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# CAT 2018 Question Paper | Quants Slot 2

###### CAT Previous Year Paper | CAT Number theory Questions | Question 18

Number Theory forms a part of the CAT Syllabus. In CAT 2018 Question Paper we saw some beautiful questions that laid emphasis on learning ideas from basics and being able to comprehend the concepts, more than remembering gazillion formulae and shortcuts. Solve this question and ace your Online CAT Preparation. Original CAT Question paper are the best place to start off your CAT Preparation online. This page provides exactly that. To check out about 1000 CAT Level questions with detailed video solutions for free, go here: 2IIM's CAT Question Bank.

Question 18 : If the sum of squares of two numbers is 97, then which one of the following cannot be their product?

1. 64
2. -32
3. 16
4. 48

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##### Method of solving this CAT Question from Number theory

Given that the sum of squares of two numbers is 97 i.e. a2 + b2 = 97
From the given options we have to find which one cannot be their product i.e. ab
A. 64 ⟹ 2ab = 128
B. −32 ⟹ 2ab = -64
C. 16 ⟹ 2ab = 32
D. 48 ⟹ 2ab = 96
2ab is found because we know that
a2 + b2 + 2ab ≥ 0
a2 + b2 - 2ab ≥ 0
By this we can know that 97 + 128 works but 97 - 128 doesn’t works so we can understand option A cannot be the product and the rest can be.
a2 + b2 ≥ |2ab|
a2 + b2 ≥ 2ab
a2 + b2 ≥ -2ab
⟹ $$frac{a^2 + b^2}{2}$ ≥ |ab| So here 2ab should lie between +97 and -97 or ab should be less than $\frac{97}{2}$ or greater than −$\frac{97}{2}$, so except option A all the other options works so option A 64 cannot be the product The question is "If the sum of squares of two numbers is 97, then which one of the following cannot be their product?" ##### Hence, the answer is 64 Choice A is the correct answer. ###### Best CAT Online Coaching Try upto 40 hours for free Learn from the best! ###### Prepare for CAT 2023 with 2IIM's Daily Preparation Schedule ###### Know all about CAT Exam Syllabus and what to expect in CAT ###### Already have an Account? ###### CAT Coaching in ChennaiCAT 2023 Classroom Batches Starting Now! @Gopalapuram ###### 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? Mobile:$91) 99626 48484 / 94459 38484
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