Data Sufficiency

In the following questions each question is followed by three statements I, II and III. Read the question and the statements carefully and choose your answer according to which set of statement(s) is/are sufficient to answer the question.
 1.What is the distance between city P and city Q?
 I.Two persons A and B started simultaneously from P to Q, with their speeds in the ratio 4 : 5
II.B reached P one hour earlier than A to Q.
III.The difference between speeds of A and B is 20 kmph
I and III only II and III only I and II only All I, II and III together

2.What is the rate of interest on a certain sum?
 I.The interest earned on the sum at the same rate of simple interest after 3 years is Rs.4500.
II.If the rate of interest is 2.5% more, the simple interest earned will be Rs.900 more.
 III.The amount received on the sum at the end of the 2 years at simple interest is Rs.15,000
I and II only II and III only All I, II and III together Any two statements together

3.What is the area of the rectangle?
 I.The ratio of length to breadth of the rectangle is 35 : 12.
II.The perimeter of the rectangle is 188 cm.
III.The length of diagonal of the rectangle is 74 cm
I and II only I and III only (I and II) or (II and III) Any two of the three

4.How many boys are there in the class?
I.The number of boys is 15 more than the number of girls.
 II.The average weight of boys is 41 kg and that of girls is 32 kg.
III.The average weight of all the students of the class is 37 kg
I and II only II and III only All I, II and III (I and II) or (II and III)

5.What is the profit percentage if a discount of 10% is offered on an article?
 I.Had there been no discount offered, the profit earned on the sale the article would be 40%.
 II.The discount offered on the article is 14% of the cost price.
III.The cost price of the article is Rs.1000
I only Either I or II All I, II & III together Each statement alone is sufficient

Line Charts

Study the following line graph and answer the questions.

Exports from Three Companies Over the Years (in Rs. crore)

1.

For which of the following pairs of years the total exports from the three Companies together are equal?

A. 1995 and 1998 B. 1996 and 1998 C. 1997 and 1998 D. 1995 and 1996 Answer: Option D Explanation: Total exports of the three Companies X, Y and Z together, during various years are: In 1993 = Rs. (30 + 80 + 60) crores = Rs. 170 crores. In 1994 = Rs. (60 + 40 + 90) crores = Rs. 190 crores. In 1995 = Rs. (40 + 60 + 120) crores = Rs. 220 crores. In 1996 = Rs. (70 + 60 + 90) crores = Rs. 220 crores. In 1997 = Rs. (100 + 80 + 60) crores = Rs. 240 crores. In 1998 = Rs. (50 + 100 + 80) crores = Rs. 230 crores. In 1999 = Rs. (120 + 140 + 100) crores = Rs. 360 crores. Clearly, the total exports of the three Companies X, Y and Z together are same during the years 1995 and 1996. 2.  Average annual exports during the given period for Company Y is approximately what percent of the average annual exports for Company Z? A. 87.12% B. 89.64% C. 91.21% D. 93.33% Answer: Option D Explanation: Analysis of the graph: From the graph it is clear that The amount of exports of Company X (in crore Rs.) in the years 1993, 1994, 1995, 1996, 1997, 1998 and 1999 are 30, 60, 40, 70, 100, 50 and 120 respectively. The amount of exports of Company Y (in crore Rs.) in the years 1993, 1994, 1995, 1996, 1997, 1998 and 1999 are 80, 40, 60, 60, 80, 100 and 140 respectively. The amount of exports of Company Z (in crore Rs.) in the years 1993, 1994, 1995, 1996, 1997, 1998 and 1999 are 60, 90,, 120, 90, 60, 80 and 100 respectively. Average annual exports (in Rs. crore) of Company Y during the given period     = 1 x (80 + 40 + 60 + 60 + 80 + 100 + 140) = 560 = 80. 7 7 Average annual exports (in Rs. crore) of Company Z during the given period     = 1 x (60 + 90 + 120 + 90 + 60 + 80 + 100) = 600 . 7 7  Required percentage = 80 x 100 %  93.33%. 600 7 3.  In which year was the difference between the exports from Companies X and Y the minimum? A. 1994 B. 1995 C. 1996 D. 1997 Answer: Option C Explanation: The difference between the exports from the Companies X and Y during the various years are: In 1993 = Rs. (80 - 30) crores = Rs. 50 crores. In 1994 = Rs. (60 - 40) crores = Rs. 20 crores. In 1995 = Rs. (60 - 40) crores = Rs. 20 crores. In 1996 = Rs. (70 - 60) crores = Rs. 10 crores. In 1997 = Rs. (100 - 80) crores = Rs. 20 crores. In 1998 = Rs. (100 - 50) crores = Rs. 50 crores. In 1999 = Rs. (140 - 120) crores = Rs. 20 crores. Clearly, the difference is minimum in the year 1996.

Pie Charts

The following pie-chart shows the percentage distribution of the expenditure incurred in publishing a book. Study the pie-chart and the answer the questions based on it.

Various Expenditures (in percentage) Incurred in Publishing a Book

1.

If for a certain quantity of books, the publisher has to pay Rs. 30,600 as printing cost, then what will be amount of royalty to be paid for these books?

A. Rs. 19,450 B. Rs. 21,200 C. Rs. 22,950 D. Rs. 26,150 Answer: Option C Explanation: Let the amount of Royalty to be paid for these books be Rs. r. Then, 20 : 15 = 30600 : r          r = Rs. 30600 x 15 = Rs. 22,950. 2.  What is the central angle of the sector corresponding to the expenditure incurred on Royalty? A. 15º B. 24º C. 54º D. 48º Answer: Option C Explanation: Central angle corresponding to Royalty = (15% of 360)º = 15 x 360 º 100 = 54º. 3.  The price of the book is marked 20% above the C.P. If the marked price of the book is Rs. 180, then what is the cost of the paper used in a single copy of the book? A. Rs. 36 B. Rs. 37.50 C. Rs. 42 D. Rs. 44.25 Answer: Option B Explanation: Clearly, marked price of the book = 120% of C.P. Also, cost of paper = 25% of C.P Let the cost of paper for a single book be Rs. n. Then, 120 : 25 = 180 : n          n = Rs. 25 x 180 = Rs. 37.50 .

Bar Charts

The bar graph given below shows the sales of books (in thousand number) from six branches of a publishing company during two consecutive years 2000 and 2001.

Sales of Books (in thousand numbers) from Six Branches - B1, B2, B3, B4, B5 and B6 of a publishing Company in 2000 and 2001.

1.

What is the ratio of the total sales of branch B2 for both years to the total sales of branch B4 for both years?

A. 2:3 B. 3:5 C. 4:5 D. 7:9 Answer: Option D Explanation: Required ratio = (75 + 65) = 140 = 7 . (85 + 95) 180 9 2.  Total sales of branch B6 for both the years is what percent of the total sales of branches B3 for both the years? A. 68.54% B. 71.11% C. 73.17% D. 75.55% Answer: Option C Explanation: Required percentage = (70 + 80) x 100 % (95 + 110) = 150 x 100 % 205 = 73.17%. 3.  What percent of the average sales of branches B1, B2 and B3 in 2001 is the average sales of branches B1, B3 and B6 in 2000? A. 75% B. 77.5% C. 82.5% D. 87.5% Answer: Option D Explanation: Average sales (in thousand number) of branches B1, B3 and B6 in 2000     = 1 x (80 + 95 + 70) = 245 . 3 3 Average sales (in thousand number) of branches B1, B2 and B3 in 2001     = 1 x (105 + 65 + 110) = 280 . 3 3  Required percentage = 245/3 x 100 % = 245 x 100 % = 87.5%. 280/3 280

Table Charts

The following table gives the percentage of marks obtained by seven students in six different subjects in an examination. The Numbers in the Brackets give the Maximum Marks in Each Subject. Student Subject (Max. Marks) Maths Chemistry Physics Geography History Computer Science (150) (130) (120) (100) (60) (40) Ayush 90 50 90 60 70 80 Aman 100 80 80 40 80 70 Sajal 90 60 70 70 90 70 Rohit 80 65 80 80 60 60 Muskan 80 65 85 95 50 90 Tanvi 70 75 65 85 40 60 Tarun 65 35 50 77 80 80

1.  What are the average marks obtained by all the seven students in Physics? (rounded off to two digit after decimal) A. 77.26 B. 89.14 C. 91.37 D. 96.11 Answer: Option B Explanation: Average marks obtained in Physics by all the seven students = 1 x [ (90% of 120) + (80% of 120) + (70% of 120) 7               + (80% of 120) + (85% of 120) + (65% of 120) + (50% of 120) ] = 1 x [ (90 + 80 + 70 + 80 + 85 + 65 + 50)% of 120 ] 7 = 1 x [ 520% of 120 ] 7 = 624 7 = 89.14. 2.  The number of students who obtained 60% and above marks in all subjects is? A. 1 B. 2 C. 3 D. None Answer: Option B Explanation: From the table it is clear that Sajal and Rohit have 60% or more marks in each of the six subjects. 3.  What was the aggregate of marks obtained by Sajal in all the six subjects? A. 409 B. 419 C. 429 D. 449 Answer: Option D Explanation: Aggregate marks obtained by Sajal     = [ (90% of 150) + (60% of 130) + (70% of 120)           + (70% of 100) + (90% of 60) + (70% of 40) ]     = [ 135 + 78 + 84 + 70 + 54 + 28 ]     = 449.

Data Interpretation

Study the following table and answer the questions based on it. Expenditures of a Company (in Lakh Rupees) per Annum Over the given Years. Year Item of Expenditure Salary Fuel and Transport Bonus Interest on Loans Taxes 1998 288 98 3.00 23.4 83 1999 342 112 2.52 32.5 108 2000 324 101 3.84 41.6 74 2001 336 133 3.68 36.4 88 2002 420 142 3.96 49.4 98

1.  What is the average amount of interest per year which the company had to pay during this period? A. Rs. 32.43 lakhs B. Rs. 33.72 lakhs C. Rs. 34.18 lakhs D. Rs. 36.66 lakhs Answer: Option D Explanation: Average amount of interest paid by the Company during the given period     = Rs. 23.4 + 32.5 + 41.6 + 36.4 + 49.4 lakhs 5     = Rs. 183.3 lakhs 5     = Rs. 36.66 lakhs. 2.  The total amount of bonus paid by the company during the given period is approximately what percent of the total amount of salary paid during this period? A. 0.1% B. 0.5% C. 1% D. 1.25% Answer: Option C Explanation: Required percentage = (3.00 + 2.52 + 3.84 + 3.68 + 3.96) x 100 % (288 + 342 + 324 + 336 + 420) = 17 x 100 % 1710  1%. 3. Total expenditure on all these items in 1998 was approximately what percent of the total expenditure in 2002? A. 62% B. 66% C. 69% D. 71% Answer: Option C Explanation: Required percentage = (288 + 98 + 3.00 + 23.4 + 83) x 100 % (420 + 142 + 3.96 + 49.4 + 98) = 495.4 x 100 % 713.36  69.45%.