# A simple Grade 8 test question [closed]

Bob has been given the following question during a test:

   x is a number.
x is half of 2(x+1).
What is x?


Can you help Bob to solve this?

• Are we allowed cyclic groups? What is your definition of number? – Lacklub Mar 18 '16 at 14:53
• My smartass answer to the puzzle: "A number." – Khale_Kitha Mar 18 '16 at 14:54

Can you help Bob to solve it?

No.

Here's the explanation of why:

Bob has been given the below question during a test:

Assisting a student with a problem during a test is cheating.

But if I were to attempt to solve the system of equations:

x is a number.
x is half of 2(x+1).
What is x?


x is a number that is half of 2(x+1). Without further definition of which operators are used, and what x represents in context no further progress may be made without assumptions.

See other answers for following this system of equations with the standard definitions used for the given operators.

x is $1$
x is a number (check)
1 is half of 2(which is 1+1) - we all assume it's multiplication, but parentheses can also be used to clarify

x = 2

because

"2" is half of "23" which is "2" "2+1".

• On the same line of thought: x=8, 2(x+1) = 18, half of which is 8 – Lacklub Mar 18 '16 at 15:14
• @Lacklub - yep. I'm sure that some interpretation like this is what Alex is after, but unfortunately, there are too many possibilities that equally match the information given. So it is a shot in the dark what was intended. – Paul Sinclair Mar 18 '16 at 15:19
• Or 3, which is half (vertically) of 8. – f'' Mar 18 '16 at 16:01

I think the answer might be

1 or 3

Reasoning

Assuming that "x is a number" implies that x is not $\infty$ then we must subscribe to a different interpretation of the second line. Given that "2(x+1)" is six characters long, it may be that we form x using three characters from that expression.

Valid solutions then for x are "(x)", "(1)" or "2+1" (given that ordering is important and any bracket must have a match). The first solution is too general to be able to determine x directly so we'll take it that it's one of the other two.

0 or 2

because

2(x+1) comes out to 2x+2. Thinking laterally, half of that could be 2x, or half could be 2. For 2x, we have x = 2x, which works for only 0. 2 is self-explanatory.

x is

Infinity. Because Inf+1 = Inf.

• infinity is not a number, though – Khale_Kitha Mar 18 '16 at 14:52
• @Khale_Kitha - sure infinity is a number. It just isn't a real number (that is, an element of the set of real numbers). It is a element of the set of extended real numbers, or the set of hyperreal numbers or the set of surreal numbers, or a host of other definitions of sets of numbers. – Paul Sinclair Mar 18 '16 at 15:15
• @Paul: Those aren't "infinity" though. Infinity is the quality of not being finite. You can have infinite numbers, but you'd need to point to a specific one, such as $\aleph_0$ or $\omega$. – Deusovi Mar 25 '16 at 3:08
• @Deusovi - let's not play semantic games, please. My point to Khale_Kitha is that it is completely valid to think of infinity as a number (but not as a Real number). I also pointed out that there are varying definitions of the concept, so you can't just assume a particular one. All of the definitions I mentioned have the quality of not being finite. – Paul Sinclair Mar 25 '16 at 12:46

Well, it's quite simple. x is :

impossible

It's a computing test. 'is' is the code to assign a string to a variable, so x="half of 2(x+1)" (a string).

$\frac{2 * (x + 1)}{2} = x$
$2*x + 2 = 2 * x$
$0 =2$ So not possible unless x is infinity or -infinity

Or

$\frac{2 * (x + 1)}{2} = x$
$x + 1 = x$
$1 =0$

Same thing as above.