NIMCET 2017 Logical Reasoning Question 68 with Solution

Question 68

Logical Reasoning Reasoning Analogies Hard

<p>The number of square in the following 4 × 6 grid is</p> <table border="1" cellpadding="1" cellspacing="1" style="height:110px;width:150px;"> <tbody> <tr> <td> </td> <td> </td> <td> </td> <td> </td> <td> </td> <td> </td> </tr> <tr> <td> </td> <td> </td> <td> </td> <td> </td> <td> </td> <td> </td> </tr> <tr> <td> </td> <td> </td> <td> </td> <td> </td> <td> </td> <td> </td> </tr> <tr> <td> </td> <td> </td> <td> </td> <td> </td> <td> </td> <td> </td> </tr> </tbody> </table> <p> </p>

(A) 36

(B) 44

(C) 50

(D) 54

View Dynamic Solution & Explanation ▼

Correct Solution: Option C

Step-by-step Solution:

Method for Counting Squares in a Grid

To find the total number of squares in a non-square grid (like a 4 × 6 grid), we must count the squares of all possible sizes and then sum them up. The largest possible square in a 4 × 6 grid is 4 × 4.

The calculation is as follows:

Number of 1 × 1 squares: 4 × 6 = 24
Number of 2 × 2 squares: (4-1) × (6-1) = 3 × 5 = 15
Number of 3 × 3 squares: (3-1) × (5-1) = 2 × 4 = 8
Number of 4 × 4 squares: (2-1) × (4-1) = 1 × 3 = 3

Total Calculation

To get the total number of squares, we add the counts for each size:

Total Squares = 24 + 15 + 8 + 3

Total Squares = 50

Conclusion

There are a total of 50 squares in a 4 × 6 grid.