12 Days of Christmas GMAT Competition 2025 - Day 10: A bakery sells

officiisestyad

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26 Dec 2025, 22:01

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Total combination of Cookies: 4x3x2 = 24
Atleast 2 features = all 3 features + any 2 features
All 3 features: Lemon + Star + Large = 1 cookie
Any 2 :
Lemon + Star = 1 cookie (if we select small)
Star + Large = 3 cookies (if we select any other flavor)
Leamon + Large = 2 cookies (if we select any other shape Heart or Circle)

So total probability: (1+1+3+2)/ 24 = 7/24

forestmayank

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26 Dec 2025, 22:35

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We have:
4 Flavors
3 Shapes
2 sizes

Total possibilities of different type of chocolate with equal number = 4 x 3 x 2 = 24 combinations
Nina wants Large, star, lemon OR at least 2 of these

She can have 1 combination with all three

Other different combinations she can have are:
(Large + star) x 3 remaining flavor = 3 combination

(Large + Lemon) x 2 remaining shapes = 2 combinations

(Lemon + star) x 1 remaining size = 1 combination

Total she can have 1 + 3 + 2 + 1 = 7 combination out of 24
Hence, probability of getting what she wants = 7/24

Answer Option C

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26 Dec 2025, 22:47

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Now first we need to final total possible events possible
Lemon , Choc, Vanilla, strawberry ---1
Star, Heart, circle ----2
Small and large ----3

Now combination between 1,2,3: with lemon flavor we can have 6 combination, similarly for other flavours
Hence total possible event is 24

Now Possible cases with Lemon, star and large we need atleast 2 to match or 3
so
with lemon and large we can have 2 different combination
with lemon and star we can have 1 different combination
and with Star and large we have 3 different combination so in total 6

and for 3 to match exactly we will have only 1 combination

Hence total combination possible is 7

Hence probability would be 7/24

Hence answer (C)

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26 Dec 2025, 23:24

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This involves a bit of critical thinking - and paying attention to key phrases / words. Good thing this competition has drilled that into my head better than anyone else could

We have four flavors of cookies: Lemon, chocolate, vanilla, strawberry (darn.. where can I get these?)

We have three shapes: Star, heart, and circle

We have two sizes: Small and large.

Now, the bakery has an equal number of cookies of each possible flavor-shape-size combination. This just means, the bakery can do any possible combination, and there's no weightage to the quantities.

Nina wants a large, star-shaped, lemon cookie.

Her friend wants to play guess-the-cookie. So, s/he's pick one from the display, and we need to find the probability that the cookie picked has AT LEAST two of the three features Nina wants.

Cool, let's go:

At least 2/3 means, 3/3 is one of the options. The probability of that happening will simply be: Lemon of the four flavors (1/4) * Star of the three shapes (1/3) * Large of the two sizes (1/2); that's 1/24.

Now, we can go on to the exact 2 of 3 three flavors. The first combination we can look at is: Large and Star-Shaped. For large, the probability is 1/2, and for Star-Shaped, it's 1/3. But here's the trick: If the flavor is still picked as lemon, that would overlap with the combination of 3/3 we've already accounted for above. So, we multiply these with any of the remaining three flavors - or 3/4.

Hence, 1/2 * 1/3 * 3/4 = 3/24, is your probability of the Large & Star-Shaped combination.

Now, remember, each combination will have a different probability, as each flavor/shape/size has different number of options.

For Large & Lemon-Cookies, the probability will be 1/2 * 1/4 (for Lemon as the flower) * 2/3 (For all sizes except star-shaped). We now get 2/24.

And for the last of these combinations, Star-Shaped and Lemon, we have 1/3 * 1/4 * 1/2 (as we're avoiding the large-size) = 1/24.

Add these 4 probabilities: 1/24 + 3/24 + 2/24 + 1/24 = 7/24, and you have your answer, C.

Bunuel

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26 Dec 2025, 23:53

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Bunuel

Cookies are of 4 flavours = Lemon, Chocolate, Vanilla and Strawberry.

Cookies are of 3 Shapes = Star, Heart and Circle.

Cookies are of 2 Sizes = Small and Large.

Total possibilities = 4*3*2 = 24

Nina wants a LARGE, STAR SHAPED , LEMON COOKIE, probability of atleast 2 = ?

= Either two or More than two.

Let the sequence be Large , Star and Lemon, that’s Size (2), Shape (3), Flavour (4)

Case 1: ( Yes, Yes, No)

1*1*3 (without lemon we have 3 flavours) = 3

Case 2: ( Yes, No, Yes)

1* 2(without star we have 2 shapes) * 1 = 2

Case 3: (No, Yes, Yes)

1*1*1 = 1

Case 4: ( Yes, Yes, Yes)

1*1*1 = 1

Total cases = 3+2+1+1 = 7

Probability = 7/24

Option C

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27 Dec 2025, 00:54

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Total possible combinations = 4*3*2 = 24

Now it says that at least two of the three features Nina wants, so there are two cases: exactly two features and exactly three features.
Case 1: Exactly 2 features
Large and star-shaped but not lemon = 3 (1 for each of the other flavours)
Large and lemon but not star-shaped = 2 (large + lemon + heart or circle)
Star-shaped and lemon but not large = 1 (star + lemon + small)

Case 2: Exactly 3 features
Large + star + lemon = 1

Total = 3+2+1+1 = 7

So 7/24, option C.

Bunuel

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27 Dec 2025, 01:33

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We have 4 flavours, 3 shapes and 2 sizes meaning total combinations equals 4x3x2= 24
Nina wants a large, star-shaped lemon cake
We want a cake that has at least two of these features meaning 2 or 3 features
A cake with all the three features =1
A cake with lemon, star and large is =1
A large, Lemon cake can either be heart or circle= 2
A large, star shaped cake that is not lemon can be chocolate vanilla and strawberry=3
Total 1+1+2+3= 7
So probability = 7/24

Bunuel

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27 Dec 2025, 01:35

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Probability AT LEAST 2/3 features of Nina want:
1. Flavor: lemon, choco, vanilla, strawberry => probability desired: 1/4; undesired: 3/4
2. Shapes: probability desired: 1/3, undesired: 2/3
3. Size: desired: 1/2, undesired: 1/2
Probability(AT LEAST 2/3): 1 - [P(ALL undesired) + P(ONLY 1 desired)] = 1 - (3/4*2/3*1/2 + 1/4*2/3*1/2 + 3/4*1/3*1/2 + 3/4*2/3*1/2) = 1 - 17/24 = 7/24. C

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27 Dec 2025, 02:07

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Only one cookie has all three features.

Cookies having only two of the three features would be

Cookies which are large, star shaped, but not lemon -3
Cookies which are small, star shaped and lemon- 1
Cookies which are large, lemon and not star shaped -2

Therefore, the numerator is 1+3+1+2=7. Total possibilities are 4*3*2=24

Hence, 7/24

Option C imo

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27 Dec 2025, 02:16

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There are total 4*3*2=24 combination of flavor-shape-size
Since the bakery has equal number of cookies of each combination, we dont have to worry about total cookies to calculate possibility

The number of choices that satisfies the friend's pick = 3+2+1+1 =7
Probability = 7/24

Answer: C

Bunuel

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27 Dec 2025, 02:57

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Total possible cookies = 4 flavors x 3 shapes x 2 sizes = 24
Nina features= large, starshaped and lemon ; want at least 2 of these
All 3 features= 1
Large & star , not lemon- other flavors =3
Large and lemon, not star - other shapes 2 = 2
Star and lemon, not large - only other size small= 1
Total 1+3+2+1=7
Probability is 7/24
Final Answer : 7/24

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27 Dec 2025, 03:06

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assuming 1 for each:
lem | choc | van | stra
s/l | s/l | s/l | s/l
star 1 1 1 1 1 1 1 1
heart 1 1 1 1 1 1 1 1
circle 1 1 1 1 1 1 1 1
total -> 24
Nina: lemon + star large
P(X at-least 2) = P(x = 2) + P(X = 3).
P(X=2) = (lemon + star + not large) + (not lemon + star + large) + (lemon + star + not large)/24 = 1 + 3 + 2 / 24 = 6/24
P(X=3) = 1/24
P(X at-least 2) = 7/24

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27 Dec 2025, 03:13

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1. Calculate the combination possibility

The combination consists of
Flavor: 4
Shapes: 3
Sized: 2

Total possibility: 4*3*2 = 24

2. Calculate the desired outcome

- Nina wants a LARGE, STAR-shaped, LEMON cookie
- Picked at least 2 out of 3 features -> calculate total possible features

2 features: 3+2+1=6

large-star (3)
- w/ choco
- w/ vanilla
- w/ strawberry

large-lemon (2)
- w/ heart
- w/ circle

star-lemon (1)
- w/ small

3 features: 1
large-star-lemon

- total desired outcome: 6+1=7

3. Calculate the probability

P= total desired outcome / total possible outcome = 7/24 (C)

Bunuel

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27 Dec 2025, 03:30

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We first need to determine the total number of cookie combinations possible and identify how many of those combinations satisfy the at-least two features condition.

Calculating the Total Combinations:
The bakery offers combinations based on three categories:
Flavors (4): Lemon, Chocolate, Vanilla, Strawberry
Shapes (3): Star, Heart, Circle
Sizes (2): Small, Large
Since there is an equal number of each combination, the total number of unique types is:4 x 3 x 2 = 24
total combinations: 24

Defining the Target Features:
Nina wants: Large (Size) Star-shaped (Shape) Lemon (Flavor)3.
Lets identify combinations with at-least two features->
We need to count combinations that have exactly two matching features and the one combination that has all three.
Case 1: Exactly 2 Features
Large + Star (but not Lemon): There are 3 non-lemon flavors (Chocolate, Vanilla, Strawberry) has 3 combinations
Large + Lemon (but not Star): There are 2 non-star shapes (Heart, Circle) has 2 combinations
Star + Lemon (but not Large): There is 1 non-large size (Small). has 1 combination

Case 2: Exactly 3 Features :
Large + Star + Lemon: This is Nina's specific choice has 1 combination

Now, calculating the Probability:
Adding the successful combinations together: 3 + 2 + 1 + 1 = 7 (favorable outcomes}
The probability is the number of favorable outcomes over the total number of outcomes: 7/24.

Hence answer IMO C.

Bunuel