1. Navigating Directions and Mastering Distances (Lecture Explanation).pptx

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📑 Outline of the 3000-Word Write-up on Remainders

1. Introduction to Remainders


2. Basic Concepts and Definitions

Dividend, Divisor, Quotient, and Remainder

Properties of Division



3. Rules and Properties of Remainders

Addition, Subtraction, Multiplication with Remainders

Division and Powers with Remainders



4. Special Theorems

Remainder Theorem (Algebra)

Fermat’s Little Theorem

Euler’s Theorem

Wilson’s Theorem

Chinese Remainder Theorem



5. Shortcut Techniques for Competitive Exams

Finding last digits

Remainders in factorials

Remainders with large powers



6. Step-by-Step Solved Examples

Easy, Moderate, and Advanced Levels



7. Applications of Remainders

Aptitude Exams (CAT, GATE, TCS NQT, etc.)

Computer Science (modulo operations, hashing)

Cryptography



8. Common Mistakes and Misconceptions


9. Practice Questions with Solutions


10. Conclusion and Tips




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1. Navigating Directions and Mastering Distances Lecture Explanation Presented by Mr. Rajendra Bhanu Teja– Aptitude Trainer

2. CONCEPT

3. Surya starts walking towards North, turns left , again turns left , again turns right , again turns left , again turns right , again turns right . In which direction is he walking now ? a. North b. South c. West d. South- East Model-1: Facing/ Moving Direction Question Solution Presented by Mr. Rajendra Bhanu Teja– Aptitude Trainer

4. Question Solution Facing to the South Mr. Karthik turns in certain ways, which of the following turns will not lead him to the same side ? a. Left , Left , Right ,Left , Left , Right b. Left , Right , Left , Right , Left , Right c. Right , Right , Left , Right , Left , Left d. Left , Right , Right , Left , Right , Left Model-1: Facing/ Moving Direction Presented by Mr. Rajendra Bhanu Teja– Aptitude Trainer

5. Model-2: Staring Direction Question Solution Raju after walking 25 m turns left , turns left , turns right , turns left , turns right , turns left , finally turns left . In the end , he was moving towards North . From which direction was he start his journey ? a. West b. North c. South d. East Presented by Mr. Rajendra Bhanu Teja– Aptitude Trainer

6. Model-2: Staring Direction Question Solution After walking for 1 m, Madhuri turned to her left and walked another 12 m. Again, she turned to her left and walked for 4 m. Now she is travelling in East direction. In which direction did she start her journey?  a. West b. East c. North d. South Presented by Mr. Rajendra Bhanu Teja– Aptitude Trainer

7. Question Solution Model-3: Distance w.r.t Direction Prasanth walked 40 metres towards South and moves 70 m towards East and then moves a distance of 40 m towards South and then moves 70 m towards West . In which direction and how long distance he is now from the starting point ? a. 60 East b. 80 South c. 70 South d. 120 East Presented by Mr. Rajendra Bhanu Teja– Aptitude Trainer

8. Question Solution Model-3: Distance w.r.t Direction I drove 50 km towards east from a city ‘S’ and then turned right and drove another 30 km. Now I turned to my left & drove another 30 km. Finally, I turned my right & drove 30 km to reach a city ‘F’. Find the shortest straight distance between cities S and F. 20 km 25 km 40 km 100 km Presented by Mr. Rajendra Bhanu Teja– Aptitude Trainer

9. Question Rajesh walked 20 m towards north. Then he turned right and walks 30 m. Then he turns right and walks 35 m. Then he turns left and walks 15 m. Finally, he turns left and walks 15 m. In which direction and how many metres is he from the starting position? 15 m West 30 m East 30 m West 45 m East Solution Model-4: Finding of Distance & Direction Presented by Mr. Rajendra Bhanu Teja– Aptitude Trainer

10. Question Solution Model-4: Finding of Distance & Direction A cyclist goes 30 km to North and then turning to East he goes 40 km. Again, he turns to his right and goes 20 km . After this, he turns to his right and goes 40 km. in which direction and how long distance is starting point from the ending point ? 0 km, South 10 km, North 10 km, South 20 km, North Presented by Mr. Rajendra Bhanu Teja– Aptitude Trainer

11. Question Solution A, B, C, D and E are five friends standing in a park. The distance between A and C and that of B and C are same. E and C are 45m apart in west-east direction.  A is towards west of C at a distance of 25m from E. C is in between B and D and in north direction with B. 9. If the distance between B and D is 35m, then calculate the distance between A and D. 15 B) 20 C) 25 D) 30 Model-4: Finding of Distance & Direction Presented by Mr. Rajendra Bhanu Teja– Aptitude Trainer

12. Question Solution Model-5: Angle A man is facing north-west. He turns 90 in the clockwise direction, then 180 in the anticlockwise direction and then another 90 in the same direction. Which direction is he facing now? South South-west South-east East Presented by Mr. Rajendra Bhanu Teja– Aptitude Trainer

13. Question Solution Model-5: Angle Ravi is facing south-west. He turns 135° to his clockwise and again turns 225° in anticlockwise direction. From there, he turns 90° in clockwise direction. Finally, he turns 45° to his anticlockwise. Which direction is he facing now? South South-East West North-West Presented by Mr. Rajendra Bhanu Teja– Aptitude Trainer

14. Question Solution Model-6: Direction Change South-East becomes North and North-East becomes West and all the rest directions are changed in the same manner, then what will be the direction for the West ? a. North-East b. South c. South-East d. South-West Presented by Mr. Rajendra Bhanu Teja– Aptitude Trainer

15. Question Solution Model-7: Clock Model Rahul put his timepiece on the table in such a way that at 6 P.M. hour hand points to North. In which direction the minute hand will point at 9.15 P.M.? South-East South North West Presented by Mr. Rajendra Bhanu Teja– Aptitude Trainer

16. Question Solution Presented by Mr. Rajendra Bhanu Teja– Aptitude Trainer Model-8: Shadow Based One morning after sunrise, Suresh was standing facing a pole. The shadow of the pole fell exactly to his right. To which direction was he facing? East West South Data is inadequate Presented by Mr. Rajendra Bhanu Teja– Aptitude Trainer

17. Question Solution Presented by Mr. Rajendra Bhanu Teja– Aptitude Trainer Model-8: Shadow Based One evening just before sunset two friends Sanju and Manju were talking to each other face to face. If Manju’s shadow was exactly to her left side, which direction was Sanju facing? North South West Data inadequate

18. Extra Questions

19. Question Solution Presented by Mr. Rajendra Bhanu Teja– Aptitude Trainer North-West becomes East and South becomes North-West and all the rest directions are changed in the same manner, then what will be the direction for the West ? a. North-East b. South c. South-East d. South-West

20. Question Solution Presented by Mr. Rajendra Bhanu Teja– Aptitude Trainer A clock showing 2:00 pm. If the hour hand is in North-East direction. Then , what will be the direction of hour hand, when the time of clock becomes 9:30 pm ? a. South b. South-East c. North-West d. South-West

21. Question Solution Presented by Mr. Rajendra Bhanu Teja– Aptitude Trainer Arvind starts from a point A and travels 3 km Eastwards to reach B and then turns left ,travels thrice that distance to reach C. He again turns left and travels five times the distance he covered between A and B and reached his destination D. The shortest distance between the starting point and the destination is: a. 17 km b. 18km c. 15 km d. 12 km

22. Thank You