Problem Solving

Which of the following equations represents a line that is
perpendicular to the line described by the equation 3x + 4y = 8 ?
· 3x + 4y = 18
· 3x - 4y = 24
· 4y - 3x = 26
· 1.5y + 2x = 18
· 8x - 6y = 24

Which of the following equations represents a line that is perpendicular to the line described by the equation 3x + 4y = 8 ?

Slope of the line 3x + 4y = 8 is -3/4. Slope of a line perpendicular to the line 3x + 4y = 8 is 4/3
(product of slopes of a line and a line perpendicular to it is -1)
A)3x + 4y = 18 - Slope of this line is -3/4. Incorrect answer choice.
B)3x - 4y = 24 - Slope of this line is 3/4.Incorrect answer choice.
C)4y - 3x = 26 - Slope of this line is 3/4. Incorrect answer choice.
D)1.5y + 2x = 18 - Slope of this line is -4/3. Incorrect answer choice.
E)8x - 6y = 24 - Slope of this line is 4/3. Bingo!

GmatKiss wrote:Which of the following equations represents a line that is
perpendicular to the line described by the equation 3x + 4y = 8 ?
· 3x + 4y = 18
· 3x - 4y = 24
· 4y - 3x = 26
· 1.5y + 2x = 18
· 8x - 6y = 24

Hi!

Although it may be somewhat time-consuming, your best bet is to rewrite the equation in the stem and in each choice into standard y=mx+b form - that way you'll be able to quickly compare the slopes.

Original:

3x + 4y = 8
4y = -3x - 8
y = -3/4(x) - 8

Slope = -3/4

Since perpendicular lines have negative inverse slopes, we want the slope in the answer to be +4/3.

One time-saver we can note is that for slope, the constant in the equation is irrelevant; accordingly, when we rewrite the choices we only worry about the x and y terms.

A) 3x + 4y = blah
4y = -3x + blah
STOP!! This line will have a negative slope: eliminate.

B) 3x - 4y = blah
-4y = -3x + blah
y = 3/4(x)+ blah
Slope of 3/4, we want 4/3: elminate

C) 4y - 3x = blah
4y = 3x
same as (B): eliminate

D) 1.5y + 2x = blah
1.5y = -2x + blah
STOP: negative slope: eliminate

On test day we should just stop and pick (E), but let's finish the work for practice:

E) 8x - 6y = blah
-6y = -8x + blah
y = 8/6x + blah
8/6 = 4/3... ding ding ding!!

Now, if we knew a fun statistical fact about the GMAT, we'd have done far less work. That fact is:

on problem solving questions including the phrase "which of the following", the answer is D or E more often than it should be by random selection.

Accordingly, on problem solving questions with the phrase "which of the following", if you're testing the choices start at the bottom and work your way up!

Anurag@Gurome wrote:

GmatKiss wrote:Which of the following equations represents a line that is
perpendicular to the line described by the equation 3x + 4y = 8 ?
· 3x + 4y = 18
· 3x - 4y = 24
· 4y - 3x = 26
· 1.5y + 2x = 18
· 8x - 6y = 24

3x + 4y = 8 or 4y = 8 - 3x
y = -3x/4 + 2
The line which will be perpendicular to the above line, should have a slope of 4/3, since the product of slope of perpendicular lines is -1.

So, let us check the answer choices to see which line has a slope of 4/3.

(A) 3x + 4y = 18 or y = -3x/4 + 9/2; here slope = -3/4
(B) 3x - 4y = 24 or y = 3x/4 - 6; here slope = 3/4
(C) 4y - 3x = 26 or y = 3x/4 + 13/2; here slope = 3/4
(D) 1.5y + 2x = 18 or y = -2x/1.5 + 18/1.5; here slope = -4/3
(E) 8x - 6y = 24 or y = 4x/3 - 4; here slope = 4/3

So, the correct answer is E.

Wonderful, you are the king of co-ordinate geometry

I took a different approach to this and sort of became stuck. My approach might be more algebra, can someone explain why it didn't work?

I got the original line equation
y = -(3/4)x + 2
Therefore, the perpendicular line equation is:
y = (4/3)x + 2

I looked for this same equation or a multiple of it in the answer choices and could not find it. I see from the approaches given here that answer is E; however, was it possible to get to E through my approach? I see that the only difference my equation and the E is +2 vs -4, which is the y-intercept (the place where line intersects the y axis)

y = (4/3)x - 4