y = (x-p)(x-q)
For x-intercept to be (2,0)
0 = (2-p)(2-q)
So we need to check whether either of p or q is 2...
Statement 1
pq = -8
value of p and q can b anything
-1*8
-8*1
2*-4
...
Insufficient
Statement 2
-2 - p = q
We are still not sure of values of p and q
Combining Statement 1 and 2
pq = -8
-2 -p = q
p = -4
q = 2
therefore x-intercept of the equation is (2,0)
Option C
X-axis
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Source: Beat The GMAT — Data Sufficiency |
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rijul007
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gmatblood wrote:Hi,
Could you please explain this part,
For x-intercept to be (2,0)
0 = (2-p)(2-q)
So we need to check whether either of p or q is 2...
thanks.
The equation is
y = (x-p)(x-q)
What do we do to find the x-intercept???
x-intercept is supposed to lie on the x-axis, which is y = 0.
so we substitute y=0 in the equation,
0 = (x-p)(x-q)
This equation tells us that value of x should either be equal to p or q......
Acc to the ques., x-intercept = (2,0)
here x = 2
This means either p or q has to be 2.
Now you need to check which statement tells that...
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HSPA
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I have y = x^2 - (p+q)x + pq
From option 1: I have pq
From option 2: I have p+q
Thus I can solve the quadratic equation x^2+2x-8 = (x+4)(x-2)
Thus when x =2 y=0 hence proved..
From option 1: I have pq
From option 2: I have p+q
Thus I can solve the quadratic equation x^2+2x-8 = (x+4)(x-2)
Thus when x =2 y=0 hence proved..
First take: 640 (50M, 27V) - RC needs 300% improvement
Second take: coming soon..
Regards,
HSPA.
Second take: coming soon..
Regards,
HSPA.
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zeusunlimited
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my 0.02$
for P(2,0),
y=0=(x-p)(x-q)=x^2-px-qx+pq
thus 0=4-2(p+q)-8
0=-4-2(p+q)
4=-2(p+q)
thus p+q=-2 & p= -2-q
subsituting
-8=pq=q(-2-q)=-2q-q^2
thus q^2+2q-8=0
s0(q+4)(q-2)=0
so if q=-4,p=2 and if q=2,p=-4.
either case, it satisfies the intercept at(2,0) and is sufficient.
similarly, you can solve for -2-p=q
for P(2,0),
y=0=(x-p)(x-q)=x^2-px-qx+pq
thus 0=4-2(p+q)-8
0=-4-2(p+q)
4=-2(p+q)
thus p+q=-2 & p= -2-q
subsituting
-8=pq=q(-2-q)=-2q-q^2
thus q^2+2q-8=0
s0(q+4)(q-2)=0
so if q=-4,p=2 and if q=2,p=-4.
either case, it satisfies the intercept at(2,0) and is sufficient.
similarly, you can solve for -2-p=q
