How and when to work backwards in a problem?

CAT Exam
What working backwards is? Working backwards from the answer choices, back-solving, plug-and-chug… no matter what you call it, you’ve probably heard of it before. Many quants questions require laborious algebra to solve, but are much faster and easier to solve by simply plugging the answer choices into the problem to see what fits. Try this problem: Ada went to the supermarket with Rs.36, expecting to buy a certain number of energy drinks. However, the store had recently raised the price of energy drinks by Re.1, causing Ada to purchase 3 fewer energy drinks than expected. How many energy drinks did she originally expect to purchase? (A) 12 (B) 10 (C) 9 (D) 8 (E) 6 If you did the algebra, you probably ran into some really ugly, messy equations. If you picked numbers, you likely had a much easier time. When are you allowed to work backwards? Here’s the rule, and it’s pretty simple: you’re allowed to work backwards from the answer choices any time a question asks you for the value of an unknown (a variable) – in other words, if you could write the question as “x= ?,” you’re allowed to work backwards.Working backwards usually does not work  if the question asked for any other kind of information: a sum, a difference, a product, a ratio / proportion, a variable in terms of another variable, etc. Consider the difference between these two ratio problems, and try working backwards for each: Eg1-At a certain animal shelter, the ratio of puppies to kittens on Monday was 4 to 5. During the week, 8 puppies and 7 kittens were adopted and left the shelter. If by Friday the ratio of remaining puppies to remaining kittens was 2 to 3, how many kittens were originally in the shelter on Monday? (A) 18 (B) 20 (C) 25 (D) 27 (E) 30 Eg2-At a certain animal shelter, the ratio of puppies to kittens on Monday was 4 to 5. During the week, 8 puppies and 7 kittens were adopted and left the shelter. If by Friday the ratio of remaining puppies to remaining kittens was 2 to 3, how many more kittens than puppies were originally in the shelter on Monday? (A) 1 (B) 2 (C) 3 (D) 4 (E) 5 Question #1 asks for the original number of kittens, in other words the value of an unknown: k= ? We’re allowed to work backwards! We can easily plug in the answer choices into the original ratio (more on how to do so in a little bit). Question #2 is asking for the difference between kittens and puppies. In other words, k – p= ? You probably had a lot more trouble working backwards on this one, so algebra probably was the most efficient strategy. How to work backwards efficiently Let’s go back to that first kittens-and-puppies problem. When you’re working backwards, it’s a good idea to create a chart to keep your information organized. kittens: 5x puppies: 4x kittens – 7 puppies – 8 A 18 B 20 C 25 D 27 E 30 Which answer choice should you start with? You’ll hear differing advice on this one: some people say to start with C, some say to start with B or D. The reasoning is that if you start with B and it’s too big, the answer must be A, and you can avoid testing a 2nd value. If it’s too small, test D. If D is too small, the answer is E. If D is too large, the answer is C. This way, you’ve tested a maximum of 2 answers. It is recommended to start with your intuition, then go with something else in the middle or whatever answer choice seems easiest. Just don’t start with A and test all 4 or 5 in a row, because you’ll be doing more work than you need to. On this problem, intuition should tell you that if the original ratio of puppies to kitten was 4 to 5, the original number of kittens had to be a multiple of 5. We can rule out A and D. Then, I’d start with C, because it’s in the middle of the 3 answers I have left: kittens: 5x puppies: 4x kittens – 7 puppies – 8 A 18 B 20 C 25 20 18 12 D 27 E 30 If there were 25 kittens, there would have been 20 puppies to create a ratio of 4 to 5. If 7 kittens and 8 puppies leave, then the new ratio is 12 to 18, or 2 to 3. Train yourself to recognize working-backwards-problems If you’re currently not using the strategy of working backwards because you “didn’t even think about it,” then you have to train yourself to recognize the signals. Step 1: Get your preferred reference book of Quants section. Glance through the questions, and without solving, just ask yourself which questions you could work backwards on. In other words, which questions ask for the value of a variable? Write the question numbers down. Step 2: Once you’re confident that you can recognize these problems, you can then go back and solve them by working backwards. Step 3: Go back and re-solve these same questions, trying algebra this time. Then compare: which strategy was more efficient for you, and on which problems? This might vary from person to person, or topic to topic.   cat quant questions with solutions pdf cat quant tricks quant questions with answers cat questions and answers pdf cat quantitative aptitude questions with answers pdf quant for cat books quant cat syllabus cat logical reasoning questions

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