# Formulae questions

## What is it?

Formulae question test your abstraction capabilities. Are you able to extrapolate a trend or a result from a set of data? Are you able to break down problems, identifying drivers and directions of causality?

## Question formats

• Which of the following formulae best approximates ....?

## Example

Forman Fisheries is engaged in packaging shrimp and other fish. There are four grades of shrimp, from A to D, reflecting their size and taste. Below are some key productivity indicators for Forman Fisheries in the shrimp packaging activities:

2012
Grade A shrimps packed in a month (a) 3,600
Grade A shrimps share of total shrimps (b) 12%
Total boxes per year (c) 8,900

Assuming that all boxes contain the same quantity of shrimps, which of the following formulas best approximates how many boxes of non-grade A shrimps were packed in the last month?

1. $\frac{a}{12*b*c} * (1-b)$
2. $\frac{a}{b*c} * (1-b)$
3. $\frac{a*b}{(1-b)*c} * 12$
4. $\frac{c-cb}{12}$

## Method

1. Homogenize your measuring units. Since we are looking for months, wherever we will need the quantity of total boxes (c), we’ll divide it by 12, since it is a yearly indicator.
2. Break down the problem into smaller steps that help you get to the ratio, in this case:

$\text{Boxes on non-grade A shrimps} = \frac{\text{Number of non-grade A shrimps}}{\text{Shrimps per box}}$

Identify how to solve this for each of the factors in the equation:

$\text{Number of non-grade A shrimps} = \text{Total shrimps}\ *\ \text{Share of non-grade A shrimps}$

$\text{Total shrimps in a month} = \frac{\text{Grade A shrimps packed in a month (a)}}{\text{Grade A shrimps share of total shrimps (b)}}$

$\text{Share of non-grade A shrimps} = 1\ -\ \text{Grade A shrimps share of total shrimps (b)}$

$\text{Shrimps per box} = \frac{\text{Total number of shrimps in a month}\ (\frac{a}{b})}{\text{Total number of boxes}\ (\frac{c}{12})}$

Therefore:

$\text{Boxes on non-grade A shrimps} = \frac{\frac{a}{b}(1-b)}{\frac{12*\frac{a}{b}}{c}}$

Simplifying:

$\text{Boxes on non-grade A shrimps} = \frac{c(1-b)}{12}$

• Total boxes per year (c): 1,200 (or $\frac{c}{12} = 100\ \text{monthly}$)
Since all boxes have the same size, non-grade A boxes will be $(1 - 10\%) * 10 = 9$.