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M04 #10

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M04 #10 [#permalink] New post 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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Re: M04: Question 15 [#permalink] New post 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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Re: M04 #10 [#permalink] New post 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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Re: M04 #10 [#permalink] New post 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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Re: M04 #10 [#permalink] New post 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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Re: M04 #10 [#permalink] New post 23 May 2010, 23:04
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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] New post 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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Re: M04 #10 [#permalink] New post 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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Re: M04 #10 [#permalink] New post 05 Jul 2010, 01:14
Zero fits the definition of "even number": it is an integer multiple of 2.
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Re: M04 #10 [#permalink] New post 12 Nov 2010, 19:30
0!=1

Oh boy... I totally forgot about this. I too thought 0!=0 /sadface.
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Re: M04 #10 [#permalink] New post 25 May 2011, 03:27
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] New post 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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Re: M04 #10 [#permalink] New post 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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Re: M04 #10 [#permalink] New post 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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Re: M04 #10 [#permalink] New post 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.

Answer: C.

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

Answer: C.

Hope it's clear.
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Re: M04 #10 [#permalink] New post 29 May 2012, 18:15
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] New post 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.

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Re: M04 #10 [#permalink] New post 29 May 2013, 04:25
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] New post 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
Re: M04 #10   [#permalink] 29 May 2013, 16:55
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