Ratios - Manhattan Gmat

[shanice]

Hi all,

In a box containing action figures of the three Fates from Greek mythology, there are three figures of
Clotho for every two figures of Atropos, and five figures of Clotho for every four figures of Lachesis.

(a)What is the least number of action figures that could be in the box?

Answer is 37 action figures

(b)What is the ratio of Lachesis figures to Atropos figures?

Answer is 6:5


Thank you.

[aneesh.kg]

(a)

C/A = 3/2
C/L = 5/4

Number of Action Figures, N = C + A + L
= C + 2C/3 + 4C/5
= (15C + 10C + 12C) / 15
= 37C/15

To have the above (N = 37C/15) as a Integral value(since the total number of toys has to be an integer), C has to be a multiple of 15 and thus, N has to be multiple of 37.
The smallest integral multiple of 37 is 37, so that is the answer.

(b)

L/A can be obtained by dividing the first equation by the second.
C/A / C/L = L/A = 3/2 / 5/4 = 6/5