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# D01-20

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Senior Manager
Status: Some status
Joined: 28 Jun 2012
Posts: 331

Kudos [?]: 66 [0], given: 372

Location: Albania
GMAT 4: 660 Q51 V49
GRE 1: 336 Q165 V166
GPA: 3.13
WE: Project Management (Health Care)

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22 Dec 2014, 08:09
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If a, b, and c are integers and $$a \lt b \lt c$$, are a, b, and c consecutive integers?

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

(2) c! is a prime number.

Kudos [?]: 66 [0], given: 372

Senior Manager
Status: Some status
Joined: 28 Jun 2012
Posts: 331

Kudos [?]: 66 [1], given: 372

Location: Albania
GMAT 4: 660 Q51 V49
GRE 1: 336 Q165 V166
GPA: 3.13
WE: Project Management (Health Care)

### Show Tags

22 Dec 2014, 08:09
1
KUDOS
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.

Kudos [?]: 66 [1], given: 372

Intern
Joined: 22 Mar 2017
Posts: 18

Kudos [?]: 1 [0], given: 75

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02 Jan 2018, 02:48
Wouldn´t knowing that c=2 be sufficient?

If a < b < c (different numbers strictly superior to one another) and if none of those numbers can be negative because otherwise the factorial is not defined, then what more integers choices are than 0 and 1 for a and b respectively?

_________________

King regards,

Rooigle

Kudos [?]: 1 [0], given: 75

Re: D01-20   [#permalink] 02 Jan 2018, 02:48
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# D01-20

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