Drill 1 :Become Comfortable with calculations:
You should have a good command on tables and Squares (up to 30).
Now we will check how to do approximate calculations
For example Dividing 283 by 1983 and finding that value as a percentage.
283/1983: whenever denominator is greater than numerator try to approximate denominator. Hence you could take 1983 as 2000.
So now our question looks like 283/2000 which is noting but 0.1415 or 14.15%. Here we change our denominator by 17 which is approximately 1% 0f 1983(19.83).
So in our answer also approximately 1% error is there. 1% of 14.15% is nothing but 0.14%. So our final answer has to be 14.15% + 0.14% = 14.29%.
Now we will check what to do if numerator is greater than denominator, for example Dividing 1132 by 1069.
1132/1069: Here we can write 1132 as 1069 + 63 which will leads to 1 + 63/1069.
So now if we do approximation, it is on very small part. 63/1069≈0.06 and our final answer is 1.06 or 106%.
I hope now the concept of approximation is clear. Just try to solve few questions:
412/6950 a) 5.9% b) 4.7% c) 5.2% d) 6.2% e) 5.72%
511/1680 a) 31.5% b) 29.3% c) 30.1% d) 32.2% e) 30.4%
6.4/6.12 a) 1.045 b) 1.053 c) 1.035 d) 1.023 e) 1.031.
Let’s start the preparation for CAT DI section:
Challenger Logic Puzzle
Saturday, Kelly and four of her friends, lured by advertisements of the "biggest sale of the year," went Christmas shopping at Tracy's. Each of the five found the sales pitch to be true, finding a gift for her dad--one buying a sweater--at a great price. Given the clues below, can you solve this Challenger Logic Puzzle by determining the item each purchased, its original price, and its price on sale Saturday?
1 The original prices ranged from a low of $30 to a high of $120, totaling $310 for the five gifts.
2 The girls ended up spending $134 total on their five gifts, from a low of $21 to a high of $36,
3 The price of Jada's gift was reduced 20% more than the price of the tie, but Jada still paid $4 more for her item than the girl who bought the tie for her dad paid.
4 The original price of Lynne's gift was $50 more than the original price of the gloves another girl bought her dad, but after Tracy's reductions Lynne spent only $8 more than the gloves purchaser did.
5 Maria saved $7 more than the girl who bought the belt did.
6 The sale price of the dress shirt was $4 more than the sale price of the item Nicole purchased.
7 The biggest discount on any of the five items was 70% and the smallest discount was 30%.
Difficult AR
Answer the questions on the basis of the information given below:
Atul and his four friends share a single room in a hostel. They have always been encouraged by their class teacher to develop their own interests. As a result, they boys started playing different games, studying different forms of literature and collecting different things. It is known that one of them plays cricket, one study poems and one collects coins. Following additional information is also available.
The boy who is studying stories collects Stamps.
The boy who plays football studies dramas.
Sachin collects buttons.
Mohit, who plays hockey, doesn’t study novels.
The boy who collects leaves plays tennis.
Raghu studies Autobiographies of the great leaders.
One Sunday, Deepak and the boy who collects pebbles went shopping together, the one who plays tennis went to practice, and the one who studies-novels remained in the hostel with the fellow student who plays Chess.
1. Who among the following plays Football?
a. Sachin b. Atul c. Deepak d. Raghu e. None of these
2. What does Deepak collect?
a. Leaves b. Stamps c. Pebbles d. Coins e. None of these
3. Which of the following statements is definitely true?
a. Raghu collects pebbles.
b. The boy, who collects coins, does not study dramas.
c. Atul plays cricket and studies poems.
d. The person who plays cricket studies novels.
e. Atul plays tennis.
4. Who among the following studies poems?
a. Atul b. Mohit c. Deepak d. Sachin e. Raghu
Purpose of DI questions in CAT
Ask an MBA aspirant about the types of questions the Data Interpretation (DI) section of CAT contains and most will answer correctly that it contains graphs and tables. Ask them a follow-up to this question, viz. “What kinds of skills are tested by this section?” Most students will now flounder. Some will say that it tests your ability to read graphs, while others will opine that it evaluates your capability to make quick calculations. Their answers often lack an incisive understanding of the real purpose of this section.
Likewise, ask students how good they are in the DI section. Most will reply that it is an easy section (compared to the dreaded Problem Solving section or the Verbal Ability and Reading Comprehension for some) but it takes time to do calculations. This kind of answer indicates the faulty approach most students often take while dealing with this section.
Listening to feedback from students about their performance in this section soon after CAT, projects a new dimension. Most students will claim that they have done fairly well while the reality may be otherwise. They get a shock when they come to know about the actual answers and blame their bad luck for their appalling performance.
Such questions and answers give a clear indication that most students have not, unfortunately, understood the purpose of this section and the approaches to develop proficiency in this section. Without such an understanding, attempting DI problems is like embarking on a journey without knowing your destination and the means of transport.
This article aims to explain the purpose of DI questions.
Unraveling the Purpose of Data Interpretation
Data Interpretation section virtually puts a student in the shoes of a Business Manager, who is inundated with useful (and not so infrequently with useless) data and has to make some quick interpretation of the data to reach important decisions. Once presented with graphs or tables, the mental processor of a manager starts whirring at the top gear and selects, prunes, manipulates, and compares the data and reaches certain conclusions. Successful operations of these processes require that a manager possesses qualities like:
o An eye for detail,
o An ability to focus on key issues quickly,
o An ability to work on numbers in different ways,
o An ability to see a trend,
o An ability to identify exceptional situations,
o An ability to work with logical relationships and
o An ability to reach a conclusion using deductive logic.
DI
Answer the following questions based on the instructions given.
Each alphabet represents unique Numerical digit from 0 to 9. Problem given below is having unique solution.
T O K Y O
--
O S A K A
____________________________
K Y O T O
____________________________
1. Alphabet O is represented by which numerical digit?
(a) 7 (b) 3 (c) 4 (d) 5
2. Alphabet Y is represented by which numerical digit?
(a) 1 (b) 4 (c) 2 (d) 3
3. Alphabet S is represented by which numeric digit?
(a) 1 (b) 2 (c) 3 (d) 5
LOGICAL DI CAT 2003
The table above provides certain demographic details of 30 respondents who were part of a survey. The demography characteristics are: gender, number of children, and age of respondents. The first number is each cell is the number of respondents in that group. The minimum and maximum age of respondents in each group is given in brackets. For example, there are 5 female respondents with no children and among these five, the youngest is 34 years old, while the oldest is 49.
Q1. The percentage of respondents aged less than 40 years is at least.
1. 10% 2. 16.67% 3. 20.0% 4. 30%
Q2. Given the information above, the percentage of respondents older than 35 can be at most.
1. 30% 2. 73.33% 3. 76.67% 4. 90%
Q3. The percentage of respondents that fall into the 35 to 40 years age group (both inclusive) is at least
1. 6.67% 2. 10% 3. 13.33% 4. 26.67%
LRDI
John, Pete, Tom, George, and Steve are brothers. One day, one of them broke a window. When their father asked them who did it, they gave the following answers:
John: "It was Pete or Tom."
Pete: "It was neither George nor me."
Tom: "Both of you are lying."
Steve: "No, only one of them is lying."
George: "No, Steve, you are wrong."
Then their mother added: "Three of my sons are telling the truth, but I do not believe what the two others said.
"My Question is Who broke the window?
LRDI
Joey has 8 drinking glasses, all of different sizes. He has lined them up from smallest to largest and numbered them 1 (smallest) to 8 (largest).
He knows that glass #4 holds 10 ounces and that glass #7 holds a pint, or 16 ounces. Now he wants to figure out how much all the others hold! He experiments by filling up different glasses with water and pouring the water back and forth into other glasses.
Here are his results: -Pouring water from glasses #1 and #2 filled glass #4. -Pouring water from glasses #1 and #3 filled glass #5. -Pouring water from glasses #2 and #3 filled glass #6. -Pouring water from glasses #1 and #5 filled glass #7. -Pouring water from glasses #1 and #7 filled glass #8. -Pouring water twice from glass #3 filled glass #7. -Pouring water twice from glass #4 filled glass #8.
How much water does each glass hold?
Analytical Reasoning
There are 5 houses in 5 different colors in a row. In each house lives a person with a different nationality. The 5 owners drink a certain type of beverage, smoke a certain brand of cigar, and keep a certain pet. No owners have the same pet, smoke the same brand of cigar, or drink the same beverage. Other facts
:1. The Brit lives in the red house.
2. The Swede keeps dogs as pets.
3. The Dane drinks tea.
4. The green house is on the immediate left of the white house.
5. The green house's owner drinks coffee.
6. The owner who smokes Pall Mall rears birds.
7. The owner of the yellow house smokes Dunhill.
8. The owner living in the center house drinks milk.
9. The Norwegian lives in the first house.
10. The owner who smokes Blends lives next to the one who keeps cats.
11. The owner who keeps the horse lives next to the one who smokes Dunhill.
12. The owner who smokes Blue masters drinks beer.
13. The German smokes Prince.
14. The Norwegian lives next to the blue house.
15. The owner who smokes Blends lives next to the one who drinks water.
The question is: WHO OWNS THE FISH?
Some basic DI tools
Here are some really basic tools to help you make calculations faster. I am not including the usual "vedic math" or "speed calc" techniques. I found that simpler methods help more!
I am sure you are all aware of that ubiquitous formula (a+b+ab/100). But I am equally certain that you (or even me, for that matter) have discovered even half of the uses of this formula. Well, for now, lets focus on its use in division.
As a really simple starter, lets take a division question:
If 1/3 = 33.33%, what is 1/2? Obviously, its 50%, silly! So, what does it have to do with that formula? Here's what:
Apart from its more popular uses like successive discounts etc, this formula holds true for ANY product of two or more quantities. In fact, this is the most generalized use of the formula. If P=AxB, then an change of a% in A and b% in B will result in a change of (a+b+ab/100)% in P. Conversely, if P has to remain constant, an a% increase/ decrease in A will necessitate a corresponding change of a/(100+a)% or a/(100-a)% in B respectively.
Now,
1/3=33.33% can also be written as 1=3 x 33.33% and
1/2=50% can also be written as 1=2 x 50%.
So, the product has remained constant at 1. 3 has decreased to 2. That's a decrease of 33.33%. According to the formula, the other factor will increase by 33.33/(100-33.33)= 50%. So, 33.33% will increase by 50% to 50%.
This may sound too obvious and easy, but take a look at what you can do with this. How would you calculate, say, 113/256? Now, we know that 113/226 = 1/2=0.50. Using this fact, we can calculate the deviation from 0.5. Since 256 is 30/226 or roughly 1/7.5 or 2/15 or 13.33% more than 226, it means that the final result will be 13.33/(100+13.33)% less than 0.5. That is, approx. 12% less than 0.5, or 0.44. That is fairly close to the correct answer that is 0.4414!
Even if you had taken 13% (instead of dividing it by 113.33), you would have been quite close at 0.45! The key is to round off the denominator to a "convenient" number. And if your denominator deviation is not more than 15%, you can simply take this same deviation as correction in your answer. To summarize, follow these steps:
1. Round off the denominator to either a multiple/ factor of the numerator, or to the nearest hundred. This way, the calculation will be easier for the new fraction.
2. Calculate the percentage deviation from the actual denominator. You may use approximations depending on the need of the hour.
3. Provided that the percentage deviation is less than 15%, adjust your answer by the same percentage in the "other direction".
Obviously, this involves a fairly high amount of calculation, but the good news is that it will get easier with a better knowledge about percentages.
Why don't you go ahead and try out the following:
135/283=? (Hint: Take 283 as 270 or 300)
178/1327=? (Hint: Take 1327 as 1300)