Hi,
Thanks ... Interesting question ...
1. -a and -b are the points where the curve meets the x-axis. However, we do not know their numeric values
a + b = -1
Implies a = 5 and b = -6
or
a = 10 and b = -11 (besides the millions of other possibilities). Hence, Insuff.
2.
y = (x + a) (x + b)
If (0,-6) lies on this graph, then
-6 = (0+a) * (0+b)
ab = -6
This implies a = -3 and b = 2
or
a = -6 and b = 1 (besides other possibilities). Hence, insuff
3. Combine both
a + b = -1
ab = -6
Here, a = -3 and b = 2
or
a = 2 and b = -3
However, the curve becomes y = (x + 2) (x - 3). The curve passes through (-2,0) and (3,0). Hence, suff.
My take is C. Please correct / confirm.
Thanks !
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xy plane graph intersect the x-axis
Source: Beat The GMAT — Data Sufficiency |
Given: y = (x + a)(x + b)
Implies the graph intersects x-axis at x = -a or x = -b.
Thus we have to find the values of a and b.
Statement 1: (a + b) = -1
Infinite numbers of values are possible for a and b.
Not sufficient.
Statement 2: The graph intersects y-axis at (0, -6)
For x = 0, y = (0 + a)(0 + b) = ab = -6
Infinite numbers of values are possible for a and b.
Not sufficient.
1 and 2 Together: (a + b) = -1 and ab = -6
Now, (a - b)² = (a + b)² - 4ab = (-1)² - 4*(-6) = 25
=> (a - b) = ±5
Thus, either (a = 2, b = -3) or (a = -3, b = 2)
In both of the cases the graph intersects x-axis at x = -3 and x = 2.
Sufficient.
The correct answer is C.
Implies the graph intersects x-axis at x = -a or x = -b.
Thus we have to find the values of a and b.
Statement 1: (a + b) = -1
Infinite numbers of values are possible for a and b.
Not sufficient.
Statement 2: The graph intersects y-axis at (0, -6)
For x = 0, y = (0 + a)(0 + b) = ab = -6
Infinite numbers of values are possible for a and b.
Not sufficient.
1 and 2 Together: (a + b) = -1 and ab = -6
Now, (a - b)² = (a + b)² - 4ab = (-1)² - 4*(-6) = 25
=> (a - b) = ±5
Thus, either (a = 2, b = -3) or (a = -3, b = 2)
In both of the cases the graph intersects x-axis at x = -3 and x = 2.
Sufficient.
The correct answer is C.
Rahul Lakhani
Quant Expert
Gurome, Inc.
https://www.GuroMe.com
On MBA sabbatical (at ISB) for 2011-12 - will stay active as time permits
1-800-566-4043 (USA)
+91-99201 32411 (India)
Quant Expert
Gurome, Inc.
https://www.GuroMe.com
On MBA sabbatical (at ISB) for 2011-12 - will stay active as time permits
1-800-566-4043 (USA)
+91-99201 32411 (India)
