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C
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Difficulty:
95%
(hard)
Question Stats:
37% (02:16) correct
63%
(02:55)
wrong
based on 191
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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
M46-21
A. 18
B. 27
C. 30
D. 36
E. 54
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Bunuel
GMAT Club Official Explanation:
Hermione's cauldron starts with 27 beans, which is 3^3. Every 6 hours, Hermione's cauldron increases by 200%, meaning it multiplies by 3. So:
• After 6 hours the number of beans = 3^3 * 3 = 3^4
• After 12 hours the number of beans = 3^4 * 3 = 3^5
• After 18 hours the number of beans = 3^5 * 3 = 3^6
• After 24 hours the number of beans = 3^6 * 3 = 3^7
• After 30 hours the number of beans = 3^7 * 3 = 3^8
• ...
Ron’s cauldron starts with 729 beans, which is 3^6. Every 18 hours, Ron’s cauldron increases by 800%, meaning it multiplies by 9 or 3^2. So:
• After 18 hours the number of beans = 3^6 * 3^2 = 3^8
• After 36 hours the number of beans = 3^8 * 3^2 = 3^10
• ...
So, after 30 hours, the two cauldrons will, for the first time, contain the same number of beans: 3^8. Hermione’s beans reach 3^8 after 30 hours, while Ron’s beans remain at 3^8 after increasing at 18 hours.
Answer: C.
General Discussion
Archit3110
23 Dec 2025, 09:15
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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
start of class
H has 27 beans and R has 729
200% @6 hours and 800% 18 hours
200% is 3 times and 800 % is 9 times
noting down time wise increase
0 to 6 for H = 27 ; R 729
6 to 12 H = 27*3 :81 ; R = 729
12 to 18 ; H = 81*3 : 243 ; R = 729
18 to 24 ; H = 243*3 ;729 R = 729*9 ; 6561
24 to 30 H = 729*3 : 2187 R = 6561
30 to 36 H = 2187*3 6561 ; R = 6561
at 30 hours both R & H have same count of beans
OPTION C ; 30
A. 18
B. 27
C. 30
D. 36
E. 54
start of class
H has 27 beans and R has 729
200% @6 hours and 800% 18 hours
200% is 3 times and 800 % is 9 times
noting down time wise increase
0 to 6 for H = 27 ; R 729
6 to 12 H = 27*3 :81 ; R = 729
12 to 18 ; H = 81*3 : 243 ; R = 729
18 to 24 ; H = 243*3 ;729 R = 729*9 ; 6561
24 to 30 H = 729*3 : 2187 R = 6561
30 to 36 H = 2187*3 6561 ; R = 6561
at 30 hours both R & H have same count of beans
OPTION C ; 30
