# CAT Quantitative Aptitude Questions | CAT Ratios, Mixtures, Alligations and Averages Questions

###### CAT Questions | Ratios and Proportions | Ratio - Number System

The question is from CAT Ratio, Mixtures and Averages. This combines number theory with ratio. We need to find the sum of all possible numbers that satisfy the given condition. CAT exam is known to test on basics rather than high funda ideas. A range of CAT questions can be asked from Ratios and Proportions, Mixtures, Alligations and Averages. Make sure you master the topics. 2IIMs CAT questions bank provides you with CAT questions that can help you gear for CAT Exam CAT 2019.

Question 3: The ratio of a two-digit natural number to a number formed by reversing its digits is 4 : 7. Which of the following is the sum of all the numbers of all such pairs?

1. 99
2. 198
3. 330
4. 132

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### Explanatory Answer

##### Method of solving this CAT Question from Ratio, Mixtures and Averages: A ratio proportion question that involves using a simple framework from number systems.

Let the two digit number be 10a + b and the number formed by reversing its digits be 10b + a.
$$frac{10a + b}{10b + a}\\$ = $\frac{4}{7}\\$ 70a + 7b = 40b + 4a 66a = 33b Therefore, $\frac{a}{b}\\$ = $\frac{1}{2}\\$ So, let us list down all possible values for a and b. a b Number Reversed Number 1 2 12 21 2 4 24 42 3 6 36 63 4 8 48 84 Hence, the sum of all the numbers would be, 12 + 21 + 24 + 42 + 36 + 63 + 48 + 84 = 330. The question is "Which of the following is the sum of all the numbers of all such pairs?" ##### Hence, the answer is "330". Choice C is the correct answer. ###### Best Online CAT CoachingSignup and try 9 classesfor free Signup Now! ###### Already have an Account? ###### CAT Coaching in ChennaiEnroll at 26,000/- Next Weekend Batch Starts Sat, August 17th, 2019 ###### Best CAT Coaching in ChennaiRegister Online, get Rs 4000/- off Intakes Closing Soon! ##### Where is 2IIM located? 2IIM Online CAT Coaching A Fermat Education Initiative, 10-C, Kalinga Colony, Bobbili Raja Salai K.K.Nagar, Chennai. India. Pin - 600 078 ##### How to reach 2IIM? Phone:$91) 44 4505 8484
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