In a box containing action figures of the three Fates from Greek

Question

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. What is the least number of action figures that could be in the box?

A. 10
B. 12
C. 15
D. 27
E. 37

This is a problem from the Fractions, Decimals & Percents Manhattan guide.

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. What is the least number of action figures that could be in the box?

This is how I went about solving the problem. 
3C=2A - Equation (1)
5C=4L - Equation (2)

Plugging in values for L,A and C that satisfy both the above equations. Plugging the value of L as 5 I get the value of C as 4 and A as 6 (All three positive integers). L+A+C = 15.

What is wrong in this approach?

he answer to this problem is 37.

Bunuel · Answer

Three figures of Clotho for every two figures of Atropos --> C:A = 3:2, so 2C = 3A, not 3C=2A.
Five figures of Clotho for every four figures of Lachesis --> C:L = 5:4, so 4C = 5L, not 5C=4L.

Hope it's clear.

cafecorridor · Answer

Ah. Didn't think even once that my equations could be wrong! While I understand the problem and its solution I'm now wondering how I could have made such a fundamental mistake. I'm done with the FDP manhattan guide and had no issues with any of the problems and so to discover this is making me evaluate my mathematical skills! The problem reads 'there are three figures of Clotho for every two figures of Atropos' A natural translation of this would be 3C=2A but C/A = 3/2 is correct which means 2C=3A. Has anyone faced such a translation issue before and how did you resolve it? Also, what difficulty level would this problem be considered on the GMAT?

EMPOWERgmatRichC · Answer

Hi cafecorridor,

In this question, we're given two facts about the ratios of 3 items:
1) There are 3 figures of Clotho for every 2 figures of Atropos
2) There are 5 figures of Clotho for every 4 figures of Lachesis.

We're asked for the LEAST number of action figures that could be in the box?

From the given ratios, we know that:
1) The number of figures of Clotho MUST be a multiple of 3 AND a multiple of 5
2) The number of figures of Atropos MUST be an equivalent multiple of 2
3) The number of figures of Lachesis MUST be an equivalent multiple of 4

To figure out the LEAST number of figures, we need to make the each of these numbers as SMALL as possible.

The smallest possible number of Clotho figures is 15.

IF....
Clotho = 15
Atropos = 10
Lachesis = 12

Total number of figures = 15+10+12 = 37

Since this question requires very little in the way of manipulation, it's not that difficult of a question. You'll likely see at least one ratio-based question that's conceptually similar to this one on Test Day.

GMAT assassins aren't born, they're made,
Rich

cafecorridor · Answer

Thank you for the response.

EMPOWERgmatRichC · Answer

Hi cafecorridor,

Understanding ratios and how they "work" is an important part of scoring at a high level in the Quant section on Test Day. The GMAT will throw ratio-based questions at you many times, and do so using different 'formats' beyond obvious ratios (fractions, percents, etc.). Knowing how to convert data from one format to another and do the necessary algebra is an essential part of picking up these points. Ratio questions are often beatable by TESTing VALUES, TESTing THE ANSWERS and the occasional bit of 'brute force' (just listing out the possibilities). So there's a bit of work involved here to get comfortable with the overall concept, but the rewards are significant.

GMAT assassins aren't born, they're made,
Rich

anu1706 · Answer

How did you get 10 & 12? I got it 15.

EMPOWERgmatRichC · Answer

Hi anu1706,

The question asks for the LEAST number of figures that could be in the box, so you have to account for all 3 types of figures.

To find the LEAST total, we have to make the number of figures as SMALL as possible while still maintaining the given ratios (and you can't have a "fraction" of a figure, so each number must be an integer).

From the given ratios, we know that:
1) The number of figures of Clotho MUST be a multiple of 3 AND a multiple of 5

The smallest possible number of Clotho figures is (3)(5) = 15.

C:A = 3:2, so when C = 15, A = 10

C:L = 5:4, so when C = 15, L = 12

The total = 15+10+12 = 37

GMAT assassins aren't born, they're made,
Rich

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In a box containing action figures of the three Fates from Greek

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