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If (10!)/(2y) is an odd integer, what is y?

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If (10!)/(2y) is an odd integer, what is y? [#permalink]

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New post 03 Oct 2015, 02:47
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If \(\frac{10!}{2^y}\) is an odd integer, what is y?

A. 5
B. 6
C. 7
D. 8
E. 10
[Reveal] Spoiler: OA

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Re: If (10!)/(2y) is an odd integer, what is y? [#permalink]

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New post 03 Oct 2015, 03:30
reto wrote:
If (10!)/(2y) is an odd integer, what is y?

A. 5
B. 6
C. 7
D. 8
E. 10


reto, check the question.

10!/16 will still give you an even integer. 10! has 2^8 in it and for obtaining an odd integer when you divide 10! by another integer, you need to cancel out all 8 2s.

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Re: If (10!)/(2y) is an odd integer, what is y? [#permalink]

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New post 03 Oct 2015, 03:51
Engr2012 wrote:
reto wrote:
If (10!)/(2y) is an odd integer, what is y?

A. 5
B. 6
C. 7
D. 8
E. 10


reto, check the question.

10!/16 will still give you an even integer. 10! has 2^8 in it and for obtaining an odd integer when you divide 10! by another integer, you need to cancel out all 8 2s.


Thanks it's done. You are very attentive!
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Re: If (10!)/(2y) is an odd integer, what is y? [#permalink]

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New post 03 Oct 2015, 04:34
reto wrote:
If \(\frac{10!}{2^y}\) is an odd integer, what is y?

A. 5
B. 6
C. 7
D. 8
E. 10


10! = 1*2*3*4*5*6*7*8*9*10

For calculating the power of 2 in 10!

\(2*4*6*8*10 have 2^1*2^2*2^1*2^3*2^1 = 2^8\)

i.e. \(10! = 2^8*Odd Numbers\)

Hence, 10!/2^8 will be an Odd Integer

Answer: option D
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Re: If (10!)/(2y) is an odd integer, what is y? [#permalink]

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New post 11 Dec 2015, 19:11
A odd number is one that does not have 2 as its one of the prime factor

10! has a total of 8 factors of 2

So, we need to remove all these 8 factors to make the number odd

If we remove < 8 2 factors, the number will be even, and > 8 => number will not be an integer

Ans. D

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Re: If (10!)/(2y) is an odd integer, what is y? [#permalink]

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New post 26 Aug 2017, 08:44
The formula for finding the number of powers of a prime number p, in the n! is
n/p+n/p^2+n/p^3 ... till p^x≤n (https://gmatclub.com/forum/math-number- ... 88376.html)

Applying formula, p=2,n=10, x=3(since 2^3<10 but 2^4>10)
so, 10/2+10/4+10/8=5+2+1=8
So since 10! has 8 powers of 2, to make it odd, 2 in denominator needs to be raised to 8.
Option D
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Re: If (10!)/(2y) is an odd integer, what is y?   [#permalink] 26 Aug 2017, 08:44
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