12 Days of Christmas GMAT Competition 2025 - Day 7: At the start of

Hermione has 27 magic beans in the cauldron. Let it be denoted by H

Ron has 729 magic beans in the cauldron. Let it be denoted by R.

H =27 , increases by 200% , so the multiplying factor is 3, and this happens every 6 hours.

R = 729, increases by 800%, so the multiplying factor is 9, and this happens every 18 hours.

Let x denote the number of times the cycle of 6 occurs.

Let y denote the number of times the cycle of 18 occurs.

Let t be the total time taken.

x = (t/6) and y= (t/18)

We need to find the time “t”, when both the cauldrons has the same number of beans.

27*3^x = 729*9^y

Since, the entire equation is a factor of 3.

3^ (3+x) = 3^(6+2y)

Equating the powers, as the base is same.

(3+x) = (6+ 2y)

x = 3+2y

If y = 0, then x=3, t= 6*3 =18

If y= 1, then x =5, t = 6*5= 30

If y=2, then x = 7, t=42

If y=3, then x =9, t=54

So, among the options given, ONLY 18, 30, 54 QUALIFY.

t=0	t=6	t =12	t=18	t=24	t=27	t =30
H 27	81	243	729	729*3	729*3^2	729*3^3
R 729	729	729	6561	729*3^3	729*3^3	729*3^3

First time both the values are same is at t=30.

Out of curiosity:

since the question mentioned for the first time, which means there is a time by which it meets for the second time.

at t=54, x =9 = 3^9

y = 3

3^3 * 3^9 = 3^9 * 3^3.

For the FIRST TIME, they meet at time t=30

Option C

jkkamau

Joined: 25 May 2020

Last visit: 23 Apr 2026

Posts: 226

Own Kudos:

190

Given Kudos: 142

Location: Kenya

Schools: Haas '25

GMAT 1: 730 Q50 V46 Verified score

GPA: 3.5

Schools: Haas '25

GMAT 1: 730 Q50 V46 Verified score

Posts: 226

Kudos: 190

23 Dec 2025, 23:54

Kudos

Bookmarks

Hermione starts with 3^3 which triples (x3) in 6 hours while Ron starts with 3^6 which increases by 3^2 after 18 hours. After 18 hours Hermione's will have increased by 3^3x3x3x3= 3^9
After h hours the two will be same meaning
3^3+h/6=3^6+h/18
Equate the powers 3+h/6=6+h/9
h/6-h/9=3
h/18=3
h=54

Bunuel

Vaishbab

Joined: 29 Jan 2023

Last visit: 08 Mar 2026

Posts: 115

Own Kudos:

Given Kudos: 81

Location: India

Concentration: Strategy, Operations

Schools: Booth (Chicago)

Posts: 115

Kudos: 51

24 Dec 2025, 01:15

Kudos

Bookmarks

Answer is 54 hours.

Attachments

AISelect_20251224_021536_Samsung Notes.jpg [ 262.05 KiB | Viewed 351 times ]

AditiDeokar

Joined: 12 Jan 2025

Last visit: 21 Apr 2026

Posts: 87

Own Kudos:

[1]

Given Kudos: 298

Location: India

Concentration: Finance

Schools: NUS ESSEC MiM '26 ESSEC MiF '26 INSEAD MiM '26 ESADE Imperial ISB '26 ESADE HEC Sept '26 IE INSEAD Jan '26

GMAT Focus 1: 525 Q77 V77 DI74 Verified score

GPA: 3.5

Schools: NUS ESSEC MiM '26 ESSEC MiF '26 INSEAD MiM '26 ESADE Imperial ISB '26 ESADE HEC Sept '26 IE INSEAD Jan '26

GMAT Focus 1: 525 Q77 V77 DI74 Verified score

Posts: 87

Kudos: 21

[1]

24 Dec 2025, 01:25

Kudos

Bookmarks

The answer is 30 Hours. Choice C. Method to reach this : Hermione has 27 beans while Ron has 729 beans, at the end of 6 hours Hermione will have 100% of what she prevously had plus the 200% of the increase which is basically 27 x 3 = 81, multiply into 3 till hour 18( to reach 729), End of hour 18, Ron has 6561 beans (729 x 9(100% of og + 80% increase). Another 6 hours go by Hermione's beans increase to 2187, another 6 hours go by and hermione's beans are now 6561, same as Rons, this is hour 30, Hour 36 is when Ron's beans icrease by 800%, therefore the answer for when they first have the same beans is 30.

gchandana

Joined: 16 May 2024

Last visit: 23 Apr 2026

Posts: 192

Own Kudos:

141

[1]

Given Kudos: 170

Location: India

Products:

Posts: 192

Kudos: 141

[1]

24 Dec 2025, 01:39

Kudos

Bookmarks

Note: $27 = 3^3, 729 = 3^6$

Now, in 18 hrs, beans in Ron's cauldron become $729*9 = 3^8$
In the same 18 hrs, beans in Hermoinie's cauldron become $27*3*3*3 = 3^6$. To reach $3^8$, we need 12 more hours, which is a total of 30 hours (beans in Ron's cauldron don't change in these 12 hours).

So in 30 hours, beans in both their cauldrons are the same for the first time.
Option C.

Bunuel

remdelectus

Joined: 01 Sep 2025

Last visit: 23 Apr 2026

Posts: 58

Own Kudos:

Given Kudos: 3

Posts: 58

Kudos: 48

24 Dec 2025, 02:13

Kudos

Bookmarks

27 beans
every 6 hrs=200% increase beans
x intervals of 6hrs
hermione beans=27X3^x
Ron's
729 beans
every 18hrs=800% increase
y intervals of 18 hrs,
Rons beans=729X9^y

27X3^x=729X9^y
27=3^3
729=3^6
9=3^2
3^3X3^x=3^6X(3^2)^y
3^(x+3)=3^(6+2y)
x+3=6+2y
x=2y+3
herm intervals=x steps of 6 hrs=6x hrs
ron intervals=y steps of 18 hrs=18y hrs
6x=18y
sub x=2y+3
6(2y+3)=18y
12y+18=18y
18=6y
y=3
n=2(3)+3=9
total time 6x=6X9=54 hrs

msignatius

Joined: 28 Aug 2025

Last visit: 09 Apr 2026

Posts: 131

Own Kudos:

[1]

Given Kudos: 31

Location: India

Concentration: Strategy, Marketing

Schools: ISB '27 NUS '26 INSEAD Jan '26 (S) IESE '26 (D) HEC (S) IMD ESADE'26 Judge '26 LBS '27

GMAT Focus 1: 705 Q86 V85 DI84 Verified score

GPA: 3.5

WE:Marketing (Consulting)

Products:

Schools: ISB '27 NUS '26 INSEAD Jan '26 (S) IESE '26 (D) HEC (S) IMD ESADE'26 Judge '26 LBS '27

GMAT Focus 1: 705 Q86 V85 DI84 Verified score

Posts: 131

Kudos: 98

[1]

24 Dec 2025, 02:16

Kudos

Bookmarks

So I miss-clicked on this one, annoyingly, D instead of Cby accidently

Anyway, here goes my attempt to flex my Harry Potter obsession onto the GMATClub platform:

Firstly, thank you for recognizing us Millennial/Gen-Z cusp oldies of this forum by referencing Harry Potter, but any real potterhead will know that there's no way Hermione has more magic beans than Ron

Okay, so we're in Severus Snape's class, somewhere down in the dungeon, and our favorite potionmaster seems to have an affinity with the table of 3. That's the first thing you muggles should recognize in this question

27 = 3^3 and 729 = 3^6.

The second thing we notice is that there's 'increasio-twohundredo' spell being put on the beans, causing them to increase by "200 percent". It's an "increase of 200 percent", so it's essentially a tripling. An increase of 100% is doubling, so we know that Hermione's adding another power to her 3 every 6 hours.

Ron, of course, by virtue of him being not half as good a wizard as Hermione, won't see a 'tripling' every 3 hours, but every 18 hours, he'll sees 800% or a 9 times increase - which just means an increase of 2 powers - 3*3 - to his bean-count. Pretty Ron-like, eh, always being the late bloomer, but blooming nonetheless.

Also, remember, we're looking for the first time they both have the same number of magic beans - that might play in as well.

So, here's the progression. Accio table!

Hours	6	12	18	24	30
Ron (3^6)			3^8
Hermione (3^3)	3^4	3^5	3^6	3^7	3^8

The correct answer is 30 hours (C), because that's when Hermione first matches Ron, as Ron'll stay where he is until the 36th hour is complete - so the framing of the sentence did come into play. If you don't account for that, you'll end up at 3^9 at hour 36 for Hermione, and Ron'll be at 3^10, and then only at hour 54 will you be at 3^12 for both.

Expecto Kudos-ium

Bunuel

Gmat860sanskar

Joined: 05 May 2023

Last visit: 23 Apr 2026

Posts: 212

Own Kudos:

113

[1]

Given Kudos: 79

Schools: ISB '26

GMAT Focus 1: 605 Q82 V78 DI80 Verified score

Products:

Schools: ISB '26

GMAT Focus 1: 605 Q82 V78 DI80 Verified score

Posts: 212

Kudos: 113

[1]

24 Dec 2025, 02:43

Kudos

Bookmarks

Bunuel

This is really interesting question because it's not a continuous growth type of question but in this question growth happen instantly once they reach the time interval.

So Hermione have 27 beans, ad it will increase 200 percent every 6 hrs, which means 3 times.
and similarly Ron's bean will increase 800 percent every 18 hours, which means 9 times

Ok, so bigger number is 18 hours (among 6 & 18) so we will see the growth number at every time interval and see if Hermione can catch it until Ron's number jump again after 18 hours

Ron's bean number at start = 729

can Hermione catch this number before 18th hour ?

Let's check it : 27 * (3)^x/6 = 729

x =18 (ok so Hermione can't catch Ron because at 18 hour Ron's number will increase by 9 times)

let's see if Hermione can catch it between 18 - 36 hour

27 * (3)^x/6 = 729 * 9

x = 30

Yaa we got our answer; our answer is C

Rahilgaur

Joined: 24 Jun 2024

Last visit: 26 Jan 2026

Posts: 162

Own Kudos:

125

Given Kudos: 47

GMAT Focus 1: 575 Q81 V82 DI72 Verified score

Products:

GMAT Focus 1: 575 Q81 V82 DI72 Verified score

Posts: 162

Kudos: 125

24 Dec 2025, 03:33

Kudos

Bookmarks

At the start of Potions class, Hermione and Ron are each given a magical cauldron. Hermione’s cauldron contains 27 magic beans, and Ron’s contains 729. At the end of every 6 hours, the number of beans in Hermione’s cauldron instantly increases by 200 percent, and at the end of every 18 hours, the number of beans in Ron’s cauldron instantly increases by 800 percent. If no beans are taken from either cauldron, after how many hours from the start of the class will the two cauldrons first contain the same number of beans?

A. 18
B. 27
C. 30
D. 36
E. 54

At the end of every t hours magic beans for hermione becomes = 27*(3)^(t/6) = 3 ^(t/6+3) ----{200% percent is equal to 3 times...........................1

Similarly, Ron will have = 729 *(9)^(t/18)= 3 ^(2*3 +2t/18)= 3^(6+t/9)...................2

On comparing power of both ...

t/6+3 = 6 +t/9

t(9-6)/54 = 3

t = 54*3/3 = 54 Answer E

linnet

Joined: 11 Dec 2025

Last visit: 22 Jan 2026

Posts: 81

Own Kudos:

Given Kudos: 1

Posts: 81

Kudos: 42

24 Dec 2025, 03:34

Kudos

Bookmarks

We write the amount of beans i powers
Herm- 27= 3^3
Ron- 729= 3^6
Growth: Herm; +200%= x 3 every 6 hrs
Ron ; +800 = x 9 or 3^2 every 18hours
Amount after X hours
Herm= 3^3 x 3^X/6= 3^3+3^3+X/6
Ron= 3^6 x 3^2(X/18)= 3^6+X/9
Set opponents equal
3+X/6=6+X/9 multiply each by 18 (LCM of 6&9) = 54+3X= 108+2X
3X-2X=108-54
X= 54

The final answer is 54

raffaeleprio

Joined: 15 Nov 2020

Last visit: 13 Apr 2026

Posts: 56

Own Kudos:

Given Kudos: 1

Location: Italy

GPA: 3.71

Posts: 56

Kudos: 59

24 Dec 2025, 04:12

Kudos

Bookmarks

Writing the evolution of the number of beans: (200% increase = *3 and 800% increase = *9)
Let n be the number of hours:

H = 27*3^[n/6]
R= 729*9^[n/18]

Imposing H=R and recalling that 27^2 = 729 we get 3^[n/6] = 3^[n/9 + 3]

==> n/6 = n/9 + 3 ==> n = 3/(1/6-1/9) = 54

IMO E!

Lizaza

Joined: 16 Jan 2021

Last visit: 29 Mar 2026

Posts: 240

Own Kudos:

282

[1]

Given Kudos: 7

GMAT 1: 710 Q47 V40 Verified score

Posts: 240

Kudos: 282

[1]

24 Dec 2025, 05:20

Kudos

Bookmarks

The original equations are: $h=27$ and $r=729=27h$
Every 6 hours, h is multiplied by 3 (which means growing by 200%). Therefore, for h to equal r, there needs to be 3 times 6 hours, since $ r=27h=h*3*3*3.$

However, over 1 hours, Ron's beans will increase ninefold (meaning +800%), so it will become $r_1=9r=27*9h$, and sadly Hermione won't be able to reach him that quickly.
But if she waits for 12 hours longer, her cauldron will have $h_1=27h*3*3=9*27h,$ while Ron's cauldron will still remain unchanged.

Therefore, the total time needed is $18+12=30$ hours, and the answer is C.

kapoora10

Joined: 13 Jul 2024

Last visit: 12 Apr 2026

Posts: 109

Own Kudos:

[1]

Given Kudos: 7

Location: India

Concentration: Real Estate, Sustainability

GMAT Focus 1: 645 Q88 V74 DI84 Verified score

GMAT Focus 2: 655 Q85 V83 DI80 Verified score

GPA: 8.03

WE:Corporate Finance (Finance: Investment Management)

Products:

GMAT Focus 2: 655 Q85 V83 DI80 Verified score

Posts: 109

Kudos: 95

[1]

24 Dec 2025, 05:33

Kudos

Bookmarks

Using the given data:
growth for Hermoine = 27 * 3^([t/6]) where [t/6] is the integer just under t/6
growth for Ron = 729 * 9^ ([t/18]) where [t/18] is the integer just under t/18
As these are discrete and Hermione's rate is less, check each option for both one by one.
upon checking when t=30 => H(30) = 25 * 3^5 = 6561 and R(30) = 729 *9 = 6561.

Hence, Answer = 30 => C

tanvi0915

Joined: 01 Oct 2025

Last visit: 22 Apr 2026

Posts: 30

Own Kudos:

[1]

Given Kudos: 6

Posts: 30

Kudos: 21

[1]

24 Dec 2025, 06:00

Kudos

Bookmarks

I think the answer is C . At the begining Hermoine has 27 beans and Ron has 729 beans.
After 6 hours H's beans increase by 200% that is it becomes 3 times more in total
Hours. H R
6 27*3=81 729
12 81*3= 243 729
18 243 *3 = 729 729 * 9
24 729 * 3 729 * 9
30 729 * 3 * 3 729 * 9

Thus at 30 hours both Ron and Hermoine have same number of beans

gemministorm

Joined: 26 May 2025

Last visit: 22 Apr 2026

Posts: 143

Own Kudos:

110

Given Kudos: 57

GMAT Focus 1: 565 Q82 V79 DI73 Verified score

GMAT Focus 2: 605 Q84 V83 DI73 Verified score

Posts: 143

Kudos: 110

24 Dec 2025, 06:43

Kudos

Bookmarks

H (27) and R(729)
acc to question: H -> 200% increase -> triple every 6 hours, so after every t hours 27*3^t/6.
R -> 800% increase -> 9 times every 18 hours, so after every t hours 729*9^t/18.
equating both 27*3^t/6 = 729*9^t/18 -> t/6 = t/9 + 3 -> t = 54

Reon

Joined: 16 Sep 2025

Last visit: 28 Mar 2026

Posts: 134

Own Kudos:

121

[1]

Given Kudos: 4

Posts: 134

Kudos: 121

[1]

24 Dec 2025, 06:45

Kudos

Bookmarks

At the start of Potions class, Hermione and Ron are each given a magical cauldron. Hermione’s cauldron contains 27 magic beans, and Ron’s contains 729. At the end of every 6 hours, the number of beans in Hermione’s cauldron instantly increases by 200 percent, and at the end of every 18 hours, the number of beans in Ron’s cauldron instantly increases by 800 percent. If no beans are taken from either cauldron, after how many hours from the start of the class will the two cauldrons first contain the same number of beans?

Hermione cauldron:
27 magic beans
In 6 hours: 200% increase

Rom cauldron:
729 magic beans
In 18 hours: 800% increase

Hermoines magic beans triple every 6 hours and roms magic beans becomes 9 times every 18th hour
Time..... Hermione ......Ron
Start......27.............729
6 hours ....27*3=81............729
12 hours...81*3=243........729
18 hours...243*3=729.......729*9=6561
24 hours...729*3=2187.....6561
30 hours....2187*3=6561......6561

The two cauldrons first contain the same number of beans at 30 hours.

adityaprateek15

Joined: 26 May 2023

Last visit: 23 Apr 2026

Posts: 346

Own Kudos:

170

Given Kudos: 323

Location: India

Schools: Ross '26 Tepper '26 McCombs '26

GPA: 2.7

Products:

Schools: Ross '26 Tepper '26 McCombs '26

Posts: 346

Kudos: 170

24 Dec 2025, 06:56

Kudos

Bookmarks

H: 27 = 3^3

After n intervals, H = 3^3*3^n = 3^(3+n)

R: 729 = 9^3 = 3^6

After m intervals, 3^6*3^2m = 3^(6+2m)

To find: 6n

We have, 3^(3+n)=3^(6+2m)

3+n=6+2m

n=3+2m

Also, 6n=18m => n=3m

3m=3+2m => m=3 and n=9

6n = 54

Bunuel

whollyshiv

Joined: 11 Aug 2024

Last visit: 22 Apr 2026

Posts: 22

Own Kudos:

Given Kudos: 8

GMAT Focus 1: 575 Q78 V82 DI75 Verified score

Posts: 22

Kudos: 16

24 Dec 2025, 07:02

Kudos

Bookmarks

Let's assume it takes 't' hours from the start of the class for the two cauldrons to contain the same amount of beans

For Hermoine, Initial amount of beans x (growth factor)^growth period = 27 x 3^t/6 (200% increase is equal to 3x increase)
For Ron, the final amount will be: 729 x 9^t/18

Since the amount will be same at the end of 't' hours
=> (3)^3 x 3^t/6 = (3)^6 x (3)^2t/18
=> 3^t/6 = 3^3+t/9
=> t/6 = 3+t/9
=> t = 27x2 = 54

bhanu29

Joined: 02 Oct 2024

Last visit: 22 Apr 2026

Posts: 358

Own Kudos:

270

[1]

Given Kudos: 263

Location: India

Schools: Anderson '27 Booth '27 Foster '27 Haas '27 Kellogg '27 Kellogg Mashall '27 McCombs '27 Ross '27 Scheller '27 Tepper '27 Yale '27 Sloan (MIT) Stanford '27

GMAT Focus 1: 675 Q87 V85 DI79 Verified score

GMAT Focus 2: 715 Q87 V84 DI86 Verified score

GPA: 9.11

WE:Engineering (Technology)

Products:

Schools: Anderson '27 Booth '27 Foster '27 Haas '27 Kellogg '27 Kellogg Mashall '27 McCombs '27 Ross '27 Scheller '27 Tepper '27 Yale '27 Sloan (MIT) Stanford '27

GMAT Focus 2: 715 Q87 V84 DI86 Verified score

Posts: 358

Kudos: 270

[1]

24 Dec 2025, 07:04

Kudos

Bookmarks

Bunuel

So H's beans triples every 6 hours
R's beans becomes 9 times every 18 hours

	H	R
6	81	729
12	243	729
18	729	6561
24	2187	6561
30	6561	6561

at 30 h
Correct Answer: C

sanjitscorps18

Joined: 26 Jan 2019

Last visit: 03 Mar 2026

Posts: 723

Own Kudos:

740

[1]

Given Kudos: 130

Location: India

Schools: IMD'26

Products:

Schools: IMD'26

Posts: 723

Kudos: 740

[1]

24 Dec 2025, 07:16

Kudos

Bookmarks

Hermione = 27
Ron = 729

Hermione's beans increase by 200% every 6 hours.
Essentially the number of beans multiply by 3 every 6 hours
In first 6 hours the beans will be = 27(1+200/100) = 27*3 = 3^4
In 12 hours = 3^5
In 18 hours = 3^6
In 24 hours = 3^7
In 30 hours = 3^8
In 36 hours = 3^9

Ron's beans increase by 800% every 18 hours
Essentially the beans multiply by 9 every 18 hours
In first 18 hours, the beans will be 729 * (1+800/100) = 729 * 9 = 729 * 3^2 = 3^8
In 36 hours = 3^8 * 9 = 3^10

Essentially at 30 hours both the cauldrons contained equal beans

Option C

Bunuel