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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 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: m0478541.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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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 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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