What is the value of integer x?

Question

(1)  |x| = \sqrt{|x|} 
 
(2)  (|x|)! = \sqrt{|x|}

M36-31

Bunuel · Accepted Answer

Official Solution:

What is the value of non-zero integer  x ? 
 
(1)  |x| = \sqrt{|x|} 
 
Square:  |x|^2=|x| ;
 
 |x|(|x|-1)=0 
 
 x=0  or  x=1  or  x=-1 . Not sufficient.
 
(2)  (|x|)! = \sqrt{|x|} 
 
Test numbers: 
 
If  x=1 , then  (|x|)! = \sqrt{|x|}=1 . Because of the absolute values  x=-1  must also be a solution. So,  x=1  or  x=-1 . Not sufficient.
 
(1)+(2) Still  x=1  or  x=-1 . Not sufficient.

Answer: E

ArunSharma12 · Answer

statement 1:
 |x| = \sqrt{|x|} 
 |x|^2 = |x| ;  |x|(|x|-1) = 0 
x =  
not sufficient

statement 2:
 (|x|)! = \sqrt{|x|}  
 (|x|)!^2 = |x| 
x =  
not sufficient

combining both statements, x can be  
not sufficient
Ans :E

ankita1905 · Answer

(1) 
case1 : Put x=-1 L.HS = RHS
case2 : Put x=0 LHS = RHS
case3 : Put x=1 LHS=RHS

Therefore statement 1 is not sufficient on its own
 
(2) 
For, x=-1,1 we get LHS=RHS .
Therefore statement 2 not sufficient.

Both statements 1 and 2 , still gives us two possibilities for x can be 1 or -1.

The question cannot be answered using both the statements together . 
Correct option

AdiBatman · Answer

In statement 2, I think x can be referred to only +1. Can there be any negative factorial.
But yes x can be 0 in statement 2. It's still not sufficient alone. Neither they are sufficient together with two answers 0 and 1.

Posted from my mobile device

GMATinsight · Answer

Question: x = ?

STatement 1 :  |x| = \sqrt{|x|}

x = 0 or 1 or -1 hence

NOT SUFFICIENT

Statement 2 :  (|x|)! = \sqrt{|x|}

x = 1 or -1 hence

NOT SUFFICIENT

Combining the two statements

x = 1 or -1 hence

NOT SUFFICIENT

Answer: Option E

stne · Answer

Hi  AdiBatman ,

Please note you cannot have  x=0  in statement 2. If you put  x=0  in statement 2 then LHS =1 and RHS = 0 hence they would not be equal. Please note 0!=1 ( Zero factorial = 1 and NOT zero )

Hope it helps.

mcolbert · Answer

What is the source of this problem? I know that the convention that 0! = 1 is not vital to the problem, as (1) and (2) each alone or together are not sufficient even ignoring this convention. But would GMAT really test knowledge of the convention that 0! = 1?

Mck2023 · Answer

(|x|)!^2 = |x| 
x =  
not sufficient

combining both statements, x can be  
not sufficient
Ans :E

Hi  ArunSharma12 
Can you please further explain the squaring og factiriL in statement 2. I mean further steps after step 2.....
Thank you.

Posted from my mobile device

ArunSharma12 · Answer

Hi  Mck2023 ,

we do not have to simplify the equation further.
 (|x|!)^2 = |x| 
we need some integer for which its factorial equals the integer itself.
I would start from  0:  0! = 1 
e 0 
1: 1! = 1 = 1
2: 2! = 2 , but  (2)^2 
e 2 
.. 
1 satisfies the equation and as the x is under mod we can also take x as -1.
possible solutions for x:

IanStewart · Answer

No, that's not something the GMAT would ever test. Factorials will only ever be applied to positive integers on the GMAT.

BrentGMATPrepNow · Answer

In order to apply the combinations formula, nCr = n!/(r!)(n-r)!, we need to know that 0! = 1
For example, if there are 3 employees, and we need to choose 3 of them for a committee, we can do this in 3C3 ways. 
Applying the formula, 3C3 = 3!/(3!)(3-3)! = 3!/(3!)(0!)
So, if we don't know that 0! = 1, we can't properly evaluate 3C3

IanStewart · Answer

Hope you're doing well Brent!

Counting formulas are unnecessary to begin with, but I imagine many test takers use them. But the answer to the question "how many different 3-person committees can you make from a group of 3 people" is obviously "one". There's no need to use a formula to answer a question like that. And that's true any time you might end up seeing "0!" somewhere, if you do answer counting questions using formulas -- it's always a situation where the answer would be immediately clear if you didn't use a formula at all.

BrentGMATPrepNow · Answer

Hey Ian,

Greetings from Vancouver Island!
I agree; from the context of a counting question, we can readily infer that 0! = 1

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What is the value of integer x?

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