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by gdk800 » Mon Dec 06, 2010 4:11 am
Q1) Does line k intersect quadrant II?
a. Slope of k is -1/6
b. Y intercept of k is -6

OA is A

Q2) Lines n and p lie in xy plane. Is slope of line n less than slope of line p?
a. Lines n and p intersect at (5, 1)
b. Y-intercept of line n is greater than y intercept of line p

OA is C
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Source: — Data Sufficiency |

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by Rahul@gurome » Mon Dec 06, 2010 4:47 am
gdk800 wrote:Q1) Does line k intersect quadrant II?
a. Slope of k is -1/6
b. Y intercept of k is -6
The answer to this question lies in the facts that:
  • 1. If slope of a line is positive then,
    • A) It'll always intersect 1st and 3rd quadrant.
      B) It'll intersect 2nd quadrant if the y-intercept is positive.
      C) It'll intersect 4th quadrant if the y-intercept is negative.
      D) It'll not intersect 2nd or 4th quadrant and pass through origin if y-intercept is zero.
    2. If slope of a line is negative then,
    • A) It'll always intersect 2nd and 4th quadrant.
      B) It'll intersect 1st quadrant if the y-intercept is positive.
      C) It'll intersect 3rd quadrant if the y-intercept is negative.
      D) It'll not intersect 1st or 3rd quadrant and pass through origin if y-intercept is zero.
There is mathematical proof for all of these. But better way to understand them is draw various types of lines in the xy plane and try to visualize each of the cases individually. Let me know if you have any problem.


Statement 1: Slope of k is -1/6
As the slope of k is negative it'll always intersect 2nd and 4th quadrant.

Sufficient.

Statement 2: y-intercept of k is -6
If slope of k is negative it'll always intersect 2nd quadrant.
But if slope of k is positive then it'll not intersect 2nd quadrant as the y-intercept is negative.

Not sufficient.

The correct answer is A.
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by Rahul@gurome » Mon Dec 06, 2010 5:49 am
gdk800 wrote:Q2) Lines n and p lie in xy plane. Is slope of line n less than slope of line p?
a. Lines n and p intersect at (5, 1)
b. Y-intercept of line n is greater than y intercept of line p
Given: Say equation of the line n is y = nx + a and equation of line p is y = px + b, where n and p are slopes of the lines and a and b are the y-intercepts of the lines respectively.
We need to determine whether n is greater than p or not.

Statement 1: Lines n and p intersect at (5, 1)
Therefore,
  • 1 = 5n + a
    1= 5p + b
Thus, (5n + a) = (5p + b) => (n - p) = (b - a)/5

As we don't know the relation between a and b, we can't determine whether n is greater than p or not.

Not sufficient.

Statement 2: Y-intercept of line n is greater than y intercept of line p
Therefore, a > b
This is clearly not enough to determine whether n is greater than p or not.

Not sufficient.

1 & 2 Together: Combining the above relations,
Thus, (n - p) = (b - a)/5 < 0 , as a > b => (b - a) < 0
=> n < p

Sufficient.

The correct answer is C.
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by gdk800 » Mon Dec 06, 2010 2:00 pm
Thanks for the detailed explanations Rahul. Hope you won't mind tackling some more.

Q3: Each employee is either a director or a manager. What % of the employees are directors?
a. The average salary of managers is $5000 less than the average of all employees
b. The average salary of directors is $15000 greater than the average of all employees

[spoiler]OA is C
[/spoiler]

Q4: Sum of positive integers x and y is 72. What is xy?
a. x = y + 1
b. x and y have same tens digit

OA is D
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by clock60 » Mon Dec 06, 2010 3:23 pm
i am not master in math, but i saw these problems ealier, sothink that can explain at least 1 one
employer=x. directors=y. we need to find y/(x+y), also a-mean salary of all work force
(1) av salary of x=a-5 insuff
(2) av salary of y=a+15 insuff
in common, total=average*number of terms, number of terms here the number of x, or y.average we are given from each st
both. a-av salary of total work force=(total salary of all)/(total number of work force), here we need weighted average
a= ((av salary of x)*x+(av salary of y)*y)/(x+y). we are given the av salary of x and y from st 1 and 2
a=((a-5)*x+(a+15)*y)/(x+y)
ax+ay=ax-5x+ay+15y, cancel ax and ay left with 5x=15y.x=3y. y/(3y+y)=y/4y=1/4-out target both are suff
to understand it better consider example
in 3 days i solved 10 problems , and in the next 5 days i solved 20 problems what is av number of problems solved in a day
a=(3*10+5*20)/(3+5)=16,25
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by clock60 » Mon Dec 06, 2010 3:27 pm
as for the next problem i am not sure in its truth
we are given that x+y=72, and from 1 st x and y are consecutive integers, it happens that one is even and other is odd
so their sum must be odd ( odd +even=odd) but in the condition x+y=72-even???
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by goyalsau » Mon Dec 06, 2010 8:48 pm
gdk800 wrote:Q1) Does line k intersect quadrant II?
a. Slope of k is -1/6
b. Y intercept of k is -6

OA is A

Q2) Lines n and p lie in xy plane. Is slope of line n less than slope of line p?
a. Lines n and p intersect at (5, 1)
b. Y-intercept of line n is greater than y intercept of line p

OA is C
I would recommend you to go through this link, It will be very Helpful

https://www.mathsisfun.com/data/straight_line_graph.html
Saurabh Goyal
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by tomada » Tue Dec 07, 2010 10:45 am
Q4 has me intrigued. You said X and Y are both integers, and their sum = 72
In Statement (1), X=Y+1. Plugging into X+Y=72, we get (Y+1) + Y = 72, or 2Y+1 = 72 or 2Y = 71, but then Y is not an integer.

gdk800 wrote:Thanks for the detailed explanations Rahul. Hope you won't mind tackling some more.

Q3: Each employee is either a director or a manager. What % of the employees are directors?
a. The average salary of managers is $5000 less than the average of all employees
b. The average salary of directors is $15000 greater than the average of all employees

[spoiler]OA is C
[/spoiler]

Q4: Sum of positive integers x and y is 72. What is xy?
a. x = y + 1
b. x and y have same tens digit

OA is D
I'm really old, but I'll never be too old to become more educated.
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by gdk800 » Wed Dec 08, 2010 7:05 am
@tomada: This is exactly what has befuddled me. That is the reason this question is here on the forum. I also want to reconfirm whether its the right question that i have got?

Anyways, i am going to put up few more very soon.

Thanks for your reverts.
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