# CAT Quantitative Aptitude Questions | CAT Permutation and Combination Questions

###### CAT Questions | Permutation Probability | Number Theory
CAT Questions

The question is from Permutation and Combination. A question which combines number theory and probability. We need to find out the probabilty of a multiple of 7 being a multiple of 5. This section hosts a number of questions which are on par with CAT questions in difficulty on CAT Permutation and Combination, and CAT Probability.

Question 19: N is a 3-digit number that is a multiple of 7; what is the probability that it will be a multiple of 5?

1. $$frac{1}{5}\\$ 2. $\frac{11}{54}\\$ 3. $\frac{13}{64}\\$ 4. $\frac{13}{66}\\$ ## Best CAT Online Coaching Try upto 40 hours for free Learn from the best! #### 2IIM : Best Online CAT Coaching. ### Video Explanation ## Best CAT Coaching in Chennai #### CAT Coaching in Chennai - CAT 2021Online Batches Available Now! ### Explanatory Answer ##### Method of solving this CAT Question from Permutation and Combination: A combination of Probability and Number Theory gives a perfect question. N is a three digit multiple of 7. N could be 105, 112, 119, 126…..994. Or, 15 * 7, 16 * 7…..142 * 7. Or there are 142–14 = 128 numbers. Within these we need to locate the multiples of 5. Or, we need to isolate multiples of 35. Or, we need to see how many numbers there are in the list 105, 140, 175…..980. 35 * 3, 35 * 4…35 * 28… Or, there are 26 such numbers. Probability $\frac{26}{128}\\$ = $\frac{13}{64}\\$ The question is "what is the probability that it will be a multiple of 5?" ##### Hence the answer is "$\frac{13}{64}\\$" Choice C is the correct answer. ###### Prepare for CAT 2022 with 2IIM's Daily Preparation Schedule ###### Know all about CAT Exam Syllabus and what to expect in CAT ###### Best CAT Online Coaching Try upto 40 hours for free Learn from the best! ###### Already have an Account? ###### CAT Coaching in ChennaiCAT 2021Enroll at 49,000/- 44,000/- Online Classroom Batches Starting Now! ###### Best CAT Coaching in Chennai Introductory offer of 5000/- Attend a Demo Class ###### Best Indore IPM & Rohtak IPM CoachingSignup and sample 9 full classes for free. Register now! ## CAT Preparation Online | CAT Permutation and Combination; Probability Videos On YouTube #### Other useful sources for Permutation and Combination Questions | Probability Questions ##### Where is 2IIM located? 2IIM Online CAT Coaching A Fermat Education Initiative, 58/16, Indira Gandhi Street, Kaveri Rangan Nagar, Saligramam, Chennai 600 093 ##### How to reach 2IIM? Phone:$91) 44 4505 8484
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