M08#36

Question

What is X ? X^2 - 1 = X + 1 X + 3 is a prime number Statement (1) ALONE is sufficient, but Statement (2) ALONE is not sufficient Statement (2) ALONE is sufficient, but Statement (1) ALONE is not sufficient BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient EACH statement ALONE is sufficient Statements (1) and (2) TOGETHER are NOT sufficien why 1 is not sufficient

GyanOne · Answer

Using (1), X^2 = X 
=> X can be 0 or 1

Using (2), X+3 is a primer number
=> X can be -1,0,2,........

Combining (1) and (2), X is 0

(C) it is.

shrive555 · Answer

Thanks:
Thats how i did. 
(X+1)(X-1) = (X+1) 
i cancelled out X+1... 
X-1 = 1
X= 2

dandarth1 · Answer

I understand that x can be 0 or 1 in the first statement. However, I'm just wondering algebraically why you couldn't cancel out (x+1) in the equation (x+1)(x-1)=x+1 ? There must be some rule broken if you do, because it will give you a definite solution, which is wrong. Any thoughts?

Bunuel · Answer

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 can not divide by zero.

So, if you divide (reduce)  x^2=x  by  x , you assume, with no ground for it, that  x  does not equal to zero thus exclude a possible solution.

Hope it's clear.

mydreammba · Answer

Hi Bunnel,

How will x=0 satisfy in the 1st equation the possible values for 1st statement are -1 and 2....so not sufficient

statement 2

From statement 2 the possible values are -1, 2 0 .....so not sufficient

Even after combining we have 2 values satisfying the above statements i.e -1 and 2 so Not sufficient

EvaJager · Answer

Your equation  x^2 = x  is incorrect. It seems that you missed the signs, as in the lefthand side you have  -1  and in the righthand side you have  +1 .
The two don't cancel out.

The correct equation is  x^2-x-2=0  or  (x+1)(x-2)=0 , which has two solutions,  x=-1  and  x=2.

dandarth1 · Answer

x=0 won't satisfy the first equation. if ur referring to the rule to not divide by zero that bunuel just mentioned, it applies to the whole expression (x+1) in this problem. you cant divide by (x+1) because it could equal zero, and it does when x=-1...x=0 does not satisfy the equation, so u are correct

M08#36

Prep Toolkit

Top 5 GMAT Debrief Videos

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards