CAT Quantitative Aptitude Questions | CAT Geometry - Mensuration Problems

This question is from CAT Mensuration in CAT Geometry.In this question, Tomatoes are grown in the shape of square for two years. It is more like an application of number theory. Mensuration Questions in the CAT exam can be solved with practical approach and thought process rather than just knowing theorems from CAT Geometry. Even if one is not completely prepared for CAT Geometry exam, he or she should be able to do well in Mensuration problems tested by the CAT Exam. Knowing Mensuration formulas is important. Make sure you master Mensuration questions for CAT exam.

Question 11: Anil grows tomatoes in his backyard which is in the shape of a square. Each tomato takes 1 cm² in his backyard. This year, he has been able to grow 131 more tomatoes than last year. The shape of the backyard remained a square. How many tomatoes did Anil produce this year?

1. 4225
2. 4096
3. 4356
4. Insufficient Data

Explanatory Answer

Method of solving this CAT Question from Geometry - Mensuration: Look closely at the number 131!! What kind of number is it ?

Let the area of backyard be x² this year and y² last year
∴ X² - Y² = 131
=> (X+Y)*(X-Y) = 131
Now, 131 is a prime number (a unique one too. Check out its properties on Google). Also, always identify the prime number given in a question. Might be helpful in cracking the solution.
=> (X+Y)*(X-Y) = 131 x 1
=> X+Y = 131
X-Y = 1
=> 2X = 132 => X = 66
and Y = 65
∴ Number of tomatoes produced this year = 66² = 4356

The question is "How many tomatoes did Anil produce this year?"

Hence, the answer is 4356

Choice C is the correct answer.