Number Properties

i feel some info is missing on P, not sure though!

IMO E.

sharmishtha_goel wrote:IMO E.

How ?

Aman verma wrote:

sharmishtha_goel wrote:IMO E.

How ?

for 50! , n = 47
48! , n = 46
47! , n = 42
46! , n = 42


If we take the factorial of a number greater than 51 n > 47
For a number less than 46 , n < 42

Not able to follow, can u pls explain in detail

GmatKiss wrote:Not able to follow, can u pls explain in detail

Now the highest power of 2 that can exactly divide 50! is 47, hence n=47,
Similarly the highest power of 2 that can exactly divide 49! & 48! is 46,
the the highest power of 2 that can exactly divide 47! & 46! is 42
Now if we take the factorial of a number greater than 51, then n > 47
For a number less than 46 ,then n < 42.Hence OA[spoiler]e)[/spoiler]

I will appreciate if anybody could suggest a better approach.

How p is considered to be 50, 49 and so on!

Aman verma wrote:

GmatKiss wrote:Not able to follow, can u pls explain in detail

Now the highest power of 2 that can exactly divide 50! is 47, hence n=47,
Similarly the highest power of 2 that can exactly divide 49! & 48! is 46,
the the highest power of 2 that can exactly divide 47! & 46! is 42
Now if we take the factorial of a number greater than 51, then n > 47
For a number less than 46 ,then n < 42.Hence OA[spoiler]e)[/spoiler]

I will appreciate if anybody could suggest a better approach.

HI,

This approach is the simplest ....i will elaborate so that you can understand the logic behind it.

10! = 1.2.3.4.5.6.7.8.9.10
To calculate the highest power of 2 that can divide 10! , first count the number or even numbers.
10/2 = 5 , i.e. 2^5 completely divides 10!
Notice that of the 5 even numbers ( 2 4 6 8 10) 4 and 8 have more than 1 power of 2.
To calculate the highest power of 2^2 i.e 4
10 / 4 = 2 (quotient only)
To calculate the highest power of 2^3 i.e 8
10 / 8 = 1 .
Adding up 5 + 2 + 1 = 8 i.e. 2^8 divides 10! completely giving you an odd quotient or you can say that the highest power of 2 in factorial 10 is 8 .
cross check : 1.2.3.4.5.6.7.8.9.10
1.2.3.2^2.5.2.3.7.2^3.9.2.5
1.2^(1+2+1+3+1).3.5.3.7.9.5
1.2^8.3.5.3.7.9.5

Hope that helps.