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jsasipriya: Senior | Next Rank: 100 Posts; Posts: 50; Joined: Sun Apr 04, 2010 7:28 amFollowed by: 1 member

by jsasipriya » Mon Aug 16, 2010 4:06 pm

In a xy plane, at what two points the graph of y=(x+a)(x+b) intersect the x-axis?

1) a+b = -1
2) the graph intersects y-axis at (0, -6)

OA C

Can someone help me with the above qn?

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Source: Beat The GMAT — Data Sufficiency | Mon Aug 16, 2010 4:06 pm

uwhusky: Legendary Member; Posts: 1172; Joined: Wed Apr 28, 2010 6:20 pmFollowed by: 4 members; Thanked: 74 times

by uwhusky » Mon Aug 16, 2010 11:51 pm

I'll give it a shot, but I am almost certain I am doing this the slow way.

In a xy plane, at what two points the graph of y=(x+a)(x+b) intersect the x-axis?

1) a+b = -1
2) the graph intersects y-axis at (0, -6)

y = x^2 + bx + ax + ab. x-intersect means that y = 0. So the goal here is to solve 0 = x^2 + bx + ax + ab.

1) x^2 + x(a + b) + ab = x^2 + (-x) + ab; 0 = x^2 + (-x) + ab; Insufficient, we need to know ab.

2) when x = 0, y = -6; (0)^2 + b(0) + a(0) + ab = -6; ab = -6. Insufficient, we don't know what b or a is.

Together sufficient, because we just needed to know what ab is to solve 1), and 2) provides exactly that.

0 = x^2 + (-x) + ab ---> 0 = x^2 -x -6 ---> (x + 2)(x - 3), x = -2, 3.

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kvcpk: Legendary Member; Posts: 1893; Joined: Sun May 30, 2010 11:48 pmFollowed by: 7 members; Thanked: 215 times

by kvcpk » Tue Aug 17, 2010 2:15 am

jsasipriya wrote:In a xy plane, at what two points the graph of y=(x+a)(x+b) intersect the x-axis?

1) a+b = -1
2) the graph intersects y-axis at (0, -6)

OA C

Can someone help me with the above qn?

y=(x+a)(x+b)
intersects the x-axis when y=0
Hence x= -a or x=-b
Hence the points are (0,-a), (0,-b)

1) a+b = -1
doesnt tell what a,b are.
INSUFF

2) the graph intersects y-axis at (0, -6)
whn x=0, y=ab
Hence -6=ab
again no info about individual values of a,b.
INSUFF

Combining:
a+b=-1
and ab=-6
2 eqtns in 2 variables.
We will get a,b values.

SUFF

pick C

hope this helps!!

"Once you start working on something,
don't be afraid of failure and don't abandon it.
People who work sincerely are the happiest."
Chanakya quotes (Indian politician, strategist and writer, 350 BC-275BC)

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