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: Word Problem - Set Theory

GMAT Math: Word Problem - Set Theory

 In a village of hundred households, 75 have at least one DVD player, 80 have at least one cell phone, and 55 have at least one MP3 player. Every village has at least one of these three devices. If X and Y are respectively the greatest and the lowest possible number of households that have all the three of these devices, X-Y is :

A) 65

B) 55

C) 45

D) 35

E) 25

Solution

Answer C

This is a really tricky one, you will encounter this on the actual GMAT if you are doing very good on the GMAT math section. This involves sets.

First we need to figure out what the maximum is. We know it is possible there are 55 with all three, since the 55 MP3 owners is smallest set of the three. (Max = # of MP3)

To calculate the fewest possible, we first need to figure out how many must have all three devices. (max possible - max without all three = minimum with all three).

Of the 80 cell phone owners, 25 cannot have an MP3 player 80 - 55 = 25.

Similarly, 20 of the DVD owners cannot have an MP3 player. 75 - 55 = 20.

If the owners who do not have all three are unique (no overlap), we get the maximum number of owners who do not own an MP3 player, and thus cannot own all three devices.

Max possible - maximum without all three = minimum number of people with all three devices.

55 - 45 = 10

Now we can solve:

55 - 10 = 45.

Question - GMAT Math - Word Problem

Question - GMAT Math - Word Problem

Jimmy invested $20,000 in a mutual fund account exactly three years ago. The value of the account increased by 10 percent during the first year and decreased 5 percent during each of the next two years. What is the value of the account today?

(A) $20,750

(B) $20,700

(C) $19855

(D) $20,000

(E) $19,000

Solution

First Year,

10% of $20,000 is 20,000(0.1) = 2,000,

so the value of the account after the first year is 20,000 + 2000 = 22,000.

Second Year,

5% of 22,000 is 22000 (.05) = 1100,

so the value of the account after the second year is 22,000 - 1100 = 20,900

Third Year

5% of 20,900 is 20900 * (.05) 1045,

so the value of the account after the third year is 20900 - 1045 = 19855

choice (C) is the correct answer