## Integrated Reasoning - Two Part Analysis

Let’s look at another Integrated Reasoning question type today – two part analysis. As complicated as it sounds, it’s actually the simplest of the IR question types in my opinion. The reason for this is that it tests no new skills; it checks your ability to handle the same old PS and CR questions.

The only reason it is new is that it reduces the probability of guessing correctly and it puts more time pressure on you! Your probability of guessing correctly is 20% in PS/CR questions; it goes down to 4% in two part analysis because you have to guess correctly twice. As for time pressure, you get about 2 mins for every PS and about 1.5 mins for every CR question. For each part of two part analysis, you have only 1.25 mins.

Anyway, let’s look at a sample question to get familiar with this question type.

Question: A grocery store sells fruits in pre packed closed bags such that individual pieces of fruit are not sold. Mangoes are sold at the rate of \$5 per bag (each bag contains two mangoes) and apples at the rate of \$8 per bag (each bag contains five apples). During a particular day, the store started with some mangoes and apples and sold them all by the end of the day. The revenue at the end of the day from selling mangoes and apples that day was \$128. Which of the following could represent the number of mangoes and the number of apples that were in the store at the beginning of that day?

Choose only one from each column: Solution:

Note that it is a PS question. Only the format of the question is different. Also, the use of the word ‘could’ in the question stem suggests that there could be multiple solutions to this problem. Let’s take a closer look at how to solve it.

Say, number of bags of mangoes is ‘m’ and number of bags of apples is ‘p’.

Then 5m + 8p = \$128 (total revenue)

Each bag of mangoes has 2 mangoes and each bag of apples has 5 apples.

So number of mangoes sold = 2m (to be selected in the first column)

Number of apples sold = 5p (to be selected in the second column)

We need to solve for this equation: 5m + 8p = 128

It is easy to see that one solution to this equation is m = 0, p = 16. The next solution will be m = 8, p = 11. Another will be m = 16, p = 6. Yet another will be m = 24, p = 1. If you are wondering how we are landing on one solution after another so effortlessly, you need to check out our explanation ofninteger solutions to equations in two variables.

So there are three solutions possible to our question: Which of the following could represent the number of mangoes and the number of apples that were in the store at the beginning of that day?

There are three different cases possible:

Case 1: Number of mangoes sold could be 16 (= 2m when m is 8). In that case number of apples sold will be 55 ( = 5p when m is 8, p is 11)

Case 2: Number of mangoes sold could be 32 (= 2m when m is 16). In that case number of apples sold will be 30 ( = 5p when m is 16, p is 6)

Case 3: Number of mangoes sold could be 48 ( = 2m when m is 24). In that case number of apples sold will be 5 (= 5p when m is 24, p is 1)

The case we select should be that of which both numbers are included in the options. Case 3 satisfies this condition. So we select 48 in the first column and 5 in the second column.

This is the only ‘exotic’ step of the two part analysis. The rest of the question is just like any other PS question.