D01-20

Question

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.

Bunuel · Accepted Answer

Official Solution:

If  a ,  b , and  c  are integers and  a < b < c , are  a ,  b , and  c  consecutive integers? 
 
Note that:
  
1. The factorial of a negative number is undefined.
 
2.  0!=1 .
 
3. Only two factorials are odd:  0!=1  and  1!=1 .
 
4. If  x!  is a prime number, then  x = 2  is the only solution.
  
(1) The median of  (a!, \ b!, \ c!)  is an odd number.
 
This implies that  b!  is odd. Therefore,  b  must be either 0 or 1. However, if  b = 0 , then  a  would be a negative number (since  a < b ), making  a!  undefined, which is not possible. Therefore,  a = 0  and  b = 1  (yielding  (a!, \ b!, \ c!)=(1, 1, c!) ). If  c = 2 , the answer is YES, but if  c  is any other number, the answer is NO. Not sufficient.
 
(2)  c!  is a prime number. 
 
This implies that  c=2 . Not sufficient.
 
(1) + (2) From the previous analysis, we know that  a = 0 ,  b = 1 , and  c = 2 . Thus, the answer to the question is YES. Sufficient.

Answer: C

Bunuel · Answer

That's NOT correct. For (2) we don't know whether a and b are positive integers. WE cannot use the info from (1) when considering the second statement.

Thoughtosphere · Answer

I got this question wrong in the test, because I didn't pay special attention to every detail given in the question.

Here's the right solution :

1. The median of a! b! c! is an odd number, it means that b is either 0 or 1. Since we can have a!, it means that a is greater than or equal to 0. We also know that a < b < c, so a = 0, b = 1, but we have no information about c. SO, this is insufficient.

2. c! is a prime number, this means that c = 2. Here we have no information about a and b, so Insufficient.

Combining 1 & 2, we get that a = 0, b = 1, c=2.

So, C

GMAT888 · Answer

I think this question is  poor  and  helpful .
I believe the given answer is incorrect and the correct one is B -> statement 2 by itself is sufficient. Indeed, if c! is prime then it must be 2 and since a < b < c and a,b,c are INTEGERS AND factorial is not defined for negative numbers then a and b have no other choice but to be 0 and 1 respectively! Thus, statement 2 is enough by itself. I would like to hear your comments. Thanks.

JarvisR · Answer

Bunuel  and others:
I have similar doubt like others. I appreciate your inputs.

Lets ignore Stmt A for now. 
Question says, If a, b, and c are integers and a<b<c, are a, b, and c consecutive integers?
Stmt(1): ignore.
Stmt(2): c! is a prime number.
only possible number is 2. !2 =2 a prime number.
Now, a<b<c and they are integers. The only possible combination i see here is 0,1,2. I ignored combination with negative numbers such as -1,1,2 because !negative is undefined. 
Where am i going wrong here?

Bunuel · Answer

You do not have factorial of a or b in stem or in (2) so you cannot ignore negative numbers.

Darkhorse12 · Answer

Bunuel 
As per the solution given: 
(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.

it says b is 0 or 1. Is 0 an odd number?

Bunuel · Answer

0 is an even integer. But 0! = 1 = odd.

praneet87 · Answer

How is 0 factorial 1?

Bunuel · Answer

0! = 1.

It's a math property you need not know why it's so but if still interested check this video:

https://www.youtube.com/watch?v=Mfk_L4Nx2ZI

Albert__ · Answer

How can we determine that c must be 2 (not any other prime number) from the :

2) c! is a prime number.

Bunuel · Answer

n! = 1*2*3*...*n

Now, if c is any other number than 2, c! will have at least 2 and 3 as its factor and we know that a prime number has only two factors 1 and itself, thus for c! to be prime c must be 2. For example, if c = 4, then c! = 4! = 1*2*3*4, which is not a prime.

Hope it's clear.

Sk18 · Answer

I think this is a  high-quality  question and I agree with explanation. Great question! Tests a mix of multiple basic facts on numbers.

dc2880 · Answer

Bunuel  Would you be able to help me with this?

How do we know that "The median of {a!, b!, c!} is an odd number" means that b is odd?

akadiyan · Answer

The important point to remember is that factorial of negative number is undefined. Option A says "The median of {a!, b!, c!} is an odd number" , which means b! is odd.

Only 2 options results in odd numbers either 0! or 1!. But since a < b, b cannot be 0 (which means a < b , and a is negative and a! is undefined) , so b is 1 (odd number).

I hope i answered your question.

BrunoAlbrecht · Answer

I think this is a  high-quality  question and I agree with explanation.

SimpleSimon123 · Answer

I think this is a  high-quality  question and I agree with explanation.

meghnajeendgar · Answer

I don't agree with the explanation. What if C=3. It is a prime number and it is greater than 1. The answer to the question will be no in this case. Would not option E make more sense?

Bunuel · Answer

(2) says that c! is prime. If c = 3, then c! = 6, which is not a prime. So, c cannot be 3.

Does this make sense?

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