gmatophobia
PS Question 1 - Dec 12
Three circles with radii of 2 cm, 3 cm and 5 cm, respectively are on the same plane. If the centers of the three circles are all on the same line and each circle is tangent to at least one of the other two circles, then what is the shortest possible distance, in cm, between the center of the largest circle and the center of the smallest circle?
A) 0
B) 1
C) 3
D) 7
E) 13
Source: EMPOWERgmat | Difficulty: Medium
nice! I was stuck with the answer as 3cm but there is a fishy thing happening with how
you "touch" these circles with each other...
I used some MS paint skills to draw two diagrams "A" and "B". to help me visualize how tangents can be drawn out to give the Minimum distance between the largest and smallest circles. It turns out 1cm is the shortest distance between them if circles are drawn like in figure "A"
gmatophobia
PS Question 2 - Dec 12
x and y are positive integers. If the greatest common divisor of x and 3y is 9, and the least common multiple of 3x and 9y is 81, then what is the value of 81xy?
A) 3^5
B) 3^6
C) 3^7
D) 3^8
E) 3^9
Source: GMATPrepNow | Difficulty: Hard
gcd(a,b) * lcm(a,b) = a*b
using this we get 3^8 as the answer