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!
