the graph intersects the x axis when y=0. So the question is asking "when is (x+a)(x+b)=0?"
It's a factored formula. the product will equal 0 when either one of the factors equal 0, i.e. either
x+a=0 (so x=-a)
OR when
x+b=0 (so x=-b)
Thus, to answer the question, we need to find a and b.
Stat. (1): single equation with two unknowns allows infinite values of a and b. Question can't be answered with a singular answer. Insufficient.
Stat. (2): tells you that when x=0, y equals =6. Plug x=0, y=6 into the graph equation y=(x+a)(x+b), and you get
-6 = (0+a)(0+b) or
-6=ab.
Again, single equation with two unknowns: can't find single value for a and b.
combined: two equations with two unknowns:
a+b=-1
ab=-6.
Two equations with two unknowns will lock a and b to a single pair of values - only 2 and -3 will satisfy both. sufficient - C.
Technically, particular pair of equations (a sum and a product of two variables) doe not lock in a and b to a single value: if you solve, you'll find that either a=2 and b=-3, or vice versa: a=-3 and b=2. But the question stem asked at which two points the graph intersects the x axis, and these two points are known : a and b are 2 and -3 (interchangeable), so the xs are the reverse -2 and 3.
Coordinate Geometry Q - DS
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Geva@EconomistGMAT
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Thanks for the explanation Geva.
Geva@MasterGMAT wrote:the graph intersects the x axis when y=0. So the question is asking "when is (x+a)(x+b)=0?"
It's a factored formula. the product will equal 0 when either one of the factors equal 0, i.e. either
x+a=0 (so x=-a)
OR when
x+b=0 (so x=-b)
Thus, to answer the question, we need to find a and b.
Stat. (1): single equation with two unknowns allows infinite values of a and b. Question can't be answered with a singular answer. Insufficient.
Stat. (2): tells you that when x=0, y equals =6. Plug x=0, y=6 into the graph equation y=(x+a)(x+b), and you get
-6 = (0+a)(0+b) or
-6=ab.
Again, single equation with two unknowns: can't find single value for a and b.
combined: two equations with two unknowns:
a+b=-1
ab=-6.
Two equations with two unknowns will lock a and b to a single pair of values - only 2 and -3 will satisfy both. sufficient - C.
Technically, particular pair of equations (a sum and a product of two variables) doe not lock in a and b to a single value: if you solve, you'll find that either a=2 and b=-3, or vice versa: a=-3 and b=2. But the question stem asked at which two points the graph intersects the x axis, and these two points are known : a and b are 2 and -3 (interchangeable), so the xs are the reverse -2 and 3.
