What is the value of x? (1) x^2 – 5 x + 6 = 0 (2) x 0

Question

What is the value of x?

(1) x^2 – 5 x + 6 = 0

(2) x > 0

CareerGeek · Answer

(1) x^2 – 5x + 6 = 0
—> x^2 - 3x - 2x + 6 = 0
—> x(x - 3) - 2(x - 3) = 0
—> (x - 3)(x - 2) = 0
—> x = 2 or 3
No unique value —>  Insufficient

(2) x > 0
Many values of x are possible 
—> x = {1, 2, 3, 4, 4.5, . . . }
—>  Insufficient

Combining (1) & (2),
—> Possible values of x = 2 or 3
No unique value —>  Insufficient

Option E

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rajatchopra1994 · Answer

Explanation:
Statement 1:
x^2–5x+6=0
x^2-2x-3x+6=0
(x-2)(x-3)=0
x=2,3
Insufficient
Statement 2: x > 0
X can be any posivtive value
Insufficient

Combining 1 & 2,
x can be = 2,3
Insufficient

IMO-E

globaldesi · Answer

1)
 x^2 - 5x +6=0 
can be factored in 
(x-3)(x-2) =0
thus x can be 2 or 3
not sufficient

2) 
x>0
clearly not sufficient
combine both
still x can be both 2, 3
no sufficient
thus E

cpn · Answer

From data A, Factorizing the equation
x^2-5x+6=0, we get (x-2)(x-3)=0
So x=2&3 Ambiguous. So A is Insufficient
B says x>0 which is also Insufficient.
Combining A & B we still do not have a unique value for x. 
So E

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Bunuel · Answer

It's possible to answer this question without factoring or solving the quadratics.

First notice that, x^2 – 5 x + 6 is not the square (meaning that it cannot be written as (x- root)^2). So, it must have two roots. Next, x cannot be negative because, if it is, then we'd have  positive + positive + positive > 0 , so both roots must be positive. Thus, (1) should give two positive roots, (2) does not help, and the answer is E.

bumpbot · Answer

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What is the value of x? (1) x^2 – 5 x + 6 = 0 (2) x > 0

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