpit crew for a long-haul 11 Jul 2026, 06:35
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Total Cases:
Hugo pilot=1*3C2=3
Hugo not pilot=3C1*6C2=45
Total=48

Prob Hugo pilot = 3/48 =1/16


Copilot with less work hour cannot fly with Hugo.
So any pilot except Hugo & one from 3 experienced copilot & one from 3 less experienced co pilot
=3C1*3C1*3C1=27

Reqd Prob =27/48 =9/16

Answer 1/16 & 9/16
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GMAT Club World Cup 2026 (Day 5): The cockpit crew for a long-haul 11 Jul 2026, 06:50
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Find total cases start with Hugo: Since he can only fly with experienced who are 3 in number we get 3C2= 3
The other two pilots 3 pilots can fly with any two so 6C2= 15
Total 3+(3x15)=48
So Hugo is the pilot is 3/48= 1/16
1 Co-pilot has less that 500 hours: For non-experienced 3C1= 3 and 3C1 for experienced =3. Total 3x3=9
This 9 combinations can only fly with any of the 3 pilots hence 3x9=27
So 1 co-pilot has less than 500 hrs= 27/48= 9/16
Bunuel
The cockpit crew for a long-haul flight must consist of 1 pilot and 2 copilots, selected from an available pool of 4 pilots and 6 copilots. One of the pilots, Hugo, is only certified to serve as pilot if each of the two selected copilots has at least 500 hours of flight experience, a qualification held by 3 of the 6 available copilots. The remaining pilots can fly with any copilot. A cockpit crew will be selected at random from all possible crew combinations that meet these conditions.

The two columns in the table refer to two separate cases, each based on the same random selection from all valid cockpit crews. In the table, for Hugo is the pilot, select the probability that Hugo is the pilot on the selected cockpit crew. For Exactly 1 copilot has less than 500 hours, select the probability that exactly 1 of the 2 copilots on the selected cockpit crew has less than 500 hours. Make only two selections, one in each column.
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GMAT Club World Cup 2026 (Day 5): The cockpit crew for a long-haul 11 Jul 2026, 06:54
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Cockpit crews = 3+15 = 48:
With Hugo as pilot, 3C2 = 3 crews
Without Hugo as pilot: 3 * 6C2 = 3 * 15 = 45

p(Hugo) = 3/48 = 1/16

Copilots: 3 (>=500), 3 (<500)
Combining: 3*3=9
Choosing pilot (only 3 available): 3*9 = 27

p(1 copilot<500) = 27/48 = 9/16

"Hugo is the pilot" = 1/16 and "Exactly 1 copilot has less than 500 hours" = 9/16
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GMAT Club World Cup 2026 (Day 5): The cockpit crew for a long-haul 11 Jul 2026, 06:59
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Bunuel
The cockpit crew for a long-haul flight must consist of 1 pilot and 2 copilots, selected from an available pool of 4 pilots and 6 copilots. One of the pilots, Hugo, is only certified to serve as pilot if each of the two selected copilots has at least 500 hours of flight experience, a qualification held by 3 of the 6 available copilots. The remaining pilots can fly with any copilot. A cockpit crew will be selected at random from all possible crew combinations that meet these conditions.

The two columns in the table refer to two separate cases, each based on the same random selection from all valid cockpit crews. In the table, for Hugo is the pilot, select the probability that Hugo is the pilot on the selected cockpit crew. For Exactly 1 copilot has less than 500 hours, select the probability that exactly 1 of the 2 copilots on the selected cockpit crew has less than 500 hours. Make only two selections, one in each column.
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Hugo = Pilot ; Possible Combination of Copilot = 3
Hugo is not the pilot ; Possible combination of Copilot = 45

Total Possible Combination

Prob. of Hugo = 3/45+3 = 3/48 = 16

Exactly 1 = Total - Both Experience - Both not experienced

=48 - (18 + 3 ) = 27

27/48 = 9/16

Hugo = 1/6
Exactly 1 copilot = 9/16
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GMAT Club World Cup 2026 (Day 5): The cockpit crew for a long-haul 11 Jul 2026, 07:03
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Given one pilot and two copilots. Pool is four pilots and six co-s.
Hugo must be with two special co-s, only three out of six are special.

First, chance: Hugo is one out of four pilots and the chances for getting him as a pilot are independent of the chances of getting a specific co-.the chances of getting the special co-s are three out of six, which is half multiplied by the chances of getting a second special co- two-fifths, total one-fifth. So, one fifth times one out of four is one out of twenty.

Having one co exactly being not special is complementary to having none special plus two special->\(\frac{3}{6}=\frac{1}{2}*\frac{2}{5}=\frac{1}{5}\)
that's the chances of both having two specials and none special.

\(\frac{1}{5}+\frac{1}{5}=\frac{2}{5}\)
\(1-\frac{2}{5}=\frac{3}{5}\)

So, the chances of having exactly one co like that are \(\frac{3}{5}\)
And the chances Of having Hugo pilot the plane are \(\frac{1}{20}\)
Bunuel
The cockpit crew for a long-haul flight must consist of 1 pilot and 2 copilots, selected from an available pool of 4 pilots and 6 copilots. One of the pilots, Hugo, is only certified to serve as pilot if each of the two selected copilots has at least 500 hours of flight experience, a qualification held by 3 of the 6 available copilots. The remaining pilots can fly with any copilot. A cockpit crew will be selected at random from all possible crew combinations that meet these conditions.

The two columns in the table refer to two separate cases, each based on the same random selection from all valid cockpit crews. In the table, for Hugo is the pilot, select the probability that Hugo is the pilot on the selected cockpit crew. For Exactly 1 copilot has less than 500 hours, select the probability that exactly 1 of the 2 copilots on the selected cockpit crew has less than 500 hours. Make only two selections, one in each column.
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GMAT Club World Cup 2026 (Day 5): The cockpit crew for a long-haul 11 Jul 2026, 07:04
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This seems to be easy question even question stem is longer but at last one the ask is to choose exactly 1 copilot with less than 500 I'm unable to solve this question choice I choose the answer choice to 9/16 bcz 3c1*3c1 = 9 but I'm not sure how to solve for this so I go with random as I already took more than 5 mins meaning learning/conceptual issue instead of longer path issue I again feel all the GMAT club official questions are not that good in langauge compare to Manhattan questions -> this is my personal observation making question unclear is GMAtclub World cup challenge how we could play with wording and convoluted still enjoying the challenge to see how unfamiliar questions can come in DI. Thanks!
Bunuel
The cockpit crew for a long-haul flight must consist of 1 pilot and 2 copilots, selected from an available pool of 4 pilots and 6 copilots. One of the pilots, Hugo, is only certified to serve as pilot if each of the two selected copilots has at least 500 hours of flight experience, a qualification held by 3 of the 6 available copilots. The remaining pilots can fly with any copilot. A cockpit crew will be selected at random from all possible crew combinations that meet these conditions.

The two columns in the table refer to two separate cases, each based on the same random selection from all valid cockpit crews. In the table, for Hugo is the pilot, select the probability that Hugo is the pilot on the selected cockpit crew. For Exactly 1 copilot has less than 500 hours, select the probability that exactly 1 of the 2 copilots on the selected cockpit crew has less than 500 hours. Make only two selections, one in each column.
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GMAT Club World Cup 2026 (Day 5): The cockpit crew for a long-haul 11 Jul 2026, 07:13
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If Hugo is the pilot, the copilots can be chosen in 3C2=3 options.
If Hugo is not the pilot, 3(number of pilots) * 6C2 = 3 * 15 = 45
3+45 = 48 options.

probability(Hugo is the pilot) = 3/48 = 1/16

3 experienced copilots
3 unexperienced copilots
3*3 = 9 options for copilots
3 posibble pilots (Hugo cannot be chosen) * 9 = 27 options for cockpit crews.

probability(Exactly 1 copilot has less than 500 hours) = 27/48 = 9/16

Hugo is the pilot: 1/16
Exactly 1 copilot has less than 500 hours: 9/16
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GMAT Club World Cup 2026 (Day 5): The cockpit crew for a long-haul 11 Jul 2026, 07:23
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The following facts are given in the question:
Total members required in a cockpit crew = 3 (2 Co-pilots CP + 1 Pilot P)
Total members from which the selection is done = 10 (6 CP + 4 P)
Out of the total 4P - Hugo - can act as pilot if - 2 CP has minimum 500 hours of flight experience each
Out of the 6 CP - Only 3 CP have minimum of 500 hours of flight experience each

First part requires us to find the probability that Hugo is the Pilot
The probability that Hugo is the pilot =>
Both CP are from the 3 CP who are experienced = 3C2 = 3 ( Select 2 out of 3 CP having experience)
When 3 people other than Hugo is a pilot = 3* 6C2 = 3* 6!/2!*4! = 3* 6*5/2= 3*15 = 45 (Select 2 CP from Total 6 CP)

Hence the probability of Hugo is 3/ (45+3) = 3/48 = 1/16

Second part requires to find probability of exactly one copilot has less than 500 hours
This is confusing and not able to get the same.
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GMAT Club World Cup 2026 (Day 5): The cockpit crew for a long-haul 11 Jul 2026, 07:29
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We are given that,
There are 4 pilots (Including Hugo) and
6 Copilots out of which 3 are experienced (atleast 500hrs experience) and 3 are inexperienced (less than 500hrs experience)

We know that each crew has
1 pilot and 2 copilot

Case 1: Hugo is the pilot
Hugo can fly if both copilots are experienced
=> Choosing 2 out of 3 experienced copilots
=> 3C2 = 3 ----- 1

Case 2: Any 1 of the other 3 pilots
They dont have restriction
=> Chossing 2 out of 6 copilots
=> 6C2 = 15

Total possible crews = 45+3 = 48

Now,
Probability when hugo is the pilot = 3 / 48 = 1/16 (From 1)

Now we need to know for when exactly one copilot has fewer than 500hrs experience
=> 1 copilot experienced and the other inexperienced
=> Possible combinations = 3C1 * 3C1 = 3*3 = 9

And 1 out of the 3 pilot possible
=> Possible crew where 1 copilot has fewer than 500hrs = 3* 9 = 27

=> Probabilty where exactly 1 copilot has fewer than 500hrs = 27/48 = 9/16

Hugo is the pilot = 1/16
Exactly one copilot has fewer than 500hrs = 9/16
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GMAT Club World Cup 2026 (Day 5): The cockpit crew for a long-haul 11 Jul 2026, 07:30
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First need to calculate number of valid crews.

If Hugo us the pilot, copilots need to be from 3 of the 6 co pilots = 3C2 = 3
If Hugo is not the captain, any of the 2 copilots can be selected = Number of pilots x number of copilot selections = 3 x 6C2 = 3 * 15 = 45
Total valid crews = 3 + 45 = 48

For column A, Hugo is the captain => number of possible crews with Hugo as captain / total number of crews = 3/48 = 1/16

For Column B, exactly one of the copilot is below 500 hours = Number of captains x number of copilot selections with less than 500 hours x number of copilot selections with more than 500 hours = 3 x 3C1 x 3C1 = 3 x 3 x 3 =27

Probability = 27/48 = 9/16
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GMAT Club World Cup 2026 (Day 5): The cockpit crew for a long-haul 11 Jul 2026, 07:30
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Bunuel
The cockpit crew for a long-haul flight must consist of 1 pilot and 2 copilots, selected from an available pool of 4 pilots and 6 copilots. One of the pilots, Hugo, is only certified to serve as pilot if each of the two selected copilots has at least 500 hours of flight experience, a qualification held by 3 of the 6 available copilots. The remaining pilots can fly with any copilot. A cockpit crew will be selected at random from all possible crew combinations that meet these conditions.

The two columns in the table refer to two separate cases, each based on the same random selection from all valid cockpit crews. In the table, for Hugo is the pilot, select the probability that Hugo is the pilot on the selected cockpit crew. For Exactly 1 copilot has less than 500 hours, select the probability that exactly 1 of the 2 copilots on the selected cockpit crew has less than 500 hours. Make only two selections, one in each column.
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For Hugo, both pilots must be experienced. Hence, 1 * 3C2 = 3

For other two pilots any copilots work. Hence, 3 * 6C2 = 45

Total valid crews = 48

Hugo is the pilot

3/48 = 1/16

Exactly One copilot has less than 500

Possible case = Any pilot other than Hugo + 1 less than 500 hours copilot + 1 greater than 500 hours copilot

=3 * 3 * 3 = 27

27/48 = 9/16

Hugo = 1/16
Exactly one pilot less than 500 hours = 9/16
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GMAT Club World Cup 2026 (Day 5): The cockpit crew for a long-haul 11 Jul 2026, 07:31
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Number of distinct cockpit crews:
Hugo: 1*3C2 = 3
No Hugo: 3*6C2 = 45
Total = 48

p(Hugo is the pilot) = 3/48 = 1/16

If 3 copilots>=500 hours then 3 copilots<500 hours
3*3=9 groups of copilots
9*3(Hugo is not eligible) = 27

p(Exactly 1 copilot has less than 500 hours) = 27/48 = 9/16

'Hugo is the pilot' is 1/16
'Exactly 1 copilot has less than 500 hours' is 9/16
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GMAT Club World Cup 2026 (Day 5): The cockpit crew for a long-haul 11 Jul 2026, 07:31
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For 3 reg pilots, each pilot can fly with any of the 2 of the copilots

3*15 = 45

For hugo

(3 2) = 3
Total valid crew: 45+3 = 48


Hugo is pilot 3/48
Which is 1/16

1 copilot has >500 hours

1 exp copilot and 1 non experience copilot

Both from 3

3*3 ,= 9

Deduct hugo from pilot

9*3 = 27

27/48 we get 9/16



Bunuel
The cockpit crew for a long-haul flight must consist of 1 pilot and 2 copilots, selected from an available pool of 4 pilots and 6 copilots. One of the pilots, Hugo, is only certified to serve as pilot if each of the two selected copilots has at least 500 hours of flight experience, a qualification held by 3 of the 6 available copilots. The remaining pilots can fly with any copilot. A cockpit crew will be selected at random from all possible crew combinations that meet these conditions.

The two columns in the table refer to two separate cases, each based on the same random selection from all valid cockpit crews. In the table, for Hugo is the pilot, select the probability that Hugo is the pilot on the selected cockpit crew. For Exactly 1 copilot has less than 500 hours, select the probability that exactly 1 of the 2 copilots on the selected cockpit crew has less than 500 hours. Make only two selections, one in each column.
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GMAT Club World Cup 2026 (Day 5): The cockpit crew for a long-haul 11 Jul 2026, 07:36
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Answer:
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GMAT Club World Cup 2026 (Day 5): The cockpit crew for a long-haul 11 Jul 2026, 07:45
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Total Valid Cases = Hugo + Not Hugo
= 1C1 * 3C2 + 3C1 * 6C2
= 3 + 45 = 48

P(H) = 3/48 =1/16

N(One pilot with less flying time) = 3C1 * 3C1 * 3C1 =27
So its P is 27/48 =9/16
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GMAT Club World Cup 2026 (Day 5): The cockpit crew for a long-haul 11 Jul 2026, 07:56
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6 copilots
3High experience and 3Low experience

With Hugo and 3 other pilots
Hugo can only fly with 2 H copilots. SO Hugo has 3 valid crews

Any of the other 3 pilots
Choosing 2 out of 6 copilots
6C2 = 15
For 3 pilots
3 x 15=45

column 1 :total valid crews
favourable crews=3
total crews=48
hugo is the pilot probability = 1/16

column 2: 1 high and 1 low, 9 ways
favourable crews = 3 x 9=27
probabilty = 27/48=9/16

So 1/16 and 9/16 is the answer
Bunuel
The cockpit crew for a long-haul flight must consist of 1 pilot and 2 copilots, selected from an available pool of 4 pilots and 6 copilots. One of the pilots, Hugo, is only certified to serve as pilot if each of the two selected copilots has at least 500 hours of flight experience, a qualification held by 3 of the 6 available copilots. The remaining pilots can fly with any copilot. A cockpit crew will be selected at random from all possible crew combinations that meet these conditions.

The two columns in the table refer to two separate cases, each based on the same random selection from all valid cockpit crews. In the table, for Hugo is the pilot, select the probability that Hugo is the pilot on the selected cockpit crew. For Exactly 1 copilot has less than 500 hours, select the probability that exactly 1 of the 2 copilots on the selected cockpit crew has less than 500 hours. Make only two selections, one in each column.
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GMAT Club World Cup 2026 (Day 5): The cockpit crew for a long-haul 11 Jul 2026, 11:24
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Hi Bunuel

Could you please review my submission. I wasn't awarded any kudos even though the response is right. Can you let me know what I am missing so that I can take care of it going forward.
chasing725


Hugo = Pilot ; Possible Combination of Copilot = 3
Hugo is not the pilot ; Possible combination of Copilot = 45

Total Possible Combination

Prob. of Hugo = 3/45+3 = 3/48 = 16

Exactly 1 = Total - Both Experience - Both not experienced

=48 - (18 + 3 ) = 27

27/48 = 9/16

Hugo = 1/6
Exactly 1 copilot = 9/16
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GMAT Club World Cup 2026 (Day 5): The cockpit crew for a long-haul 11 Jul 2026, 11:28
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You wrote Hugo = 1/6, whereas it should be 1/16
Also, you wrote the probability of Hugo = 3/45+3 = 3/48 = 1/16, but you wrote 16 only.

Probably that mismatch made a decision.
chasing725
Hi Bunuel

Could you please review my submission. I wasn't awarded any kudos even though the response is right. Can you let me know what I am missing so that I can take care of it going forward.

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GMAT Club World Cup 2026 (Day 5): The cockpit crew for a long-haul 11 Jul 2026, 11:41
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alamin8
You wrote Hugo = 1/6, whereas it should be 1/16
Also, you wrote the probability of Hugo = 3/45+3 = 3/48 = 1/16, but you wrote 16 only.

Probably that mismatch made a decision.

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Thanks for pointing out. I didn't realize the typo until now :cry:
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