Elevate Your Skills in Coordinate Geometry, Inequalities, and Idioms and Phrases using Targeted PYQs- Day 49

Part-1: Quantitative Aptitude for CAT exam

Important Concept/Formula Used in Coordinate Geometry Questions

Formulas Used in CAT Questions on Coordinate Geometry are given below:

• Distance Formula

• Application of distance formula

• Section Formula

• Equation of line, Circle, and other geometrical figures.

• Concept of slope

• Distance between two lines etc

Previous Year CAT Geometry Questions: Coordinate Geometry Questions

Q1. CAT coordinate geometry questions are given below:

The points (2, 1) and (-3, -4) are opposite vertices of a parallelogram. If the other two vertices lie on the line x + 9y + c = 0, then c is [CAT 2020, slot 3]

1. 15
2. 13
3. 14
4. 12

Solution: [3]

Diagonals of a parallelogram bisects each other.

So, the mid-point of (2, 1) and (-3, -4) must lie on the other diagonal also i.e. on the line x + 9y + c = 0.

Co-ordinate of mid-point of (2, 1) and (-3, -4) = {(2-3)/2, (1-4)/2} = (-1/2, -3/2)

This point satisfies x + 9y + c = 0.

So, -1/2 +9(-3/2) +c = 0

c = 14.

Q2. CAT coordinate geometry questions are given below:

A triangle ABC has an area of 32 sq units and its side BC, of length 8 units, lies on the line x = 4. Then the shortest possible distance between A and the point (0,0) is [CAT 2018, Slot 2]

1. 4√2 units
2. 2√2 units
3. 4 units
4. 8 units

Solution: [3]

Since BC = 8 units

½ x Height x BC = 32

Height = 8 units

Since the base lies on x = 4 and has a vertical height is of length = 8 units, A can either lie on the line x = 12 or on x = - 4

So, shortest possible distance to A from the point (0,0) = 4 units

CAT Exam Important Topic: Strategy to Prepare for “Coordinate Geometry” as well as for coordinate geometry questions

CAT Questions on Coordinate Geometry

• Learn different form equations of the line.
• Slopes of two parallel lines are equal.
• y coordinate of x-axis is 0.
• x coordinate of y-axis is 0.
• If the area of a triangle is 0, then the triangle will not be formed and the points are collinear.
• Divide the problems into sub-categories while practising.
• Practice as much as you can to understand the variations in questions.

CAT entrance exam: Prerequisite to Coordinate Geometry Questions

1. Basics of Geometry
2. Cartesian System
3. Linear Equation

CAT study material: References to Study (Theory) Coordinate Geometry Questions

1. NCERT Mathematics Class 11 and 12
2. Mission CAT (YouTube Channel: https://www.youtube.com/watch?v=pMfvgQCZrFs)

CAT study material: References to Practice CAT Questions on Coordinate Geometry

1. How to prepare quantitative Aptitude for CAT by Arun Sharma.
2. CAT Funda: YouTube (https://www.youtube.com/watch?v=P4Tpp9Fe4Ew)
3. Practice Sample Papers

Part-2: CAT 2024 Preparation Tips: CAT DILR tips (Logical Reasoning and Data Interpretation)

CAT 2024 Syllabus Topic: Strategy to prepare “Inequality” for CAT

Important Concepts/Formula Used in Inequality

Set of elements with several coded relationships mentioned using the inequality symbols are as follows:

• A < B means A cannot be greater than or equal to B.
• A > B means A cannot be less than or equal to B.
• A ≤ B means A cannot be greater than B.
• A ≥ B means A cannot be less than B.
• A ≠ B means A is either greater or lesser than B.

Previous Years Questions on Inequality from CAT/ MBA Entrance Exam:

Q1. Statement: A < H > Y, Y ≤ N, N = X

Conclusion I: A = X

Conclusion II: H > N

1. Only conclusion I is true
2. Only conclusion II is true
3. Both conclusions I and II are true
4. Neither conclusion I nor II is true
5. Either conclusion I or II is true

Solution: [2]

A < H > Y, it concludes that H is greater than both A and Y but we can not relate A and Y.

From 2nd and 3rd statements

Y ≤ N = X

So, from the above discussion we can not establish any relation between A and X.

Therefore, only conclusion II is true.

Q2.

Direction: Based on the information given below, answer the following questions:

A @ B, means B is greater than A

A & B, means B is smaller than A

A $ B, means B is equal to A

A # B, means B is greater than equal to A

A % B, means B is smaller than or equal to A

Statement: D @ Q $ R % S # X % U

Conclusion I: D % U

Conclusion II: R @ X

1. Only conclusion I is true
2. Only conclusion II is true
3. Both conclusions I and II are true
4. Neither conclusion I nor II is true
5. Either conclusion I or II is true

Solution: [4]

Using codes rewrite the question statement.

D @ Q $ R % S # X % U

Statement:

D > Q = R ≤ S ≥ X≤ U

Conclusion I: D % U (D≤ U)

Conclusion II: R @ X (R > X)

From statement D > Q = R ≤ S ≥ X≤ U, the relation between D and U cannot be established since between D and U, both signs of ‘greater than’ and ‘less than’ are there. So, the conclusion I will not follows.

For the same reason, the relation between R and X also cannot be established.

Tips and Tricks for CAT Inequality

1. Make a well understanding of symbols.

2. Make rough diagrams while solving questions for a better understanding of codes.

3. Learn properties of Inequality in reasoning.

4. Understand the types of questions asked in Exams.

CAT entrance exam: Pre-requisite

1. Linear Inequalities

2. Coding-Decoding , Blood Relation

References to CAT Study (Theory)

1. A new approach to Reasoning (B.S. Sijwali & S. Sijwali Arihant)

2. Mock Zone: MBA Preparation (YouTube: https://www.youtube.com/watch?v=K7HSUc8hv2A)

References to Study (Practice)

1. Verbal and Non-Verbal Reasoning by R S Agrawal.

2. MBA Entrance Previous years Papers and Sample Papers.

3. (YouTube: https://www.youtube.com/watch?v=V9UjrHAuZUw)

Part-3: CAT Exam Preparation 2024: CAT exam tips for VARC (Verbal Ability & Reading Comprehension)

CAT Exam Important Topic: Strategy to Prepare “Idioms and Phrases questions for cat exam” (Part-1). Students can download the idioms and phrases for CAT exam pdf

Previous Years Questions on Idioms and Phrases for MBA exams

Also, idioms for CAT exam are given below -

1. Hear it on the grapevine:

Meaning: To hear news from someone who heard the news from someone else

E.g. I heard through the grapevine that she is leaving the flat-is it true?

2. Shot in the dark:

Meaning: A wild, unsubstantiated guess; also, an attempt that has little chance of success.

E.g. You can try looking for your ring but I think it’s a shot in the dark.

3. Zero in on something:

Meaning: Focus all attention on one thing.

E.g. Researchers are hoping to zero in on the research.

4. The best of both worlds:

Meaning: The benefits of widely differing situations, enjoyed at the same time.

E.g. I have the best of both worlds- an amazing family and great work.

5. Cut your coat according to your cloth:

Meaning: Actions should suit circumstances or resources.

E.g. We belong to a middle-class family, and we always cut our coats according to our clothes.

6. To step into a dead man’s shoes:

Meaning: To take over the position or role of someone who has died.

E.g. It is ill waiting for a dead man’s shoes.

7. Halcyon Days:

Meaning: A very happy or successful period in the past.

E.g. I remember those halcyon days when everyone was friendly in nature.

8. To backbite a person:

Meaning: To say mean things about a person.

For E.g. Neha always backbites her friend

9. If the cap fits, wear it:

Meaning: Used as a way of suggesting that someone should accept a generalized remark or criticism as applying to themselves.

E.g. I told the council members what I think and I told them that if the cap fits, they should wear it.

10. To make bricks without straw:

Meaning: Important and essential things.

E.g. You can’t crack the CAT examination If you have no command over verbal ability topics. You can’t make bricks without straw.

Tips and Tricks to Solve CAT Questions on Idioms and Phrases

• Understand the context in which an idiom or phrase has been used. It will help you to understand and remember a particular idiom crystal clearly.
• Prepare the list of idioms and phrases and write their meaning and context to learn them efficiently.
• Pick 5, 7, or 10 idioms out of the list and use them in your day-to-day sentences.
• If you find difficulty in learning any idiom and phrase, try relating them with the stories or things in order to ease the difficulty.

CAT 2024: Pre-requisite to Idioms and Phrases

1. The basic idea of sentence structure.

2. Good Vocabulary.

References to Study (Theory) idioms for CAT exam

1. 200 Practical English Idioms by Alex Makar

2. Word Power Made Easy by Norman Lewis

References to Practice idioms and phrases questions for CAT exam

1. 200 Practical English Idioms by Alex Makar

2. Word Power Made Easy by Norman Lewis

3. engvid.com (Web)

Tomorrow we'll be back with Day 50, so practice and stay focused.