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# M04 #10

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M04 #10 [#permalink]

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25 Dec 2008, 13:27
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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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Re: M04: Question 15 [#permalink]

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25 Dec 2008, 23:15
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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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Re: M04 #10 [#permalink]

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22 May 2010, 12:12
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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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Re: M04 #10 [#permalink]

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22 May 2010, 22:10
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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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Re: M04 #10 [#permalink]

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23 May 2010, 02:49
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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Re: M04 #10 [#permalink]

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24 May 2010, 00:04
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I say answer is C

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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Re: M04 #10 [#permalink]

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19 Jun 2010, 23:43
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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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Re: M04 #10 [#permalink]

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03 Jul 2010, 14:45
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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Re: M04 #10 [#permalink]

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05 Jul 2010, 02:14
Zero fits the definition of "even number": it is an integer multiple of 2.
Source: wiki

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Re: M04 #10 [#permalink]

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12 Nov 2010, 20:30
0!=1

Oh boy... I totally forgot about this. I too thought 0!=0 /sadface.
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Re: M04 #10 [#permalink]

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25 May 2011, 04:27
The answer is C.

(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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Re: M04 #10 [#permalink]

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25 May 2011, 09:55
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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Re: M04 #10 [#permalink]

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29 May 2011, 04:25
Caught the 0! = 1 and 1! = 1 but it took me a while to realize that 0 is even.
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Re: M04 #10 [#permalink]

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29 May 2012, 06:31
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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Re: M04 #10 [#permalink]

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29 May 2012, 06:44
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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.

Answer: C.

Hope it's clear.
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Re: M04 #10 [#permalink]

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29 May 2012, 06:53
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.

Answer: C.

Hope it's clear.

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Re: M04 #10 [#permalink]

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29 May 2012, 19:15
Good question...
The answer is C and many people have already explained it.
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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Re: M04 #10 [#permalink]

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29 May 2013, 03:20
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]

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29 May 2013, 05:25
What is x?

S1: x! = odd
0! = 1; 1! = 1; 2! = 1*2; and so on.
=> x must be either 0 or 1.
S1 is not sufficient. Eliminate AD.

S2: x = even
x = 0, 4, 6, ... and so on.
S2 is not sufficient. Eliminate B.

Both S1 and S2: gives x = 0.
Both are sufficient. Correct answer is C.

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Re: M04 #10 [#permalink]

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29 May 2013, 17:55
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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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Re: M04 #10   [#permalink] 29 May 2013, 17:55

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# M04 #10

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