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Coordinate Geometry + Probability questions

Problem Solving — algebra and arithmetic (GMAT Focus Edition)
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Coordinate Geometry + Probability questions

by aliona » Wed Sep 09, 2009 12:18 pm
Question 1:
If K is a Line in the XY plane what is the slope of k?

1) X intercept of K is 2
2) Y intercept of K is 3


Answer: C- both statements are sufficient...


Question 2:
In the XY plane line K has positive slope and X intercept 4. If the area of the priangle formed by line K and two axes is 12 what is the y intercept of line K?

Answer: -6.


Question 3:
A certain manufacturer of cake, muffin and bread mixture has 100 buyers, of whom 50 purchase cake mixture, 40 muffin mixture and 20 - both (cake + muffin). If a buyer is to be selected at random from 100 buyers what is the probability that the buyer selected will be the one who purchases neither cake nor muffin mixture?

Answer: 3/10

In my understanding the questionis : what is the prob that the buyer will be a bread mixture buyer, right?

Any help would be appreciated!
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by bharathh » Wed Sep 09, 2009 12:54 pm
What help do you need? You seem to have the answers :?
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by aliona » Wed Sep 09, 2009 1:29 pm
Sorry if was not specific.
The answers are from the test. I did not know how to solve these problems :-).
Hope somebody will show how to attack them.
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by bharathh » Wed Sep 09, 2009 3:25 pm
Answer to q1

An intercept is a point on the x or y axes through which a line passes through.

x intercept means the point where the line/graph intersects the x axis... i.e y=0

y intercept is the point where the line/graph intersects the y axis ... i.e x=0

So what are you supposed to do in this question? You are supposed to know if you have enough information to know what the slant of the graph is.


Statement 1:

We are told that when Y=0, X=2
So we know that the graph goes through the point (2,0)

However does that give us enough information to know what the slope is? No. There are an infinite number of lines that can be drawn through a single point. So no this statement is not sufficient.


Statement 2:

Again we know what the value of Y is when x = 0... So we know a point on the y axis that this graph passes through. You should be careful to remember that in these problems you should temporarily forget what you did with Statement 1.

You know that the graph goes through (0,3).

Again 1 point - infinite possibilities of lines. So again this statement is insufficient.


However now that we've said that we can't do much just taking each statement on its own... we look at our results from both statements. We have 2 points that the graph passes through!

(2,0) and (0,3). So we can find the slope because there is only one way a line can pass through 2 points.

Therefore we can end here and say the answer is C.
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by bharathh » Wed Sep 09, 2009 3:36 pm
Ans to Q2

We are told that the line has a positive slope. What that means is that the as the positive value of x increases, the value of y also increases and vice versa

So we know that it has an X intercept of 4. so it crosses the x axis (when y=0) when x=4

So we have one point for our graph = (4,0)

At this point let's draw what we have. Fig 1 is attached

So we know that the line will intersect the y axis at some point. The value of y will be negative because it is below the x axis.

We don't know what that point is. However note that the line makes a right angled triangle with the x and the y axis.

More importantly we know that the length of 1 side is 4 (the X intercept)

If we can somehow find the height of the triangle, we will know the value of the Y intercept.

We are given the area.

The area of a right-angled triangle is 1/2*b*h

b=4
Area = 12

So plugging in our values, h = 6.

Therefore our Y intercept is 6 away from the origin. However like I mentioned earlier, because it is below the x axis its value will be negative. So, its value is -6.
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by bharathh » Wed Sep 09, 2009 3:40 pm
Q3

This is straightforward.

I am told that there are 50 ppl who buy cake mixture and 40 ppl who buy muffin mixture.

However 20 ppl buy both of these things. So they have been counted two times (once among those who bought cake mixture and a second time among those bought muffin mixture).

So the number of ppl who only bought cake mixture = 50-20 = 30

Likewise the number of ppl who only bought muffin mixture = 40-20 = 20.

Therefore the total number of ppl that bought cake mixture and muffin mixture = 30+20+20 = 70

70 out of 100 ppl bought cake/muffin/both

So there are 100-70 ppl that did not buy either cake/muffin mixture = 30

The probability of picking one of these ppl is 30/100 = 3/10
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