IIMs Admission Criteria
CAT Daily Target
whatsapp
Join Coachify CAT Club
coachify logo
Formula PDF

Question 18.

The number of distinct pairs of integers (m, n) satisfying |1+mn| < |m+n| < 5 is

A
B
C
D
Previous Question
Rate this Solution★★★★★
Next Question

You have read 5 explanations without login

Text Explanation

Let us break this up into 2 inequations [ Let us assume x as m and y as n ]

| 1 + mn | < | m + n |

| m + n | < 5

Looking at these expressions, we can clearly tell that the graphs will be symmetrical about the origin.

Let us try out with the first quadrant and extend the results to the other quadrants.

We will also consider the +X and +Y axes along with the quadrant.

So, the first inequality becomes,

1 + mn < m + n

1 + mn - m - n < 0

1 - m + mn - n < 0

(1-m) + n(m-1) < 0

(1-m)(1-n) < 0

(m - 1)(n - 1) < 0

Let us try to plot the graph.

If we consider only mn < 0, then we get 

But, we have (m - 1)(n - 1) < 0, so we need to shift the graphs by one unit towards positive x and positive y.

So, we have,

So, if we look for only integer values, we get

(0,2), (0,3),.......

(0,-2), (0, -3),......

(2,0), (3,0), ......

(-2,0), (-3,0), .......

Now, let us consider the other inequation as well, in which |x + y| < 5

Since one of the values is always zero, the modulus of the other value is less than or equal to 4.

Hence, we get 

(0,2), (0,3), (0,4)

(0,-2), (0, -3), (0, -4)

(2,0), (3,0), (4,0)

(-2,0), (-3,0), (-4,0)

Hence, a total of 12 values.

Video Explanation

Master CAT Preparation with Previous Year Papers

Practicing CAT previous year papers is one of the most effective strategies for CAT exam preparation. By solving questions from CAT 2021 quant-slot-3 and other previous years, you can understand the exam pattern, difficulty level, and types of questions asked in the Common Admission Test.

Why Practice CAT Previous Year Questions?

  • Understand Exam Pattern: CAT previous papers help you familiarize yourself with the question format, marking scheme, and time management required for the actual exam.
  • Identify Important Topics: By analyzing CAT solved questions from multiple years, you can identify frequently asked topics and focus your preparation accordingly.
  • Improve Speed and Accuracy: Regular practice of CAT previous year papers enhances your problem-solving speed and accuracy, which are crucial for scoring well in the exam.
  • Build Confidence: Solving CAT previous year questions builds confidence and reduces exam anxiety by making you comfortable with the exam format.

How to Use CAT Previous Papers Effectively

  1. Solve Under Exam Conditions: Attempt CAT previous year papers in a timed environment to simulate the actual exam experience.
  2. Analyze Your Performance: After solving each CAT previous paper, analyze your mistakes and identify areas that need improvement.
  3. Review Solutions Thoroughly: Study the detailed solutions and explanations provided for each question to understand the correct approach and methodology.
  4. Focus on Weak Areas: Use CAT solved questions to identify your weak areas and dedicate more time to improving them.

CAT Exam Sections Covered

Our comprehensive collection of CAT previous papers covers all three sections of the exam:

  • VARC (Verbal Ability & Reading Comprehension): Practice reading comprehension passages, para jumbles, and other verbal ability questions from CAT previous years.
  • DILR (Data Interpretation & Logical Reasoning): Master DI and LR questions with detailed solutions from CAT previous year papers.
  • QA (Quantitative Ability): Solve arithmetic, algebra, geometry, and other quantitative ability questions from CAT solved papers.

Additional CAT Preparation Resources

Looking for more CAT preparation materials? Explore our comprehensive collection of:

Note: Regular practice of CAT previous year papers, combined with a structured study plan, is essential for achieving a high percentile in the CAT exam. Make sure to solve questions from all sections and review the solutions thoroughly to maximize your preparation effectiveness.

Quant Essentials
Quant Essentials