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GMAT Diagnostic Test Question 20 Field: Statistics Difficulty: 700

If a, b & 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.

A. Statement (1) ALONE is sufficient, but Statement (2) ALONE is not sufficient B. Statement (2) ALONE is sufficient, but Statement (1) ALONE is not sufficient C. BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient D. EACH statement ALONE is sufficient E. Statements (1) and (2) TOGETHER are NOT sufficient
_________________

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.

Why is "a" assumed to be 0? "a" can take any value right? only b! is odd and nowhere it is given that "a" is lesser than b? Am I missing something here?

Why is "a" assumed to be 0? "a" can take any value right? only b! is odd and nowhere it is given that "a" is lesser than b? Am I missing something here?

Actually it is given: "If a, b & c are integers and a < b < c. Are a, b, c consecutive integers?"
_________________

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.

The correct answer is C

I think only B is ok because - c! is prime number -> c = 2 - a < b < c and a, b, c is integers -> a = 0, b= 1

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.

The correct answer is C

I think only B is ok because - c! is prime number -> c = 2 - a < b < c and a, b, c is integers -> a = 0, b= 1

Can you give me explanation? tks alot.

The problem with statement 2 alone is that a and b can be negative too. c we know is 2 but a can be -2 and b can be 1 or many other cases. Only statement 1 uses a! and b! which implies that a and b cannot be negative and hence should be 0 and 1. Therefore, we need both statements to get the answer.