Find the maximum value of n such 157!is perfectly divisible
1. by 12^n Answer A 77 B 76 C 75 D 78
2. 18^n Answer A37 B 38 C 39 D 40
1. by 12^n Answer A 77 B 76 C 75 D 78
2. 18^n Answer A37 B 38 C 39 D 40
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Number Systems
Source: Beat The GMAT — Problem Solving |
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theCodeToGMAT
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Sukhman, as advised by Experts, please post ONLY ONE question per thread; this is required to avoid any confusion that may creep in while discussing multiple questions in a same thread.
Q1:
12 = 2 x 2 x 3
Lets find out the power of "3" in 157!
157/3 = 52
52/3 = 17
17/3 = 5
5/3 = 1
So,52+17+5+1 = 75
We know that using the same method if we calculate the value for power of "2" then it would be much greater than 75.
So, we can conclude that we need n = 75 to have prefect divisible
Q1:
12 = 2 x 2 x 3
Lets find out the power of "3" in 157!
157/3 = 52
52/3 = 17
17/3 = 5
5/3 = 1
So,52+17+5+1 = 75
We know that using the same method if we calculate the value for power of "2" then it would be much greater than 75.
So, we can conclude that we need n = 75 to have prefect divisible
R A H U L
-
theCodeToGMAT
- Legendary Member
- Posts: 1556
- Thanked: 448 times
- GMAT Score:650
Q2:
18 = 3 x 3 x 2
Lets find out the power of "3" in 157!
157/3 = 52
52/3 = 17
17/3 = 5
5/3 = 1
So,52+17+5+1 = 75
We know that using the same method if we calculate the value for power of "2" then it would be much greater than 75.
Now, we know that 3^75 would be in numerator. So, we would need n=37
If we take n=38 then the situation will become 3^75/3^76
So, 37
18 = 3 x 3 x 2
Lets find out the power of "3" in 157!
157/3 = 52
52/3 = 17
17/3 = 5
5/3 = 1
So,52+17+5+1 = 75
We know that using the same method if we calculate the value for power of "2" then it would be much greater than 75.
Now, we know that 3^75 would be in numerator. So, we would need n=37
If we take n=38 then the situation will become 3^75/3^76
So, 37
R A H U L
