If a, b and c are integers and a

Question

If a, b and c are integers and a < b < c. Are a, b, c consecutive integers?

(1) The median of {a!, b!, c!} is an odd number.
(2) c! is a prime number.

Source => GMAT Quant Diagnostic..!!! => https://gmatclub.com/forum/gmat-diagnost ... 79347.html

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Official Answer

C

Bunuel · Accepted Answer

If a, b, and c are integers and a < b < c, are a, b, and c consecutive integers? 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. Check here: https://gmatclub.com/forum/new-set-numbe ... l#p1205364

stonecold · Answer

Hey  Bunuel  
Is there any theory available which correlates Mean , Median , Standard deviation of an AP series.
I have major issues with this amalgamation Standard deviation and AP since most of the SD questions i have seen are concerned around an AP series

Regards
Stone Cold

AMahmoodi · Answer

Hi,

is a,b& c consecutive ints?

st1. because a,b & c factorials are defined they should be non-negative integers, in addition if the median is an odd integer then b!=1 (just 0! & 1! are odd integers) therefore we conclude that a=0 b=1 and c should be any other positive integer greater than 1. insuff.

st2. if C! are prime then it must be 2! as 0! and 1! are not prime and every other facorials are even numbers greater than 2 which is not prime. up to know we just know the value of c and a,b could be (a<b) could be other integers even negative.

st1+2) we have a=0 b=1 and c=2 sufficient

please correct we if i'm wrong.

gmattesttaker556 · Answer

5. If a, b, and c are integers and a < b < c, are a, b, and c consecutive integers?

(1) The median of {a!, b!, c!} is an odd number.
(2) c! is a prime number

In regards to the above question--the OA that was given on the forum and in the answer keys was C but I am confused as to why B is not sufficient for the following reason:

If c! is a prime number this implies that it must be 2!; given this we know that a and b are less than 2 and are also integers; a cannot be negative because it would be undefined, thus a must be 0!; given that a is 0! and c is 2! b must be 1!

Could someone please explain why the answer has been marked as C?

https://gmatclub.com/forum/if-a-b-c-are ... 23845.html

Bunuel · Answer

For (2) we only know that c = 2 but you cannot use info from (1) when considering (2) to deduce that a and b must be non-negative.

If a, b and c are integers and a < b < c. Are a, b, c consecutive

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