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Question 1 : The numbers 1, 2,..., 9 are arranged in a 3 X 3 square grid in such a way that each number occurs once and the entries along each column, each row, and each of the two diagonals add up to the same value. If the top left and the top right entries of the grid are 6 and 2, respectively, then the bottom middle entry is: [TITA]

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Method of solving this CAT Question from Number Theory

Given that the numbers 1,2,.., 9 are arranged in a 3 × 3 square grid such that each number occurs once and the entries along each row, column and diagonals should add upto the same value.
So the total of all these should be $$frac{9 × 10}{2}$ = 45 and since there are 3 rows and 3 columns $\frac{45}{3}$ = 15 Hence each row or column or the diagonal would add upto 15. And it is also given that top left and top right entries of the grid are 6 and 2 respectively. We have to find the bottom middle entry Since in the first row 6 + 2 = 8 the middle value is 7, we know that from 1,.... 5 .... , 9, 5 is the middle number so 5 comes in the middle of the second row. 7 + 5 = 12 so the other number is 3. We know that each row ,column and each diagonal would add up to 15 and therefore we can fill the rest of the rows and columns. Hence the bottom middle entry is found to be 3. The question is "The numbers 1, 2,..., 9 are arranged in a 3 X 3 square grid in such a way that each number occurs once and the entries along each column, each row, and each of the two diagonals add up to the same value. If the top left and the top right entries of the grid are 6 and 2, respectively, then the bottom middle entry is: [TITA]" Hence, the answer is 3 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! 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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