GMAT MATH : Word Problem - Geometry

Question

A point on the rim of a circular tire that is rotating in a plane is 6 inches from the center of the rim. What is the distance traveled, in inches, by this point in 10 seconds when the tire turns at the rate of 250 revolutions per minute?

A) 36000π
B) 6000π
C) 3000π
D) 500π
E) 1000π 

 Solution

 Answer D

Area covered by a circle is equal to its circumference, which is calculated by 2πR 
If a point is 6 inches from the center of the rim and it rotates in a circle, then radius (R) of the circle is 6 inches.
So the distance covered by one rotation of the rim is  2 (π) (6) = 12π
Distance cover in one minute; based on the information provided in the Question the rim makes 250 revolutions per minute.
Distance covered in 250 revolutions = 12 (π) (250).
The Question wants us to know how far the rim travels in 10 seconds. This can be calculated by multiplying the total distance traveled by (10/60) (10 seconds of 60 seconds of minute).
   12 (π) (250) (10/60) = 500π

 

 

GMAT Math Practice - Coordinate Geometry

GMAT Math Practice - Coordinate Geometry 

Question

Line P is described by the equation 3x + 2y - 4 = 0.  Which of the following lines is parallel to P and has the same x-intercept as the line  5x - y + 5 = 0?
a) 6x = -5y + 20
b) -y = (3/2)x +20
c)  -4x - 6y =8
d)  y = -3x - 3
e) - 4y = -6x-12

Solution

 For some reason, many GMAT test takers seem to be confused with such a question and they immediately start by plotting points on the axes.

 You need to know simple rule for parallel lines.

Lines are parallel when they have the same slopes, and the slope is easiest to see when a line is written in slope intercept from y = mx + b.

Converting P to that form we get
y = -3x + 4 or
y = -3x + 4
So the slope of any parallel line will be -3. The second condition is given by the 2nd equation.  Its x-intercept is the x-value where y = 0.

That is 5x - 0 + 5 = 0
5x = -1 so
x = -1 .

For each of the given answer choices, we can start by looking for either a matching slope or x-intercept, and then if it matches one, see if it matches both.

Answer D is y = -3 x - 3.

y = -(3)x -3

Therefore the slope is -3, and parallel to P.  Furthermore, substituting in x = -1.y = -3 x -3

y = 3 - 3 = 0 

So this line also has the desired x intercept.