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# M04 #10

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25 Dec 2008, 12:27
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What is the value of $$X$$ ?

1. $$X!$$ is odd
2. $$X$$ is even

Source: GMAT Club Tests - hardest GMAT questions

[Reveal] Spoiler:
In this partcular problem the OA is C. according to me it should be A.

From S1 we get x=0 or x=1. 0 is even in GMAT, Hence only value of x is 1, sufficient.

SOLUTION IS HERE: m04-78541.html#p1090321
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29 May 2012, 05:44
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Cosmas wrote:
Statement 1 is sufficient because it results in one answer....that's 0!=1; and 1!=1 and 1 is odd.

Welcome to GMAT Club. Note that the answer to this question is C, not A.

What is the value $$x$$ ?

(1) $$x!$$ is odd --> two values satisfy this condition 0 and 1: $$0!=1$$ and $$1!=1$$. Not sufficient.

(2) $$x$$ is even --> $$x$$ can be any even number. Not sufficient.

(1)+(2) Since from (1) $$x$$ is either 0 or 1 and (2) says that $$x$$ is even then $$x=0=even$$. Sufficient.

Hope it's clear.
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25 Dec 2008, 22:15
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Stmt1 does not say that x is odd. It says factorial of x is odd. And this is true for both x = 0 and x = 1. Hence, stmt1 by itself is insufficient.
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29 May 2013, 16:55
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X! is odd is possible only when X! = 1 because for X>1 it will always have an even multiple .

X! means X can be 0 or 1 , Stmt 1 not sufficient

Stmt 2 says X is even , which doesn't uniquely identifies the value .

Combining both we get the answer as 0 . Therefore ,C
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22 May 2010, 21:10
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statement 1:
===========
X can either be Zero or One since both the factorial values are odd.So insuff.

Statement 2:
==========
X is even.Certainly insuff.

combining both,we get X = 0.so suff.

I will go with option C
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19 Jun 2010, 22:43
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kevinw1081 wrote:
Are all factorials even? except for 1?

All factorials are even, except for 0 and 1 whose factorials are odd and the same; 0! = 1! = 1.
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22 May 2010, 11:12
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i think the trick here is not to recall that factorial of zero is one
making two correct values for statement1.

Even numbers N = 2n (n=0,1,2, 3...) That is 0,2,4,6 are all even numbers
OA is C, as stmt2 has clarified that X is even (i.e 0)
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23 May 2010, 23:04
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1) X! is odd. 0! is 1 and 1! is 1. You have two options.

2) X is an even number. 0 is considered an even number.

So 0 is the value of X.
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11 Aug 2013, 01:14
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gilda wrote:
eventually, is 0 even or it is neither even nor odd?

Zero is an even integer. (Zero is neither positive nor negative).

An even number is an integer that is "evenly divisible" by 2, i.e., divisible by 2 without a remainder and as zero is evenly divisible by 2 then it must be even (in fact zero is divisible by every integer except zero itself).

Hope it's clear.
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23 May 2010, 01:49
Statement 1 impliies x can be 0 or 1..so not sufficient.
Statement 2 x is even...not sufficient.
Combining 1 & 2 x = 0,
hence C
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03 Jul 2010, 13:45
gattupalli wrote:
I completely agree with Adhiraj even I assume that 0 is not even either but the answer says is C. My answer was E too... should I take it like a thumb rule that 0 is even in GMAT?

Even = 2n.
where n: {0, 1, 2, ...}
list of even nos: {0, 2, 4, ...} - 0 is inclusive.
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05 Jul 2010, 01:14
Zero fits the definition of "even number": it is an integer multiple of 2.
Source: wiki
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12 Nov 2010, 19:30
0!=1

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25 May 2011, 03:27

(1) says x can be 0 or 1, where x! = 1

Insufficient

(2) says x is even

Insufficient

So (1) + (2) = 0

Sufficient.
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25 May 2011, 08:55
Clean bowled on this one! I guess I learned two things here.

1. 0! = 1, 0! & 1! are the only Odd factorials
2. 0 is an Even number (this was a surprise!)

I also think that the key is too look out for answer choices that seem 'too good to be true'; 95% of the time in such instances, the GMAT is playing around with you.
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29 May 2011, 03:25
Caught the 0! = 1 and 1! = 1 but it took me a while to realize that 0 is even.
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29 May 2012, 05:31
Statement 1 is sufficient because it results in one answer....that's 0!=1; and 1!=1 and 1 is odd.
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29 May 2012, 05:53
Thanks mate. i see now.lol

Bunuel wrote:
Cosmas wrote:
Statement 1 is sufficient because it results in one answer....that's 0!=1; and 1!=1 and 1 is odd.

Welcome to GMAT Club. Note that the answer to this question is C, not A.

What is the value $$x$$ ?

(1) $$x!$$ is odd --> two values satisfy this condition 0 and 1: $$0!=1$$ and $$1!=1$$. Not sufficient.

(2) $$x$$ is even --> $$x$$ can be any even number. Not sufficient.

(1)+(2) Since from (1) $$x$$ is either 0 or 1 and (2) says that $$x$$ is even then $$x=0=even$$. Sufficient.

Hope it's clear.
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29 May 2012, 18:15
Good question...
A small information regarding even and odd numbers. Even and odd numbers are defined for integers ie., -2,-4 etc are also even numbers. So, zero is obviously an even number.
E = {...-4,-2,0,2,4...}
O = {..-3,-1,1,3...}

PS: I am new to the forum and this is my first post..
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29 May 2013, 02:20
sandipchowdhury wrote:
What is the value of $$X$$ ?

1. $$X!$$ is odd
2. $$X$$ is even

[Reveal] Spoiler: OA
C

Source: GMAT Club Tests - hardest GMAT questions

In this partcular problem the OA is C. according to me it should be A.

From S1 we get x=0 or x=1. 0 is even in GMAT, Hence only value of x is 1, sufficient.

theory required:
1==> factorial is defined only for non negative numbers.
2==>factorial 0= 1
3==> 0 is an even number.
4==> for a product of numbers to be odd all numbers should be odd.

now in our question:
statement 1: $$X!$$ is odd===> this clearly means we can take only 0 or 1 but this is not sufficient.
statement 2: $$X$$ is even===> this alone doesnt say anything hence not sufficient.

combining both in 0 and 1 ....0 is even so sufficient.

hope it helps.

SKM
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Re: M04 #10   [#permalink] 29 May 2013, 02:20

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# M04 #10

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