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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!

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Stuart Kovinsky, B.A. LL.B.
Kaplan Test Prep & Admissions
Toronto Office
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www.kaptest.com

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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.

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Anurag Mairal, Ph.D., MBA
GMAT Expert, Admissions and Career Guidance
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In the coordinate plane, there infinite numbers of lines which are perpendicular to a certain line. All those lines will have the same slope, but they will differ in terms of y-intercept.
For example, for this problem there can be many lines which are perpendicular to 3x + 4y = 8
Refer to the diagram below,

The red line represents 3x + 4y = 8
All the other three lines are perpendicular to it.

From the given information, we can only conclude that the slope of the perpendicular line will be -1/(-3/4) = 4/3, but not its y-intercept.

What you have done is you've assumed an y-intercept for the line and got a specific solution (which is indeed perpendicular to the 3x + 4y = 8) but not in the option.

What you should've done is assumed a general equation for the perpendicular, for example : y = (4/3)x + c, where c is the y-intercept. So, 3y = 4x + 3c. After that we have to check the option to find out which one of them satisfy this form of equation.

Hope that helps.

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Anju Agarwal
Quant Expert, Gurome

Backup Methods : General guide on plugging, estimation etc.
Wavy Curve Method : Solving complex inequalities in a matter of seconds.

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