Table of Contents:

• Data Interpretation
• Logical Reasoning
• Data Sufficiency

Data Interpretation for understand the data presented in different forms like bar graphs, tables, charts, line graphs etc. The questions are given with a set of data and candidate is required to deduce the required results from the data set.

A bar chart or bar graph is a chart with rectangular bars with lengths proportional to the values that they represent. Bar charts are used for comparing two or more values that were taken over time or on different conditions, usually on small data sets. The bars can be horizontally oriented (also called bar chart) or vertically oriented (also called column chart). Sometimes a stretched graphic is used instead of a solid bar. It is a visual display used to compare the amount or frequency of occurrence of different characteristics of data and it is used to compare groups of data.

A pie chart (or a circle graph) is a circular chart divided into sectors, illustrating relative magnitudes or frequencies. In a pie chart, the arc length of each sector (and consequently its central angle and area), is proportional to the quantity it represents. Together, the sectors create a full disk. It is named for its resemblance to a pie which has been sliced.

A line graph is most useful in displaying data or information that changes continuously over time.

One of the graph below represent the market share of five different brands of T.V sold in a particular city. The total number of TV sold was 25,000.
The other one shows the unit sales price and the Tax the brand is subjected to. Tax is calculated on the sales price.

1. What is the difference in number of units sold by the most popular brand and the second most popular brand ?                       

Solution: Revenue earned Before tax = Number of Units sold * Unit Price
Revenue earned by Brand A = (18*25000/100 ) * 14,500= 65,250,000
Revenue earned by Brand B = (14*25000/100 ) * 16,000= 56,000,000
Similarly the revenue earned by C = 66,000,000.
Revenue earned by D= (26*25000/100)*13,000= 84,500,000
Revenue earned by E= 67,500,000
So maximum revenue is earned by D 3. Which Brand earned the maximum revenue after Tax ? Solution: Revenue earned after Tax = Revenue earned before Tax -Tax

SALES Tax % Tax paid Revenue
BRAND A 65,250,000      149,135,000     56,115,000
BRAND B 56,000,000      116,160,000     49,840,000
BRAND C 66,000,000      106,600,000     59,400,000
BRAND D 84,500,000       97,605,000      76,895,000
BRAND E 67,500,000       117,425,000    60,075,000
TOTAL      339,250,000     36,925,000      302,325,000

So Brand D earned the maximum revenue after Tax.

In logic, three kinds of logical reasoning can be distinguished: deduction, induction and abduction. Given a precondition, a conclusion, and a rule that the precondition implies the conclusion, they can be explained in the following way:

• Deduction means determining the conclusion. It is using the rule and its precondition to make a conclusion. Example: "When it rains, the grass gets wet. It rains. Thus, the grass is wet."
• Induction means determining the rule. It is learning the rule after numerous examples of the conclusion following the precondition. Example: "The grass has been wet every time it has rained. Thus, when it rains, the grass gets wet."
• Abduction means determining the precondition. It is using the conclusion and the rule to support that the precondition could explain the conclusion. Example: "When it rains, the grass gets wet. The grass is wet, it must have rained."

Examples:

1. Whenever A sings, B gets a headache and C complains. If C is not complaining, which of the following statements must be true?

(A)  A is singing and B has a headache.
(B)  B has a headache but A is not necessarily singing.
(C)  A is singing, but B does not necessarily have a headache.
(D)  A has been singing and B is beginning to get a headache.
(E)  A is not singing.

Solution: Since if A sings, then B gets a headache and C complains. Then we're told that C is not complaining. Using the contrapositive, we get the following logic: If B doesn't have a headache and/or if C isn't complaining, then A must not be singing. So if C is not complaining, then there is no way that A is singing, and choice (E) is the answer.

2.   A will eat the apple if B does not cook.

Based only on the information above, which of the following must be true?

(A)  A will not eat the apple if B cooks.
(B)  If A did not eat the apple, B did cook.
(C)  If A eats the apple, then B did not cook.
(D)  If B does not cook, A will not eat the apple.
(E)  If A did not eat the apple, B did not cook.

Solution: The sentence can be rearranged to read: "If B does not cook, then A will eat the apple. Whenever a Logical Reasoning question gives you an "If...then"sentence, the only thing that must be true is called the "contrapositive"—take the opposite of each half of the statement, and flip the two halves. For this question, the contrapositive is "If A did not eat the apple, then B did cook." Choice (B) matches this perfectly.

A. Statement 1 alone is sufficient but statement 2 alone is not sufficient to answer the question asked.
B. Statement 2 alone is sufficient but statement 1 alone is not sufficient to answer the question asked.
C. Both statements 1 and 2 together are sufficient to answer the question but neither statement is sufficient alone.
D. Each statement alone is sufficient to answer the question.
E. Statements 1 and 2 are not sufficient to answer the question asked and additional data is needed to answer the statements.

Tips to solve DS questions

1. learn the answer choices.

2. read the question thoroughly and make any deductions from the data.

3. focus and think about what you need to solve in the question.

4. consider the statements one at a time.

5. do not actually solve the problem

Examples:

Use the following answer choices for the questions below.

   1. Statement 1 alone is sufficient but statement 2 alone is not sufficient to answer the question asked.
   2. Statement 2 alone is sufficient but statement 1 alone is not sufficient to answer the question asked.
   3. Both statements 1 and 2 together are sufficient to answer the question but neither statement is sufficient alone.
   4. Each statement alone is sufficient to answer the question.
   5. Statements 1 and 2 are not sufficient to answer the question asked and additional data is needed to answer the statements.

1. If the average size of 3 accounts is $1 million, is the smallest account less than $500,000?

   1. The largest account is $1.3 million.

   2. One of the accounts is $0.7 million.
 
a. A
b. B
c. C
d. D
e. E

Solution: (c) Recall that the sum of the 3 accounts is $3 million. If the largest is $1.3 million, then the sum of the other two accounts must be $1.7 million. Since the second-largest account could be $1.29 million, then the smallest account could be $0.41 million, which is less than $0.5 million. Hence, Statement 1 by itself is insufficient.

However, if we know the value of 2 of the variables (as we do if we read statements 1 and 2 together), and the average value of all three variables (as we do from reading the question), then we can determine the value of the third variable. If the largest account is worth $1.3 million and the smallest is worth $0.7 million, then the third variable must be $1.0 million. With the value of all 3 variables, we can quickly determine the value of the smallest variable. Statements 1 and 2 together give us the information needed to answer the question.

2. Is the product of x and y greater than 60?

   1. The sum of x and y is greater than 60.
   2. Each of the variables is greater than 2.
 
a. A
b. B
c. C
d. D
e. E

Solution: (c) Statement 1 by itself is not sufficient. One of the two variables could be a small fraction. (Think of 500 and 0.01.) Statement 2 by itself could yield the product of 3 and 4. However, the information from both statements is taken together, we can definitively state that the answer to this question is "true."