If 10 - ax = bx then what is value of |a-b|?

\(10 - ax = bx\)
i.e. \(ax + bx = 10\)
i.e. \(x(a + b) = 10\)

Question : \(|a-b|\) = ?

Statement 1: \(a\) and \(b\) are prime numbers

Since, \(x(a + b) = 10\)
Case1: so a=3, b=7 and x=1 and \(|a-b| = 4\)
Case2: so a=2, b=3 and x=2 and \(|a-b| = 1\)

NOT SUFFICIENT

Statement 2: \(x\) is an integer

No information about a and b so
NOT SUFFICIENT

Combining the two statements

Since, \(x(a + b) = 10\) and \(x\) is an Integer
Case1: so a=3, b=7 and x=1 and \(|a-b| = 4\)
Case2: so a=2, b=3 and x=2 and \(|a-b| = 1\) so
NOT SUFFICIENT

Answer: Option E[/quote]

I tried solving it this way,

10-ax =bx..........10 = (a+b)x
option 1 and 2 are individually insufficient. but when combined...

(a + b) and x can be either 5 or 2 (considering X is an integer)
if x =5 then (a+b) =2 which means a and b should be 1..........not prime
hence (a+b) = 5 ....so a and b should be 2 and 3.......|a-b| =1

my answer is C

please help me find out the mistake in my solution.[/quote]

Factors of 10are 1, 2, 5, 10

So (a+b) can be 10 when x=1
For a+b= 10, a can be 3 and b can be 7 (both prime)
So absolute value of a+b can be 4 as well

Also it's nowhere given that x is an integers so we would have taken that into account at secondary step if this question had given soneheadway but we could prove without it that the information is NOT sufficient so solve question.

But statement 2 says that x is an integer?

I arrived at the same result, if x is an integer and a and b must be prime:

x(a+b) = 10 is only a result if a and b are 2 and 5 respectively...

the absolute value of 2-5 or 5-2 is always 3. So C imho as well

I am not sure if you are checking any previous comment I made here right above your comment.
Here it is again.
Factors of 10 are 1, 2, 5, 10

So (a+b) can be 10 as well when x=1
For a+b= 10, a can be 3 and b can be 7 (both prime)
So absolute value of a+b can be 4 as well

And if (a+b) =5 and x=2
The a and b can be 2 and 3 and absolute value of a-b will be 1

Inconsistent values so NOT SUFFICIENT

The information is NOT sufficient so solve question.
_____

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