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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 
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Using (1), X^2 = X => X can be 0 or 1 [not sufficient] Using (2), X+3 is a primer number => X can be -1,0,2,........ [not sufficient] Combining (1) and (2), X is 0 [sufficient] (C) it is.
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dandarth1 wrote: GyanOne wrote: Using (1), X^2 = X
=> X can be 0 or 1 [not sufficient]
Using (2), X+3 is a primer number
=> X can be -1,0,2,........ [not sufficient]
Combining (1) and (2), X is 0 [sufficient]
(C) it is. 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? 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.
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Thanks: Thats how i did. (X+1)(X-1) = (X+1) i cancelled out X+1... X-1 = 1 X= 2
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GyanOne wrote: Using (1), X^2 = X
=> X can be 0 or 1 [not sufficient]
Using (2), X+3 is a primer number
=> X can be -1,0,2,........ [not sufficient]
Combining (1) and (2), X is 0 [sufficient]
(C) it is. 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?
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Bunuel wrote: dandarth1 wrote: GyanOne wrote: Using (1), X^2 = X
=> X can be 0 or 1 [not sufficient]
Using (2), X+3 is a primer number
=> X can be -1,0,2,........ [not sufficient]
Combining (1) and (2), X is 0 [sufficient]
(C) it is. 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? 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. 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
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GyanOne wrote: Using (1), X^2 = X
=> X can be 0 or 1 [not sufficient]
Using (2), X+3 is a primer number
=> X can be -1,0,2,........ [not sufficient]
Combining (1) and (2), X is 0 [sufficient]
(C) it is. 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.
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mydreammba wrote: Bunuel wrote: GyanOne wrote: Using (1), X^2 = X
=> X can be 0 or 1 [not sufficient]
Using (2), X+3 is a primer number
=> X can be -1,0,2,........ [not sufficient]
Combining (1) and (2), X is 0 [sufficient]
(C) it is. 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? 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. 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 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
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