DS problem - could not understand
This topic has expert replies
- Uva@90
- Master | Next Rank: 500 Posts
- Posts: 490
- Joined: Thu Jul 04, 2013 7:30 am
- Location: Chennai, India
- Thanked: 83 times
- Followed by:5 members
Hi Pradeepss,
Given : Y= (X+a)(X+b) ---(1)
To Find : At which point does statement (1) intersect X-axis.
We know that along the line of X-axis the value of Y is 0.
So, 0 = (X+a)(X+b) => X=-a;X=-b;
If we find the value of 'a' and 'b' we can find the two points.
Statement 1: a+b=-1 -----(2), which is not enough to find the value of 'a' and 'b'(Two variabless one equation). So insufficient.
Statement 2: The graph passes through the point (0,-6). Substitute the point in the statement (1).
-6 = (a)(b) => ab=-6-----(3). Which is insufficient to find the value of 'a' and 'b'(Two variables one equation).
Combining Statement 1 and statement 2:
Solve for the equation (2) and (3). Yes, Two equation and two variables we can now get the value of 'a' and 'b'. Hence Sufficient.
OA is C
Regards,
Uva.
-----------------------------------------------------------
Correct me if I am wrong.
GMAT/MBA Expert
- Brent@GMATPrepNow
- GMAT Instructor
- Posts: 16207
- Joined: Mon Dec 08, 2008 6:26 pm
- Location: Vancouver, BC
- Thanked: 5254 times
- Followed by:1268 members
- GMAT Score:770
Uva's solution is great. I thought I'd add my solution because it addresses the two statements combined in a little more detail.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 at (0, -6)
Target question: At which two points of the graph does y=(x+a)(x+b) intersect the x-axis?
IMPORTANT: Let's examine the point where a line (or curve) crosses the x-axis. At the point of intersection, the point is on the x-axis, which means that the y-coordinate of that point is 0. So, for example, to find where the line y=2x+3 crosses the x-axis, we let y=0 and solve for x. We get: 0 = 2x+3
When we solve this for x, we get x= -3/2.
So, the line y=2x+3 crosses the x-axis at (-3/2, 0)
Likewise, to determine the point where y = (x + a)(x + b) crosses the x axis, let y=0 and solve for x.
We get: 0 = (x + a)(x + b), which means x=-a or x=-b
This means that y = (x + a)(x + b) crosses the x axis at (-a, 0) and (-b, 0)
So, to solve this question, we need the values of a and b
Aside: y = (x + a)(x + b) is actually a parabola. This explains why it crosses the x axis at two points.
Now let's rephrase the target question:
Rephrased target question: What are the values of a and b?
Statement 1: a + b = -1
There's no way we can use this to determine the values of a and b.
Since we can answer the target question with certainty, statement 1 is NOT SUFFICIENT
Statement 2: The line intercepts the y axis at (0,-6)
This tells us that when x = 0, y = -6
When we plug x = 0 and y = -6 into the equation y = (x + a)(x + b), we get -6 = (0 + a)(0 + b), which tells us that ab=-6
In other words, statement 2 is a fancy way to tell us that ab = -6
Since there's no way we can use this information to determine the values of a and b, statement 2 is NOT SUFFICIENT
Statements 1 and 2 combined:
Statement 1 tells us that a+b = -1
Statement 2 tells us that ab = -6
Rewrite equation 1 as a = -1 - b
Then take equation 2 and replace a with (-1 - b) to get: (-1 - b)(b) = -6
Expand: -b - b^2 = -6
Set equal to zero: b^2 + b - 6 = 0
Factor: (b+3)(b-2) = 0
So, b= -3 or b= 2
When b = -3, a = 2 and when b = 2, a = -3
In both cases, the two points of intersection are (3, 0) and (-2, 0)
Since we can answer the target question with certainty, the combined statements are SUFFICIENT
Answer = C
Cheers,
Brent