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

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If a, b and c are integers and a < b < c. Are a, b, c consecutive [#permalink]

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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..!!! => http://gmatclub.com/forum/gmat-diagnost ... 79347.html
[Reveal] Spoiler: OA

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If a, b and c are integers and a < b < c. Are a, b, c consecutive [#permalink]

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stonecold wrote:
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.




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


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: http://gmatclub.com/forum/new-set-numbe ... l#p1205364
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Re: If a, b and c are integers and a < b < c. Are a, b, c consecutive [#permalink]

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New post 17 Aug 2016, 06:42
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

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Re: If a, b and c are integers and a < b < c. Are a, b, c consecutive [#permalink]

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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.

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Re: If a, b and c are integers and a < b < c. Are a, b, c consecutive [#permalink]

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New post 19 Nov 2017, 21:38
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

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Re: If a, b and c are integers and a < b < c. Are a, b, c consecutive [#permalink]

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New post 19 Nov 2017, 22:33
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gmattesttaker556 wrote:
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


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.
_________________

New to the Math Forum?
Please read this: Ultimate GMAT Quantitative Megathread | All You Need for Quant | PLEASE READ AND FOLLOW: 12 Rules for Posting!!!

Resources:
GMAT Math Book | Triangles | Polygons | Coordinate Geometry | Factorials | Circles | Number Theory | Remainders; 8. Overlapping Sets | PDF of Math Book; 10. Remainders | GMAT Prep Software Analysis | SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) | Tricky questions from previous years.

Collection of Questions:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


What are GMAT Club Tests?
Extra-hard Quant Tests with Brilliant Analytics

Kudos [?]: 135696 [1], given: 12706

Re: If a, b and c are integers and a < b < c. Are a, b, c consecutive   [#permalink] 19 Nov 2017, 22:33
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