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Help me with those 2 Datta Sufficiency problems

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Help me with those 2 Datta Sufficiency problems

by sapuna » Thu Jul 17, 2014 11:07 am
Since there are images, I uploaded them to a site
here are the links

problem # 1 : https://prikachi.com/images.php?images/242/7476242Q.jpg

problem # 2 :https://prikachi.com/images.php?images/245/7476245x.jpg

p.s. The answers I`ve marked are WRONG. I can tell you which ones are the correct , but I`d like you to explain them first if possible.

Thank you in advance !
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Source: — Data Sufficiency |
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by GMATGuruNY » Thu Jul 17, 2014 11:38 am
In the xy-plane, what is the y-intercept of line L?

(1) The slope of line L is 3 times its y-intercept
(2) The x-intercept of line L is (-1/3)
The equation of a line is y = mx + b, where m is the slope and b is the y-intercept.

Statement 1: The slope of line L is 3 times its y-intercept
Case 1: b=1
Since the slope is 3 times the y-intercept, m = 3b = 3*1 = 3.
Resulting equation:
y = 3x + 1.
In this case, the y-intercept is 1.

Case 2: b=2
Since the slope is 3 times the y-intercept, m = 3b = 3*2 = 6.
Resulting equation:
y = 6x + 2.
In this case, the y-intercept is 2.

Since the y-intercept can be different values, INSUFFICIENT.

Statement 2: The x-intercept of line L is -1/3
Implication:
(-1/3, 0) is on line L.
Check whether (-1/3, 0) is on the lines yielded by Cases 1 and 2.

Case 1: y = 3x + 1
(-1/3, 0) is on this line.
Thus, it's possible that the equation for line L is y = 3x + 1, in which case the y-intercept is 1.

Case 2: y = 6x + 2
(-1/3, 0) is on this line.
Thus, it's possible that the equation for line L is y = 6x + 2, in which case the y-intercept is 2.

Since the y-intercept can be different values, INSUFFICIENT.

Statements combined:
Since both statements are satisfied by Cases 1 and 2, it's possible that the y-intercept is 1 or that the y-intercept is 2.
Since the y-intercept can be different values, INSUFFICIENT.

The correct answer is E.
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by Brent@GMATPrepNow » Thu Jul 17, 2014 11:40 am
In the xy-plane, what is the y-intercept of line l?

1) the slope of line l is 3 times its y-intercept
2) the x-intercept of line l is -(1/3)
Target question: What is the y-intercept of line L?

IMPORTANT: If the x-intercept is -1/3 (as per statement 2), the slope of the line is GUARANTEED to be 3 times its y-intercept (as per statement 1).

Here's why...
From statement 2, we know that (-1/3, 0) is one point on the line. Let's let (0, k) be the coordinates of the y-intercept of the line. In other words, let's let the y-intercept equal k.
Using the slope formula, the slope = (k - 0)/(0 - (-1/3)) = k/(1/3) = 3k
So, if the y-intercept is k, the slope must be 3k.

In other words, statement 1 provides no new information beyond the information that statement 2 provides. So, if statement 2 is sufficient, then statement 1 must also be sufficient (since it provides no new info). Conversely, if statement 2 is NOT sufficient, then statement 1 is NOT sufficient. At this point, we know that the answer must be either D (they're both sufficient) or E (neither is sufficient).

So, which is it?

Well, if we examine statement 2 on its own (the x-intercept is -1/3), we can see that we do not have enough information to determine the y-intercept of line L.
Since we cannot answer the target question with certainty, statement 2 is NOT SUFFICIENT
Since statement 1 provides no additional information, it too is NOT SUFFICIENT.
So, the combined statements are NOT SUFFICIENT

Answer = E

For additional proof, consider these two lines:
Image
Both lines satisfy the conditions in statements 1 and 2, however the y-intercepts are different.

Cheers,
Brent
Last edited by Brent@GMATPrepNow on Sun Jul 31, 2016 6:01 am, edited 1 time in total.
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by Brent@GMATPrepNow » Thu Jul 17, 2014 11:41 am
NOTE: In the future, please post only one question per thread. Otherwise things can become pretty complicated when there are discussions on multiple questions.

Cheers,
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by sapuna » Thu Jul 17, 2014 12:59 pm
Brent@GMATPrepNow wrote:NOTE: In the future, please post only one question per thread. Otherwise things can become pretty complicated when there are discussions on multiple questions.

Cheers,
Brent
Thank you both for your quick reply.

Sorry for the two questions . I`ll keep that in mind from now on.

p.s. Should I post a new thread for the first problem or will we address it here ?
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by GMATinsight » Thu Jul 17, 2014 6:51 pm
The answer to the first question is as follows:

Image

Image
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by GMATGuruNY » Thu Jul 17, 2014 6:59 pm
Image

In the figure above, if x and y are each less than 90 and PS||QR, is the length of segment PQ less than the length of segment SR ?

(1) x>y

(2) x+y>90

Statement 1: x>y
EXAGGERATE the difference.
Redraw the figure so that x is MUCH, MUCH BIGGER than y.
Case 1:
Image
With the figure redrawn, it's easy to see that PQ < SR.
SUFFICIENT.

Statement 2: x+y > 90
Case 1 also satisfies statement 2:
Image

Case 2 is also possible:
Image

Since PQ < SR in Case but PQ > SR in Case 2, INSUFFICIENT.

The correct answer is A.
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by GMATinsight » Fri Jul 18, 2014 10:48 pm
In the xy-plane, what is the y-intercept of line L?

(1) The slope of line L is 3 times its y-intercept
(2) The x-intercept of line L is (-1/3)
In the least word I would like to explain this question in the following manner (alongwith building generalized concepts)

Statement 1) The slope of line L is 3 times its y-intercept
Slope of line can be positive or Negative both therefore Y intercept can also be Positive or negative
therefore INSUFFICIENT
[Learning: Slope of line (except infinite slope i.e line parallel to Y-axis) has nothing to do with y-intercept because line with any slope can have any value of y-intercept]

Statement 2) The x-intercept of line L is (-1/3)
For any X-intercept of line, Y intercept can also be Positive or negative
therefore INSUFFICIENT
[Learning: X-intercept of line doesn't specify the slope of the line therefore the specific graph of line can't be drawn. To identify the exact graph we need either slope or another point that the line passes through alongwith X-intercept of the line]

Combining the statements gives us X-intecept but doesn't give us the slope instead it only gives a relation between slope and Y-intercept which can be positive or negative both.
Therefore INSUFFICIENT

Answer: Option E
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