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02 Jan 2021, 11:06
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Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
55%
(hard)
Question Stats:
66% (01:48) correct
34%
(02:14)
wrong
based on 301
sessions
History
Date
Time
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Not Attempted Yet
From the options below, which is the smallest number such that when multiplied by 100! is divisible by 3^50?
(A) 42
(B) 72
(C) 144
(D) 216
(E) 789
(A) 42
(B) 72
(C) 144
(D) 216
(E) 789
What is the least number that should be multiplied to 100! to make it perfectly divisible by 3^50?
(a) 144
(b) 72
(e) 108
(d) 216
(e) 789
(a) 144
(b) 72
(e) 108
(d) 216
(e) 789
Shadyshades
Joined: 02 Nov 2020
Last visit: 21 Apr 2026
Posts: 113
Given Kudos: 1,150
Location: India
Schools: Yale '20 (D)
GMAT 1: 220 Q2 V2
02 Jan 2021, 12:14
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(X * 100 !) / 3^50
Highest power of 3 in 100 ! is 48. How ? 100/3 = 33, 33/3=11, 11/3=3, 3/3=1
Total= 33+11+3+1= 48
so we need at least two 3s to divide 100! from 3^50.
Therefore, the correct option will be multiple of 9 (3*3)
Check the options with the smallest number -
a) 42 is not a multiple of 9. Eliminate it.
b) 72 is a multiple of 9. Mark the option and move on. No need to check other options because we are looking the smallest number. Other options are higher than option B.
Option B
Highest power of 3 in 100 ! is 48. How ? 100/3 = 33, 33/3=11, 11/3=3, 3/3=1
Total= 33+11+3+1= 48
so we need at least two 3s to divide 100! from 3^50.
Therefore, the correct option will be multiple of 9 (3*3)
Check the options with the smallest number -
a) 42 is not a multiple of 9. Eliminate it.
b) 72 is a multiple of 9. Mark the option and move on. No need to check other options because we are looking the smallest number. Other options are higher than option B.
Option B
General Discussion
02 Jan 2021, 11:53
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Considering 100!
Taking first all powers of single 3.
3,6,9,12...till 99. Thus one power of 3 will be 33.
Next considering multiples of 9 since we need to take extra powers of 3 for that - 11 multiples. Thus total 33+11=44.
Then taking power of 3 - 27,54,81 - another 3 taking total to 47.
Then power of 4 - only 1 - 81. total 48.
Thus we need 2 more for it to be divisible by 3^50.
Thus Answer is B. 72 (3^2*2^3)
Taking first all powers of single 3.
3,6,9,12...till 99. Thus one power of 3 will be 33.
Next considering multiples of 9 since we need to take extra powers of 3 for that - 11 multiples. Thus total 33+11=44.
Then taking power of 3 - 27,54,81 - another 3 taking total to 47.
Then power of 4 - only 1 - 81. total 48.
Thus we need 2 more for it to be divisible by 3^50.
Thus Answer is B. 72 (3^2*2^3)
