Data Sufficiency

Hi folks...
Got a question on DS...I seem to freak out any geometry questions to do with graphs.Please help.
Q1.In the xy plane, at what two points does the graph of y=(x+a)(x+b) intersect the x-axis?
1)a+b=1
2)The graph intersects the y-axis t (0,-6)

Hi,
Is it a GMAT question, coz the graph of y = (x+a)(x+b) results in a parabola. It has 1 y-intercept and 2 x-intercepts.

Here is what I could glean .. not sure how much of this is correct.

From the Q stem, the two x intercepts are x = -a and x = -b.

1) says a+b = 1. Insufficient.

2) graph intercepts the y axis at (0,-6) => y intercept is at (0, -6).
Still insufficient, cannot find the x-intercepts.

Hence E

Can someone pls comment on this. I am not sure of this.

thanks
-Vittal

I think it could be solved from the second statement point (0,-6) exists on parabola.

--> ab=-6

--> x^2 -6x -6=0 (for solutions) solve ! therefore sufficient!

souna

sounanouna wrote:I think it could be solved from the second statement point (0,-6) exists on parabola.

--> ab=-6

--> x^2 -6x -6=0 (for solutions) solve ! therefore sufficient!

souna

Yes, it can be solved by using both the equations.

imo C

y = (x+a)(x+b) = x^2 +x(a+b) + ab

from eq 1. a+b = 1

therefore,

x^2 + x + ab = y

from eq 2. x = 0 and y = -6

therefore,

0^2 + 0 + ab = -6
or
ab = -6

so, plugging ab into the equation we get:

x^2 + x -6 = y

Now, set y = 0 to find the points where the graph intersects the x axis

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

Hence, imo C

Vittal and Souna, thanks for your response....though the answer is C.

Rohungupta thanks. for the clear explanation on getting the answer.

I have 2 more DS questions , kindly explain how to determine their sufficiency?

Q1)
A certain list consists of several different integers.Is the product of all the integers in the list positive?
1)The product of the greatest and smallest of the integers in the list is positive.
2)There is an even number of integers in the list.


Q2)
In the rectangular coordinate system,are the points (r,s) and (u,v) equidistant from the origin?
1)r+s=1
2)u=1-r and v=1-s

Q3)
What was a certain company's revenue last year?
1)Last year the company's gross profit was $4100
2)Last year the company's revenue was 50% greater than its expenses


Q4)
If the symbol @ represents either multiplication or addition,which operation does it represent?
1)a@b = b@a for all numbers a and b
2)a@(b-c)=(a@b)-(a@c) for all numbers a,b and c

Let me take a crack at this one
Q1)
A certain list consists of several different integers.Is the product of all the integers in the list positive?
1)The product of the greatest and smallest of the integers in the list is positive.
2)There is an even number of integers in the list.

Before looking at statements 1 or 2, the following can be deduced from teh Question stem
1. list could contain +ve , -Ve , 0
2. In order for the product of the list to positive any of the foll should be true.
a) All the numbers are +ve numbers.
b) If there are -ve numbers, an even number of -ve numbers should be present.

Now lets look at stmts
1. Insufficient. it talks only about hte product of 2 numbers greatest and least. The sign and magnitude of other numbers determine if the product is -ve or +ve or even 0.

2. The integers themselves can be +ve or -ve. So the product is indeterminate. So Insufficient.

1 and 2 together.
Still insufficient. lets assume that there are even number of ints (say 4 ints - {-4 , -3, 4, 5}
from 1. the product of smallest and largest is -ve number.
and from 2) there are even number of ints. The signs of the other numbers (other than smallest and largest) also play an equally important role in determining the final product.
SO E

Hope I havent missed anything.

Q1)
A certain list consists of several different integers.Is the product of all the integers in the list positive?
1)The product of the greatest and smallest of the integers in the list is positive.
2)There is an even number of integers in the list.


IMO: C
(1) in order the product of the smallest and the largest number be positive, both of them must be either negative or positive. If all the numbers are positive, then the statement would be sufficient. But, what if the integers are negative and their number is odd, it leads to ambiguity, so INSUFFICIENT to solve the problem

(2) the number of positive integers and that of negative ones can be different, so INSUFFICIENT.

Together: the product of the largest and smallest integer is positive, and the number of integers is EVEN. SO, the product of entegers is Positive.

Hence, C

Let me know if I missed smth.

Hello!

Is the Q4 a DS question?

ya i thought the same as feruza

it's C

Feruza Matyakubova wrote:Hello!

Is the Q4 a DS question?

ya it's ds question.

statement 1 is true for both multiplication and addition but statement 2 is possible only for multiplication, I therefore thinks its B.

nothinglessthan780 wrote:Vittal and Souna, thanks for your response....though the answer is C.

Rohungupta thanks. for the clear explanation on getting the answer.

I have 2 more DS questions , kindly explain how to determine their sufficiency?

Q1)
A certain list consists of several different integers.Is the product of all the integers in the list positive?
1)The product of the greatest and smallest of the integers in the list is positive.
2)There is an even number of integers in the list.


Q2)
In the rectangular coordinate system,are the points (r,s) and (u,v) equidistant from the origin?
1)r+s=1
2)u=1-r and v=1-s

Q3)
What was a certain company's revenue last year?
1)Last year the company's gross profit was $4100
2)Last year the company's revenue was 50% greater than its expenses


Q4)
If the symbol @ represents either multiplication or addition,which operation does it represent?
1)a@b = b@a for all numbers a and b
2)a@(b-c)=(a@b)-(a@c) for all numbers a,b and c

sol Q2

you can find out its sufficiency by taking different value of r and s
let r=0 than s=1....., r=1 than s=0.....r=2 than s=-1
now put this value in statement second we got value of v and u as..

for r=0 and s=1....u=1 and v=0, r=1 and s=0 ......u=0 and v=1 and for r=2 and s=-1 .....u=-1 and v=2, so by putting this value in rectangular coordinate it is clear that points (r,s) and (v,u) are equidistance from origin.