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Hi Everyone,

Came across 2 DS ques where I got stuck.

Q-1 Of the computer surveyed about the skills they required in prospective employees, 20 percent required both computer skills and writing skills. What percent of companies required neither computer skills nor writing skills?

(1) Of those companies surveyed that required computer skills, half required writing skills. (2) 45 percent of the companies surveyed required writing skills but now computer skills.

Q-2 In the xy-plane if line k has negative slope and passes through the point (-5,r), is the x-intercept of line k positive ?

(1) the slope of line K is -5 (2) r > 0

explanations would be appreciated...

Last edited by greatchap on 25 Jun 2008, 01:17, edited 1 time in total.

Stmt 1: slope is -5 and hence the equation will be y = -5x + c solving for (-5, r)

r = 25 + c or c = r - 25. Thus the equation is y = -5x + r - 25. X intercept will be (r-25)/5. This does not tell if it will be + or -. Hence, insufficient.

Combining Stmt 2: r > 0. But, r could be less than 25 or more than 25 making X intercept + or -. Hence, insufficient.

Can someone varify my answer to Q-1? I hope the final authority bunuel can confirm on this issue. However answer is C in both cases but just to check the method i am posting this. According to bigtreezl the percentage of people don't need computer or writing skill is 31% but as per my calculation i am getting 15%. Can someone confirm which one is correc? Below is provided how i arrive at 15% N(computer and writing) = 20 st-1 : half of the people are also required to know writing So N(Only writing) = N (writing and computer) = 20 st-2 N(only writing) = 45

With these two statements, 100 = N(Only writing) + (Only computer) + N(Writing and computer) + N(neither computer nor writing) 100 = 45+ 20+ 20+ X X = 15 so, 15% requireneither writing skill not computer skill.

Can someone varify my answer to Q-1? I hope the final authority bunuel can confirm on this issue. However answer is C in both cases but just to check the method i am posting this. According to bigtreezl the percentage of people don't need computer or writing skill is 31% but as per my calculation i am getting 15%. Can someone confirm which one is correc? Below is provided how i arrive at 15% N(computer and writing) = 20 st-1 : half of the people are also required to know writing So N(Only writing) = N (writing and computer) = 20 st-2 N(only writing) = 45

With these two statements, 100 = N(Only writing) + (Only computer) + N(Writing and computer) + N(neither computer nor writing) 100 = 45+ 20+ 20+ X X = 15 so, 15% requireneither writing skill not computer skill.

Yes answer is C (15%). I think making a table would be the best way to solve such kind of problems.

Note that statement (1) says that "of those companies surveyed that required computer skills, half required writing skills" --> if \(y\) required computer skills, then of those \(y\) who required computer skills, \(\frac{y}{2}\) also required writing skills (# of companies required computer and writing skills is \(\frac{y}{2}=20\)).

Does someone know what the OA for Q2 is ? I think that (2) suffices and answer should be B?

Thanks

This question can be done with graphic approach (just by drawing the lines ) or with algebraic approach. Below is algebraic approach:

In the xy-plane, if line k has negative slope and passes through the point (-5,r), is the x-intercept of line k positive?

Equation of a line in point intercept form is \(y=mx+b\), where: \(m\) is the slope of the line, \(b\) is the y-intercept of the line (the value of \(y\) for \(x=0\)), and \(x\) is the independent variable of the function \(y\).

We are told that slope of line \(k\) is negative (\(m<0\)) and it passes through the point (-5,r): \(y=mx+b\) --> \(r=-5m+b\).

Question: is x-intercept of line \(k\) positive? x-intercep is the value of \(x\) for \(y=0\) --> \(0=mx+b\) --> is \(x=-\frac{b}{m}>0\)? As we know that \(m<0\), then the question basically becomes: is \(b>0\)?.

(1) The slope of line \(k\) is -5 --> \(m=-5<0\). We've already known that slope was negative and there is no info about \(b\), hence this statement is insufficient.

(2) \(r>0\) --> \(r=-5m+b>0\) --> \(b>5m=some \ negative \ number\), as \(m<0\) we have that \(b\) is more than some negative number (\(5m\)), hence insufficient, to say whether \(b>0\).

(1)+(2) From (1) \(m=-5\) and from (2) \(r=-5m+b>0\) --> \(r=-5m+b=25+b>0\) --> \(b>-25\). Not sufficient to say whether \(b>0\).

Some notes: If the slope of a line is negative, the line WILL intersect quadrants II and IV. X and Y intersects of the line with negative slope have the same sign. Therefore if X and Y intersects are positive, the line intersects quadrant I; if negative, quadrant III.

When we take both statement together all we know is that slope is negative and that it crosses some point in II quadrant (-5, r>0) (this info is redundant as we know that if the slope of the line is negative, the line WILL intersect quadrants II). Basically we just know that the slope is negative - that's all. We can not say whether x-intercept is positive or negative from this info.

Below are two graphs with positive and negative x-intercepts. Statements that the slope=-5 and that the line crosses (-5, r>0) are satisfied.

\(y=-5x+5\):

Attachment:

graph.php.png [ 9.73 KiB | Viewed 5832 times ]

\(y=-5x-20\):

Attachment:

graph.php (1).png [ 10.17 KiB | Viewed 5837 times ]

More on this issue please check Coordinate Geometry chapter of Math Book (link in my signature).