I don't agree with the explanation. i think A should be the answer because a set (1,1,c!) will have a median of 1 always na

Official Solution:


Note that:

A. The factorial of a negative number is undefined.

B. 0!=1.

C. Only two factorials are odd: 0!=1 and 1!=1.

D. Factorial of a number which is prime is 2!=2.

(1) The median of {a!, b!, c!} is an odd number. This implies that b!=odd. Thus b is 0 or 1. But if b=0, then a is a negative number, so in this case a! is not defined. Therefore a=0 and b=1, so the set is {0!, 1!, c!}={1, 1, c!}. Now, if c=2, then the answer is YES but if c is any other number then the answer is NO. Not sufficient.

(2) c! is a prime number. This implies that c=2. Not sufficient.

(1)+(2) From above we have that a=0, b=1 and c=2, thus the answer to the question is YES. Sufficient.


Answer: C

bunuel
why not you consider values of negative integer for a?
for ex. a=-1,-2,-3.. these numbers also satisfy given condition

I think this is a poor-quality question and I don't agree with the explanation. 0! 1! 2!

0! 1! 3!

I think this is a high-quality question and I don't agree with the explanation. Option B: Statement 2 alone is sufficient.
The only factorial which gives prime is 2. Implies c is 2. And given a<b<c. Implies a=0,b=1. Therefore it answers the question a,b,c are consecutive integers.

Your doubt is already addressed in this thread. Please re-read. Hope it helps.