In the Reasoning section of SSC JE exam, we often encounter questions which ask us to count the number of shapes within an image. For example, we are given a square and inside the square, there are a number of smaller squares. You would be asked to count the number of squares. These are called SSC JE Discrimination Questions. Now, the counting could be done in the direct way, where you manually count all the squares. However, that would take a lot of time. But don’t worry! There are some easy ways to count different shapes. Let us take a look at some of the techniques that you can try out to solve SSC JE discrimination questions.

## Different Types of SSC JE Discrimination Questions

In SSC JE exam, you are asked to count three main types of shapes. They are:

• Square
• Rectangle
• Triangle

You can surely expect that you would be asked to count at least one of these shapes in SSC JE 2019 as well. So, knowing shape counting techniques would definitely help you in your SSC JE reasoning preparation. Let us look at the ways in which you can count a range of different kind of shapes in  SSC JE reasoning questions.

## Solving SSC JE Discrimination Questions

### Square Counting Techniques in SSC JE exam

Squares can be arranged in different ways. Either in an identical number of rows and columns, like 3×3, 4×4 etc., or they the numbers of rows and columns might be different, like 4×3, 5×4. Let us first take the case of the identical rows and columns one. Assume you are given a 4×4 square. Now, what you have to do is just mark the rows like this: What you need to do now is just square the numbers of the rows and then add them, like this

12+22+32+42

The total number is 30. So, the number of squares in the above figure would be 30. This same technique can be used to count the number of squares in 3×3, 5×5 or any other such grids.

Now, what if the number of rows and columns differ? Well, there are methods for counting in that scenario as well. Let us take the example of a 5×4 grid now. Now, a 5×4 grid would definitely have a 4×4 grid inside it. Therefore, we are going to have at least 30 squares inside it. If you are taking a 4X4 grid out of a 5×4 grid, you would only be left with 5 squares, right? Now, you just need to add all the numbers from 5 to 1 and then add it to 30, just like this:

30+5+4+3+2+1 = 45

Hence, the total number of squares in such a case is 45.

### Rectangle Counting Techniques for Discrimination questions in SSC JE Exam

Counting rectangles are even easier. Let us assume that you are given a number of rectangles arranged in a grid of 5×4. Now, what you have to do is just mark the rows and columns of the rectangles just like you did with the squares. Like this: You just need to add the number of rows like this:

1+2+3+4=10

Repeat the same process with the number of columns as well:

1+2+3+4+5=15

Multiply the numbers you got for the rows and the columns:

10×15=150

Hence, the total number of rectangles is 150. You can use this process for counting any grid of rectangles.

### Triangle Counting Technique for Discrimination questions in SSC JE Exam

In order to count triangles, we need to use different techniques in different scenarios. It all depends on the way the triangles are drawn. For example, consider the following figure In case you are given a triangle which dissected by a number of lines running across, then you need to mark the smaller triangles just the way shown in the figure. Now, we have one big triangle, so we would write one and then just write the number of smaller triangles formed by the dissecting lines. So, we have 1 and then 6. Write it beside one another and you have 16. That’s the correct answer! You can use this technique to solve any such questions but please note that the lines should fully dissect the triangle.

You can also be given a figure such as the following: Again, mark the triangles as shown above. You need to add the numbers on either side of the parallel line like this:

1+2+3+4=10

10+10=20

So, the number of triangles in the above figure is 20. You can also be given a figure like this: In such a figure the number of triangles is 8. Now, when you combine two such figures like this: In such a case, you would need to add 2 more triangles to the 8 triangles each within the boxes. So, we would have

8+8+2 =18

These were some of the tips that you can follow to solve SSC JE discrimination and observation questions easily.

## General Tips for Solving SSC JE Discrimination Questions

1. There would be instances when you can’t use any such techniques. In such cases, you have to proceed manually. First count the big shapes, mark their boundaries and then move on to smaller shapes. This would help you to solve such questions quickly.
2. Sometimes, you would be asked to find the number of squares within a circle. This is done to confuse you. Just keep calm and only try to look at the images that you need to find. If you can observe a grid or a pattern, try to follow the tips given above.
3. Use a pen or a pencil to mark the boundaries. Marking the boundaries with numbers would be a little less confusing than marking them over and over with lines.

## Practice Questions for Discrimination Section

Question 1: Find the number of rectangles in the below figure? Options:

(a)20
(b) 18
(c) 28
(d) more than 29

Question 2: Find the number of triangles in the below figure? Options:

(a) 12
(b) 10
(c) 20
(d) 14

Question 3: Find the number of triangles in the below figure? (a) 5
(b) 6
(c) 7
(d) 9