M08-36

Question

What is the value of  x ?

(1)  x^2 - 1 = x + 1 
 
(2)  x + 3  is a prime number

Bunuel · Answer

Official Solution:

What is the value of  x ? 
 
(1)  x^2-1=x+1 
 
Rearrange to obtain  (x-1)(x+1)-(x+1)=0 ;
 
Factor out  x+1  to obtain  (x+1)(x-2) = 0 . Either  x = -1  or  x = 2 . Not sufficient.
 
(2)  x + 3  is a prime number. Clearly insufficient by itself.
 
(1) + (2) Both values from (1) satisfy statement (2) as well, so  x  can still be either -1 or 2. Not sufficient.

Answer: E

RushikeshT · Answer

Hi Bunuel ,

For statement (1) why can't i factories like
 x^2−1=x+1
(x+1) (x-1) = x+1 and then cancel out x+1 from both sides?

nalinnair · Answer

Hi  RushikeshT

There are two reasons.
1. If  x = -1  (which in fact is one of the solutions to the quadratic equation in this statement), then  x+1 = 0.  Cancelling out  (x+1)  from both sides of the equation essentially mean that you are dividing both sides by  (x+1)  (i.e. by 0). This would be wrong as you know there is no definite answer when you divide any number by 0.

2. If you cancel out  (x+1)  from both sides, you will get  x = 2 . This of course solves the quadratic equation  x^2 - 1 = x +1 . Just replace  x = 2 
 2^2 - 1 = 2+ 1 
 3 = 3 .
But, there is another value of  x  that can solve  x^2 - 1 = x + 1 . i.e.  x = -1 
 (-1)^2 - 1 = -1 + 1 
 0 = 0 
So, if you cancel out  (x+1)  then you will not get the second value of  x . You will end up considering this statement as sufficient and choosing a wrong answer. Always remember, a quadratic equation can be solved by two values of the variable, unless the quadratic equation is in the form of  (a+b)^2  or  (a-b)^2 .

Hope this helps!!

gupta87 · Answer

I think this is a  high-quality  question and I don't agree with the explanation. why cant we solve it like below:
(x+1)(x-1)=(x+1)
=x-1=1 => x=2

Why not Ans A?

Bunuel · Answer

You cannot reduce by x+1 because x+1 can be 0 and we cannot divide by 0. Never reduce equation by variable (or expression with variable), if you are not certain that variable (or expression with variable) doesn't equal to zero. We cannot divide by zero. You should solve the way it's shown in the solution.

An78w · Answer

Hi Banuel,

I have a question on the rules of DS.

Suppose I get two values of x from statement 1, say 1 & -2.
From statement 2 also (alone, not with statement 1), I get the same 2 values , 1 & -2.

What to mark in such case? Both together not sufficient or both together sufficient? Would be grateful if you share the reason also.

Reason for confusion - If by both statements we are getting the same values, then by 1 & 2 together we can say that these two values of x are the required values, right?

Bunuel · Answer

The point is that when a DS question asks to find the value, then the statement is sufficient ONLY if you can get the  SINGLE  numerical value.

So, if for (1)+(2) you get that x = 1 or x = -2, then you do NOT have the single numerical value of x, so the answer would be E.

Bunuel · Answer

I have edited the question and the solution by adding more details to enhance its clarity. I hope it is now easier to understand.

M08-36

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