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Nijo: Senior | Next Rank: 100 Posts; Posts: 45; Joined: Thu Jun 12, 2014 8:41 pm; Thanked: 1 times

by Nijo » Fri Aug 15, 2014 5:38 am

What is the y-intercept of line l?
1) Slope of line l is 3 times its y intercept
2) X intercept of the line is -1/3

OA is E

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Source: Beat The GMAT — Data Sufficiency | Fri Aug 15, 2014 5:38 am

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Brent@GMATPrepNow: GMAT Instructor; Posts: 16207; Joined: Mon Dec 08, 2008 6:26 pmFollowed by: 1268 members; Location: Vancouver, BC; Thanked: 5254 times; GMAT Score:770

by Brent@GMATPrepNow » Fri Aug 15, 2014 5:45 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)

NOTE: When posting questions, please use the spoiler function to hide the correct answer. This will allow others to attempt the question without seeing the final answer.

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 1 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:

Both lines satisfy the conditions in statements 1 and 2, however the y-intercepts are different.

Cheers,
Brent

Brent Hanneson - Creator of GMATPrepNow.com

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GMATGuruNY: GMAT Instructor; Posts: 15539; Joined: Tue May 25, 2010 12:04 pmFollowed by: 1906 members; Location: New York, NY; Thanked: 13060 times; GMAT Score:790

by GMATGuruNY » Fri Aug 15, 2014 5:53 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)

An alternate approach is to TEST CASES.

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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GMATinsight: Legendary Member; Posts: 1100; Joined: Sat May 10, 2014 11:34 pmFollowed by: 24 members; Location: New Delhi, India; Thanked: 205 times

by GMATinsight » Fri Aug 15, 2014 11:36 am

Nijo wrote:What is the y-intercept of line l?
1) Slope of line l is 3 times its y intercept
2) X intercept of the line is -1/3

OA is E

CONCEPT : To specify a Line on X-Y Plot we need two inputs
e.g. X-Intercept and Slope
or Y-Intercept and Slope
or X-Intercept and Y-Intercept
or any two points on the line

Question : Y intercept of the Line?

Statement 1) Slope = 3 x Y-Intercept
Infinite values of slopes are possible and therefore infinite of Y intercepts

INSUFFICIENT

Statement 2) X intercept of the line is -1/3
For the same X-Intercept, Line may have positive or negative slope therefore various values of Y-Intercepts are possible

INSUFFICIENT

Combining the two Statements
For a Given X-Intercept, Line may have positive or negative slope therefore various values of Y-Intercepts are possible
INSUFFICIENT

Answer: Option E

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Matt@VeritasPrep: GMAT Instructor; Posts: 2630; Joined: Wed Sep 12, 2012 3:32 pmFollowed by: 119 members; Location: East Bay all the way; Thanked: 625 times; GMAT Score:780

by Matt@VeritasPrep » Sun Aug 17, 2014 4:49 pm

Just to piggyback on Brent's response, we know that the x-intercept of the line y = mx + b is -b/m. (Supposing that m is not 0.) Here's how!

Suppose we have the line y = mx + b. At the x-intercept, we know the y-value will be 0, so this gives us the equation 0 = mx + b. Subtracting b from both sides gives -b = mx. We then divide by m to find -b/m.

This is a useful trick to remember, not least for a question like this.

S1 tells us that m = 3b. Not sufficient.
S2 tells us that -1/3 = -b/m, which (after crossmultiplying) is just m = 3b. Not sufficient either.
S1 + S2 just says the same thing twice, so the answer is E.

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