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# GMAT Diagnostic Test Question 20

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GMAT Diagnostic Test Question 20 [#permalink]

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06 Jun 2009, 21:58
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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
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Last edited by Bunuel on 06 Oct 2013, 23:22, edited 3 times in total.
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Re: GMAT Diagnostic Test Question 19 [#permalink]

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02 Jul 2009, 02:36
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Explanation:

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.

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Last edited by bb on 29 Sep 2013, 10:38, edited 1 time in total.
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Re: GMAT Diagnostic Test Question 19 [#permalink]

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13 Mar 2014, 19:59
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tiendungdo wrote:
dzyubam wrote:
Explanation:

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.

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.

(C)
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Re: GMAT Diagnostic Test Question 20 [#permalink]

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18 Feb 2014, 07:12
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?
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Re: GMAT Diagnostic Test Question 20 [#permalink]

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18 Feb 2014, 07:53
stuffs88 wrote:
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?"
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Re: GMAT Diagnostic Test Question 20 [#permalink]

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18 Feb 2014, 08:04
Duh! I think, we go blind when we panic! Happens to me at least.

Thank you for clarifying
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Re: GMAT Diagnostic Test Question 19 [#permalink]

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13 Mar 2014, 17:54
dzyubam wrote:
Explanation:

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.

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.
Re: GMAT Diagnostic Test Question 19   [#permalink] 13 Mar 2014, 17:54
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# GMAT Diagnostic Test Question 20

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