Latest self Aptitude Question SOLUTION: what is the highest power of 3 available in the expression 58!-38! 1.17 2.18 3.19 4.none

• Placement Papers
• /
• self

self Question Papers:

(#M40008998) SELF question Keep an EYE

what is the highest power of 3 available in the expression 58!-38!
1.17
2.18
3.19
4.none

sahithi (12 years ago)

Unsolved Read Solution (3)

Is this Puzzle helpful?   (19)   (10) Submit Your Solution

Read Solution (3) :

Pargat Pal Singh  (12 years ago)

1.17

58!-38!= 38!*( 58!/38! -1)

Here 38! is multiple of 3 whereas ( 58!/38! -1) is not a multiple of 3.
Now 38! is having 17 as highest power of 3.
3,6,12,15,21,24,30,33..1 power each......... total 8
9,18,36 ----- 2 powers each.................. total 6
27 ........... 3 powers...........................3

Sum total =17

Is this solution Helpfull? Yes (9) | No (4)  

Flower  (12 years ago)

Answer: 17

highest power of 3 available in above expression is max number of 3s in 38! = 17

Is this solution Helpfull? Yes (7) | No (6)  

Vignesh  (12 years ago)

4. None

58!-38! = 20!

As per the given Option,

3^17 = 129140163(Carry 9 digits)
3^18 = 387420289(Carry 9 digits)
3^19 = 1162261467(Carry 10 digits)

20! = 20*19*18*17*16*15*......*3*2*1

20*19*18*17*16*15*14 = 390700800(Carry 9 digits)
20*19*18*17*16*15*14*13 = 5079110400(Carry 10 digits)

So, No maximum power of 3 as per the Options in given expression.

Answer = Option 4.None

Is this solution Helpfull? Yes | No (15)  

Please Login to Read Solution.