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What is the product of all positive odd integers less than 1

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Director
Joined: 29 Nov 2012
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What is the product of all positive odd integers less than 1  [#permalink]

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Updated on: 05 Oct 2013, 04:41
4
6
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Difficulty:

65% (hard)

Question Stats:

59% (01:52) correct 41% (02:20) wrong based on 142 sessions

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What is the product of all positive odd integers less than 10000?

A. $$\frac{10000!}{{(5000!)^2}}$$

B. $$\frac{10000!}{2^{5000}}$$

C. $$\frac{9999!}{2^{5000}}$$

D. $$\frac{10000!}{2^{5000}. 5000!}$$

E. $$\frac{5000!}{2^{5000}}$$

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Originally posted by fozzzy on 05 Oct 2013, 02:36.
Last edited by Bunuel on 05 Oct 2013, 04:41, edited 1 time in total.
Edited the question.
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Re: What is the product of all positive odd integers less than 1  [#permalink]

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07 Oct 2013, 01:16
6
You can always test this concept on smaller numbers the same applies to larger numbers ...

If you have to find the product of all odd integers from 1 to 10 inclusive

The normal way would be 1*3*5*7*9 = 945

Since the answer choices in this option are in factorials

For the smaller example would be$$\frac{10!}{2*4*6*8*10}$$

$$\frac{10!}{2^5 ( 1*2*3*4*5)}$$ = 945
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Joined: 14 Aug 2013
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Re: What is the product of all positive odd integers less than 1  [#permalink]

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05 Oct 2013, 02:53
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fozzzy wrote:
What is the product of all positive odd integers less than 10000?

A) $$\frac{10000!}{{(5000!)^2}}$$
B) $$\frac{10000!}{2^{5000}}$$
C) $$\frac{9999!}{2^{5000}}$$
D) $$\frac{10000!}{2^{5000}. 5000!}$$
E) $$\frac{5000!}{2^{5000}}$$

Product of all odd positive integers less than 10000 is 1*3*5*7.......*9999

which can be written as (1*2*3*4.....10000)/2*4*6*...*10000

where as 2*4*6*...*10000=(2^5000)(1*2*3*....*5000)...since 2 is taken as common from 2,4,6,8,..10000 which has 5000 terms

given equation becomes (1*2*3*4*....*10000)/(2^5000)(1*2*3*....*5000)

=>10000!/(2^5000)(5000!)

Ans D...Hope my logic is right
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Re: What is the product of all positive odd integers less than 1  [#permalink]

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05 Oct 2013, 04:17
fozzzy wrote:
What is the product of all positive odd integers less than 10000?

A) $$\frac{10000!}{{(5000!)^2}}$$
B) $$\frac{10000!}{2^{5000}}$$
C) $$\frac{9999!}{2^{5000}}$$
D) $$\frac{10000!}{2^{5000}. 5000!}$$
E) $$\frac{5000!}{2^{5000}}$$

Product of all odd integers less than 10,000= product of all integers less than 10,000/product of even integer less than 10,000=10,000!/2^5000(5000!)

Product of even integer=2*4*6*8…..10,000=2^5000(1*2*3*4……5000)=2^5000(5000!)

So the answer is D.
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Re: What is the product of all positive odd integers less than 1  [#permalink]

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16 Oct 2017, 10:38
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Re: What is the product of all positive odd integers less than 1 &nbs [#permalink] 16 Oct 2017, 10:38
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