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by rohittk » Thu Oct 08, 2009 1:50 am
(a) In the xy co-ordinate plane, line l and line k intersect at the point(4,3). Is the product of their slopes negative?
(1) Product of the x intercept of line l and k is positive.
(2) Product of the y intercept of the lines l and k is negative.


(b) If k is a positive integer, is k a square of an integer?
(1) K is divisible by 4.
(2) k is divisible by exactly 4 different prime numbers.


I will appreciate answers with explanations to the above two questions. Thank You.
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Source: — Data Sufficiency |
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by ershovici » Thu Oct 08, 2009 3:39 am
First one.
We need two lines, so we should make a scetch. Then try to drow this lines.
St. 1 is insufficient because their x intercept could be both positive or both negative.
St. 2 is insufficient because, because two lines could have different x intercepts and tehir slopes cold vary.
Both St. together are sufficient, and we have only one posibility - both x intercepts are positive and y intercepts - one positive and one negative.

The answer is C
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by mehravikas » Thu Oct 08, 2009 8:42 pm
I think statement 'B' is sufficient for the first question.
ershovici wrote:First one.
We need two lines, so we should make a scetch. Then try to drow this lines.
St. 1 is insufficient because their x intercept could be both positive or both negative.
St. 2 is insufficient because, because two lines could have different x intercepts and tehir slopes cold vary.
Both St. together are sufficient, and we have only one posibility - both x intercepts are positive and y intercepts - one positive and one negative.

The answer is C
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by ershovici » Fri Oct 09, 2009 3:55 am
I am still sure that the answer is C
Here is my reasoning:
Just imagine a line that intersepts Y = 1 and a line which intersepts Y at -1, if both line s also intersept a point 4:3 the product of their slopes would be positive. but if one of the lines intersept Y axis at a point greater that Y =3 and they still have both X intersepts positive, so they would have oposite slopes and their product would be positive.
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by Katrusya » Fri Oct 09, 2009 11:31 am
Rohittk,
I think in (a) the answer is C because we need to know about both Y and X interseptions in order to figure out the slopes of both lines.

(b)
1. K could be 12,16,20 - some of them are not square - not sufficient
2. Let's take for example that K is divisible by 2,3,5,and 7. Product of these gives as 210 (not square)
OR
3,5,7,11 that give us 1155 which is not square also. I think B is the answer here
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by mehravikas » Fri Oct 09, 2009 1:58 pm
My mistake - For the first question answer should be 'C' we need both the statements to find out the sign of the slopes.
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by crackgmat007 » Fri Oct 09, 2009 5:49 pm
Katrusya wrote:Rohittk,
I think in (a) the answer is C because we need to know about both Y and X interseptions in order to figure out the slopes of both lines.

(b)
1. K could be 12,16,20 - some of them are not square - not sufficient
2. Let's take for example that K is divisible by 2,3,5,and 7. Product of these gives as 210 (not square)
OR
3,5,7,11 that give us 1155 which is not square also. I think B is the answer here
I think answer is E for second question.

A - K could be 16 or 24 - not sufficient
B - Lets say the number is 3*5*7*11*3*5*7*11. This number is a perfect sqare - not sufficient

A&B K can be 3*5*7*11*2*2 (not a perfect square) or 3*5*7*11*3*5*7*11*2*2 (a perfect square) Hence E

Both 1 & 2
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by imanemekouar » Wed Jan 06, 2010 6:35 am
can you lease explain the problem. I really did not get it.
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