Question: Two line l and k intersect at a point (4, 3). Is the product of their slopes -1?

(1) x intercepts of line l and k are positive
(2) y intercept of line l and k are negative

1. Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.
2. Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.
3. BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.
4. EACH statement ALONE is sufficient.
5. Statements (1) and (2) TOGETHER are not sufficient.

Correct Answer: B
Solution and Explanation:
Approach Solution 1:
IF....

X-intercept of K = 1
X-intercept of L = 2

The lines are NOT perpendicular and the answer to the question is NO.

IF.....

X-intercept of K = 1
X-intercept of L = 7

The lines ARE perpendicular and the answer to the question is YES.

Fact 1 is INSUFFICIENT
Fact 2: The Y-intercepts of both lines are negative.

This Fact proves that the slopes of BOTH lines are positive (since they cross the Y-axis at a negative number then move UP and to the RIGHT to the point (4,3)), so there is NO WAY for them to cross and be perpendicular. The answer to the question is ALWAYS NO.
Fact 2 is SUFFICIENT.

Approach Solution 2:
Statement 1:
x intercepts of line l and k are positive. Lines may be located on many options, including perpendicular manners. Answer Yes and No. So, INSUFFICIENT

Statement 2:
y intercepts of line l and k are negative. Both lines cannot have negative y intercept if they are perpendicular. Answer No. SUFFICIENT

Approach Solution 3:
If two lines are perpendicular to each other, the slope of one will be the negative reciprocal of the slope of the other (that is, if one slope is m, the other slope will be -1/m). 'Is the product of their slopes -1?' is just another way of asking whether this is true, since m(-1/m) = -1. So, translate the question as "are the two lines perpendicular?"

Now, let's draw. The goal is to prove insufficiency, so we'll be trying to draw, if possible, two pairs of lines for each statement: one pair that fits the statement and IS perpendicular, and one pair that fits the statement and ISN'T perpendicular. If that's impossible, then the statement must be sufficient.

Statement 1: both x intercepts are positive. That is, they both intercept the x axis to the right of 0.

Here's a perpendicular pair of lines that fits:

Here's a non perpendicular pair of lines that fits:

Statement 2: Both y intercepts are negative. That is, they both intercept the y axis below 0.
Here's a NON perpendicular pair of lines that fits:

However, it isn't possible to draw a pair of perpendicular lines that fit both the info in the question stem (intersect at (4,3)) and this statement. The angle between the two lines, marked here, is always going to be significantly less than 90 degrees if we only use lines that have negative y intercepts.

Therefore, using this statement, the answer to the question is definitely "no." So, the statement is sufficient and the answer is B.

“Two line l and k intersect at a point (4, 3). Is the product of their”- is a topic of the GMAT Quantitative reasoning section of GMAT. GMAT Quant section consists of a total of 31 questions. GMAT Data Sufficiency questions consist of a problem statement followed by two factual statements. GMAT data sufficiency comprises 15 questions which are two-fifths of the total 31 GMAT quant questions.

Suggested GMAT Data Sufficiency Questions

• What is x? (1) |x| < 2 (2) |x| = 3x – 2 GMAT Data Sufficiency
• Is P – 1 Even?, GMAT Data Sufficiency
• Buster Leaves the Trailer at Noon and Walks Towards the Studio at a Constant Rate of B Miles Per Hour., GMAT Data Sufficiency
• If ab = ac is b = 2?, GMAT Data Sufficiency
• The symbol ∆ Denotes One of The Four Arithmetic Operations GMAT DATA Sufficiency, GMAT Data Sufficiency
• Is Quadrilateral ABCD a Rectangle?, GMAT Data Sufficiency
• If \(x^2\)=\(2^x\), What is the Value of x ?, GMAT Data Sufficiency
• A Pentagon With 5 Sides Of Equal Length And 5 Interior Angles Of Equal measure is Inscribed in a Circle, GMAT Data Sufficiency
• If m is a positive integer, is \(\sqrt{m}>25\) ? , GMAT Data Sufficiency
• What is the value of \(6x^2+9y^2\)?, GMAT Data Sufficiency
• If x and y are integers and \(x=\frac{y}{5}+2\) , is xy even?, GMAT Data Sufficiency
• A rectangular solid has length, width, and height of L cm, W cm, and H cm, respectively GMAT Data Sufficiency
• What is the circumference of circle C ? (1) The radius of circle C is 2π GMAT Data Sufficiency
• Triangle ABC is right angled at B. BD, the median to hypotenuse AC, is 5 units GMAT Data Sufficiency
• If each side of parallelogram P has length 1, what is the area of P? GMAT Data Sufficiency
• Is the positive integer n a multiple of 24? GMAT Data Sufficiency
• Did Insurance Company K have More than $300 Million in Total Net Profits Last Year? GMAT Data Sufficiency
• Is 1/(a - b) > b - a ? GMAT Data Sufficiency
• Is |x-10| > |x-30| GMAT Data Sufficiency
• If J≠0, What Is The Value Of J? GMAT Data Sufficiency
• When 120 is Divided by Positive Single-Digit Integer M the Remainder GMAT Data Sufficiency
• There are twenty students in a class, all of whom scored between 0 and 100 GMAT Data Sufficiency
• There are 8 red tegu lizards in the reptile house at a local zoo GMAT Data Sufficiency
• A certain fruit stand sold a total of 76 oranges to 19 customers GMAT Data Sufficiency
• Three dice, each with faces numbered 1 through 6, were tossed onto a game board GMAT Data Sufficiency
• If Jeff has four movies, and must choose to watch either 1, 2, or 3 different movies GMAT Data Sufficiency
• Jeff plans to lose weight by reducing his daily calorie intake each we GMAT data sufficiency
• Given that (P + 2Q) is a positive number, what is the value of (P + 2Q)? GMAT Data Sufficiency
• Bonnie Can Paint a Stolen Car in x hours, and Clyde Can Paint GMAT Data Sufficiency
• Alice has $15, which is enough to buy 11 muffins and GMAT Data Sufficiency
• The product of three distinct positive integers is equal to the GMAT Data Sufficiency
• What is the total value of Company H's stock? GMAT Data Sufficiency
• Is PQ > 1? GMAT Data Sufficiency
• How Many of the Students in a Certain Class are Taking Both a History and a Science Course? GMAT Data Sufficiency
• The Set S of Numbers has the following Properties GMAT Data Sufficiency
• A Contractor Combined x Tons of a Gravel Mixture that Contained 10 percent Gravel G GMAT Data Sufficiency
• If Jeff has four movies, and must choose to watch either 1, 2, or 3 different movies GMAT Data Sufficiency
• From a Group of M Employees, N Will be Selected, at Random, GMAT Data Sufficiency
• Given that (P + 2Q) is a positive number, what is the value of (P + 2Q)? GMAT Data Sufficiency
• Juan Bought Some Paperback Books That Cost $8 GMAT Data Sufficiency
• The symbol ∆ Denotes One of The Four Arithmetic Operations GMAT DATA Sufficiency
• X is Older Than Y, Z Is Younger Than W And V is Older Than Y. Is Z Younger Than X? GMAT Data Sufficiency
• 2x+3y GMAT Critical Reasoning
• The Selling Price of an Article is Equal to the Cost of the Article GMAT Critical Reasoning
• Equilateral triangle BDF Is Inscribed in Equilateral Triangle ACE GMAT Data Sufficiency
• What is the value of x if x^3 < x^2? GMAT Data Sufficiency
• If x ≠0, then what is the value of (|x|)x? GMAT Data Sufficiency
• What is the probability that a student randomly selected from a class of 60 students will be a male who has brown hair? GMAT Data Sufficiency
• Does The Equation y = (x – p)(x – q) Intercept The x-axis At GMAT Data Sufficiency
• S is a Set of n Consecutive Positive Integers. Is the Mean of the Set GMAT Data Sufficiency