n! = n * (n-1) * (n-2)... 1, where n is a positive integer, which of the following is (are) true?

Since it asks for correctness of three cases, let's take these cases one by one..I 26 is not a factor of 25!

25! Is multiple of all numbers less than and equal to 25.

Also 26=2*13 but 25!=1*2*3*.....*12*13*14*.....24*25

25! Is a multiple of both 2 and 13 thus multiplof 2*13 or 26.

Hence the statement is not true.

II 29 is a factor of 25!

29 is a prime number greater than 25 ..

But 25 is a multiple of only prime numbers till 25. Hence 29 is not a factor.

Not true.

III 1000000 is a factor of 25!

1000000=\(10^6=2^65^6\)

So let's check if there are atleast six 5s in 25!

# of 5s =\(\frac{25}{5}+\frac{25}{25}=5+1=6\)

Therefore 25! Contains six 5s and thus 1000000 is a factor of 25!

True

Only III true

A. None

B. III Only

C. I and II only

D. II and III only

E. I, II, and III

B

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1) Absolute modulus : http://gmatclub.com/forum/absolute-modulus-a-better-understanding-210849.html#p1622372

2)Combination of similar and dissimilar things : http://gmatclub.com/forum/topic215915.html

3) effects of arithmetic operations : https://gmatclub.com/forum/effects-of-arithmetic-operations-on-fractions-269413.html

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